Welcome to the Piano World Piano Forums
Over 2 million posts about pianos, digital pianos, and all types of keyboard instruments
Join the World's Largest Community of Piano Lovers (it's free)
It's Fun to Play the Piano ... Please Pass It On!

SEARCH
the Forums & Piano World

This custom search works much better than the built in one and allows searching older posts.
(ad 125) Sweetwater - Digital Keyboards & Other Gear
Digital Pianos at Sweetwater
(ad) Pearl River
Pearl River Pianos
(ad) Pianoteq
Latest Pianoteq add-on instrument: U4 upright piano
(ad) P B Guide
Acoustic & Digital Piano Guide
PianoSupplies.com (150)
Piano Accessories Music Related Gifts Piano Tuning Equipment Piano Moving Equipment
We now offer Gift Certificates in our online store!
(ad) Estonia Piano
Estonia Piano
Quick Links to Useful Stuff
Our Classified Ads
Find Piano Professionals-

*Piano Dealers - Piano Stores
*Piano Tuners
*Piano Teachers
*Piano Movers
*Piano Restorations
*Piano Manufacturers
*Organs

Quick Links:
*Advertise On Piano World
*Free Piano Newsletter
*Online Piano Recitals
*Piano Recitals Index
*Piano Accessories
* Buying a Piano
*Buying A Acoustic Piano
*Buying a Digital Piano
*Pianos for Sale
*Sell Your Piano
*How Old is My Piano?
*Piano Books
*Piano Art, Pictures, & Posters
*Directory/Site Map
*Contest
*Links
*Virtual Piano
*Music Word Search
*Piano Screen Saver
*Piano Videos
*Virtual Piano Chords
Page 1 of 10 1 2 3 ... 9 10 >
Topic Options
#2194834 - 12/09/13 02:32 AM CHAS for Dummies
pinkfloydhomer Offline
Full Member

Registered: 03/07/08
Posts: 228
I have read the threads about CHAS, and I must admit I don't get it, even if I have a solid mathematical background.

Can someone explain it to me in plain terms? Or at least in mathematically unambiguous terms?

Would it be possible to tune CHAS with TuneLab?
_________________________
Amateur pianist working on: Bach. And amateur tuning, regulation and servicing of my own piano.
Piano: Frustrating and cheap Dongbei Nordiska 120CA upright from 2004.

Top
(ad PTG 568) Grand Action Regulation in 37 Steps
Grand Action Regulation in 37 Steps
#2194862 - 12/09/13 04:43 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Chas is based on equal beating 12ths and 15ths.

The Chas paper (it's on the web) gives the equation; the semitone ratio comes out at 1.059486544. You can work out parameters for Tunelab from that.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2194891 - 12/09/13 07:56 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: pinkfloydhomer
I have read the threads about CHAS, and I must admit I don't get it, even if I have a solid mathematical background.

Can someone explain it to me in plain terms? Or at least in mathematically unambiguous terms?

Would it be possible to tune CHAS with TuneLab?


If it looks like a duck, walks like a duck, quacks like a duck, then it is a duck.

CHAS looks, walks and quacks like self promotion wrapped in hodge-podge mathematic camouflage. Surely you have better things to do. smile
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2194892 - 12/09/13 07:58 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Chris Storch Offline
Full Member

Registered: 08/13/09
Posts: 200
Loc: Massachusetts
Pinkfloyd, you're not alone with the "I don't get it" sentiment.

Withindale, here I was thinking I was just too stupid to get it. Thanks for a simple and direct answer. Can you explain the bow and arrow part?
_________________________
Chris Storch
Acoustician / Piano Technician

Top
#2194907 - 12/09/13 08:47 AM Re: CHAS for Dummies [Re: Chris Storch]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: Chris Storch
Can you explain the bow and arrow part?

My arrows have a nasty habit of missing the target.

The aural tuning sequence is described here in an English translation.

I imagine the finer points might be lost when using Tunelab (and its inharmonicity model) to tune Chas by numbers, just as they might be if the target were pure octaves or pure twelfths.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2194923 - 12/09/13 09:58 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
TuneLab 15may give an approximation, or may help to gauge the even beating later.

With a temperament based one one octave it is yet something but only one octave can be tuned, anyway that is what I get when I tried.

The chas principle is to draw a curve not based on 2:1 3:1 or whatever, but with a balance between 3:1 et 4:1.
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2194966 - 12/09/13 11:36 AM Re: CHAS for Dummies [Re: Withindale]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Withindale
Chas is based on equal beating 12ths and 15ths.

The Chas paper (it's on the web) gives the equation; the semitone ratio comes out at 1.059486544. You can work out the offsets for Tunelab from that.

CHAS is crackpottery, that paper is nonsensical gibberish. Those tunelab "offsets" are nonsense, as they are too small to have any effect or be tunable.

Kees

Top
#2194982 - 12/09/13 12:21 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England

Nevertheless, Kees, the Chas paper gives the equation and the result. Some, if not all, versions of Tunelab allow for custom offsets. You are right that the differences will be small.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2194986 - 12/09/13 12:29 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
pinkfloydhomer Offline
Full Member

Registered: 03/07/08
Posts: 228
Well, TuneLab only takes offsets for the temperament octave and then only one type of octave tuning (e.g. 6:3) for the entire range below the temperament octave and one type of octave tuning (e.g. 4:1) for the entire range above the temperament octave. There is no way to make TuneLab use the same ratio between semitones for the entire range (if that is the point of CHAS?) and there is no way to choose compromises between octave types (for instance, halfway between 6:3 and 4:2 or equal beating 12ths and 15ths). Probably TuneLab could be used in a more manual fashion to do this.
_________________________
Amateur pianist working on: Bach. And amateur tuning, regulation and servicing of my own piano.
Piano: Frustrating and cheap Dongbei Nordiska 120CA upright from 2004.

Top
#2194988 - 12/09/13 12:34 PM Re: CHAS for Dummies [Re: Withindale]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Withindale

Nevertheless, Kees, the Chas paper gives the equation and the result. Some, if not all, versions of Tunelab allow for custom offsets. You are right that the differences will be small.

Not just small, these "offsets" are completely overwhelmed by effects caused by inharmonicity, hence irrelevant to piano tuning.

Equal beating 12/15ths in piano tuning is explained properly here:
http://www.billbremmer.com/articles/aural_octave_tuning.pdf

Kees

Top
#2194990 - 12/09/13 12:36 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: pinkfloydhomer
Well, TuneLab only takes offsets for the temperament octave and then only one type of octave tuning (e.g. 6:3) for the entire range below the temperament octave and one type of octave tuning (e.g. 4:1) for the entire range above the temperament octave. There is no way to make TuneLab use the same ratio between semitones for the entire range (if that is the point of CHAS?) and there is no way to choose compromises between octave types (for instance, halfway between 6:3 and 4:2 or equal beating 12ths and 15ths). Probably TuneLab could be used in a more manual fashion to do this.

Reading the manual will show you how to do that.

Kees

Top
#2195001 - 12/09/13 12:58 PM Re: CHAS for Dummies [Re: DoelKees]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: DoelKees
Originally Posted By: Withindale

Nevertheless, Kees, the Chas paper gives the equation and the result. Some, if not all, versions of Tunelab allow for custom offsets. You are right that the differences will be small.

Not just small, these "offsets" are completely overwhelmed by effects caused by inharmonicity, hence irrelevant to piano tuning.

Equal beating 12/15ths in piano tuning is explained properly here:
http://www.billbremmer.com/articles/aural_octave_tuning.pdf

Kees


Does it follow that equal beating 12/15ths cannot be tuned with an ETD like Tunelab without adjustments made aurally?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2195007 - 12/09/13 01:11 PM Re: CHAS for Dummies [Re: Withindale]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
It is not an equation, Withindale. It is an equality.

Everyone has to bear in mind that the CHAS paper was not written by a mathematician, but a piano tuner who just wished to express his ideas more precisely. In this way, it is almost innocent and well-meaning if one does not take it too seriously.

Alfredo doesn't understand the need for precision in mathematics, as evidenced by his paper. He was loosely fluffing out an artistic concept. The paper was meant to explore the mystery of his ideas, rather than offer a scientific one with clarity.

When I made a mathematical differentiation in a thread months ago about the equality, Alfredo could not say which solution was the relevant one he intended to describe. This shows a disconnect between what he is hearing, and what he understands of the math behind it.

One valid concept that I think Alfredo has offered that I agree with, is the concept of nodal tuning (or the idea that tuning is not a continuous function). Hitting alignment points is important and stretch is dependent upon this.

From an earlier conversation with Alfredo:

Originally Posted By: Alfredo Capurso
(3-x)^(1/19)=(4+x)^(1/24)

Tunewerk: What this equation does to my understanding is simply define a new width for the semitone - the basis for a new width of ET rather than the 12th root of 2 - which could also be seen as a specific measure of theoretical stretch before inharmonicity, the mean between the pure octave fifth and the double octave.

Alfredo: Yes, as you say, the algorithm defines "a new width for the semitone", and to me it surely is "the basis for a new width of ET rather than the 12th root of 2", and it does stretch the scale before iH. Then, more than a "mean", the algorithm may be seen as the representation of many possible step widths, depending on the "s" value. This, in my view, describes the correct approach to the definition of the scale frequencies.

Tunewerk: It has only one solution for x, which makes this an equality or a point rather than an equation.

Alfredo: Yes, in my mind it makes a precise point. In 2006 Chas equation was plotted in MathLab, I seem to remember that 0.002125 was one out of perhaps 4 or 5 solutions. Should I/we check?

Tunewerk: I plotted out the curves, and there is one solution for 'x' in the real domain at approx. 0.00218. There is only one other solution, and it is imaginary.

This equality is then literally describing the same quantity x being taken away from the ratio 3/1 as is added to the ratio 4/1 to achieve a semitone size which will satisfy this requirement.

Alfredo: Yes, two "differences" from two partial matchings (3:1 and 4:1), chromatically (all across the scale) relative to two intervals now determine the scale incremental ratio, and consequently the scale frequencies. Using your words, 12 root of two achieves "a semitone size that will satisfy" the 2:1 ratio as referred to frequencies; CHAS equation, in its basic form, satisfies the 1:1 ratio referred to differences on two other ratios, in our case 3:1 and 4:1.

Tunewerk: It would not be the equal beating point theoretically (though in reality I doubt one could tell).

Alfredo: Good point. Perhaps saying "equal differing" would be more correct. I too could not tell whether, in my final tuning form, the beat rates for 12ths and 15ths were "perfectly" even. But that perception of mine took me to the idea of two equal differences for two intervals; in fact, within my tuning form I was looking for a "difference ratio" that could relate two intervals, and a for a single constant that I could use for modeling. [...] So, by managing "s" we can generate any incremental ratio and aim at any point. As I've mentioned, if I were to tune equal beating 12ths and 15ths there and then, I would not gain the final form I want.


I want to add one thing on the end here. After reading what Kees wrote above, I realized something that I had forgotten.

Originally Posted By: DoelKees
Not just small, these "offsets" are completely overwhelmed by effects caused by inharmonicity, hence irrelevant to piano tuning.


This is an extremely important point that most tuners (and Kees) are missing. These aren't offsets.

What Alfredo was describing (despite the rough math) is an entire concept of thinking about and understanding tuning that is not in the common lexicon. To put CHAS offsets into a tuning machine is to not understand what he was saying.

Machines are part of the problem in the way they approach tuning - as a series of point solutions from an algorithm, rather than an interrelated whole.

I know everyone's bullshit alarms will go off when I use these terms, but there's an important idea here:

You can't put CHAS offsets into a machine and have it work, because the way machines work, these offsets will be overwhelmed by the larger effects of inharmonicity. However, if you tune with the ideas represented by CHAS (not exclusive to CHAS, by the way), they can be incorporated into the inharmonicity. In this way, the tuning can be completed to a higher level, where small changes are maintained because of aural cross-referencing, and not a single-variable output.

I'm not a big fan of CHAS because I feel it is overinflated and confused in its technical scope. However, there are some important ideas within it, which are represented in many other areas of the tuning community.


Edited by Tunewerk (12/09/13 01:59 PM)
_________________________
www.tunewerk.com

Unity of tone through applied research.

Top
#2195008 - 12/09/13 01:12 PM Re: CHAS for Dummies [Re: Withindale]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Withindale
Originally Posted By: DoelKees
Originally Posted By: Withindale

Nevertheless, Kees, the Chas paper gives the equation and the result. Some, if not all, versions of Tunelab allow for custom offsets. You are right that the differences will be small.

Not just small, these "offsets" are completely overwhelmed by effects caused by inharmonicity, hence irrelevant to piano tuning.

Equal beating 12/15ths in piano tuning is explained properly here:
http://www.billbremmer.com/articles/aural_octave_tuning.pdf

Kees


Does it follow that equal beating 12/15ths cannot be tuned with an ETD like Tunelab without adjustments made aurally?

In tunelab you can set the tuning curve to have pure 12ths or pure 15ths. Then manually tweak the curve to be the average of those. That will get you close enough.

Kees

Top
#2195016 - 12/09/13 01:21 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
I was just thinking about the Title for this Topic:

CHAS for Dummies

Yep, that says it all!

laugh laugh laugh
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2195038 - 12/09/13 01:56 PM Re: CHAS for Dummies [Re: DoelKees]
pinkfloydhomer Offline
Full Member

Registered: 03/07/08
Posts: 228
Originally Posted By: DoelKees
Originally Posted By: pinkfloydhomer
Well, TuneLab only takes offsets for the temperament octave and then only one type of octave tuning (e.g. 6:3) for the entire range below the temperament octave and one type of octave tuning (e.g. 4:1) for the entire range above the temperament octave. There is no way to make TuneLab use the same ratio between semitones for the entire range (if that is the point of CHAS?) and there is no way to choose compromises between octave types (for instance, halfway between 6:3 and 4:2 or equal beating 12ths and 15ths). Probably TuneLab could be used in a more manual fashion to do this.

Reading the manual will show you how to do that.

Kees


Do what exactly? I _have_ read the manual, many times.
_________________________
Amateur pianist working on: Bach. And amateur tuning, regulation and servicing of my own piano.
Piano: Frustrating and cheap Dongbei Nordiska 120CA upright from 2004.

Top
#2195046 - 12/09/13 02:12 PM Re: CHAS for Dummies [Re: Tunewerk]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: Tunewerk
It is not an equation, Withindale. It is an equality.

Quote:
(3-x)^(1/19)=(4+x)^(1/24)

Tunewerk: What this equation ...



Originally Posted By: Tunewerk
What Alfredo was describing (despite the rough math) is an entire concept of thinking about and understanding tuning that is not in the current lexicon. To put in CHAS offsets into a tuning machine is to not understand what he was saying.

Machines are part of the problem in the way they approach tuning - as a series of point solutions from a stretch algorithm, rather than an interrelated whole...

You can't put CHAS offsets into a machine and have it work, because the way the machine works, these offsets will be overwhelmed by the larger effects of inharmonicity. However, if you tune with ideas represented by CHAS (not exclusive to CHAS, by the way), they can be incorporated into the inharmonicity. In this way, the tuning can be completed to a higher level, where small changes are maintained because of aural cross-referencing, and not single variable output.

Yes, I realise that. I think you have answered the OP's question.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2195062 - 12/09/13 02:37 PM Re: CHAS for Dummies [Re: Tunewerk]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Tunewerk
Originally Posted By: DoelKees
Not just small, these "offsets" are completely overwhelmed by effects caused by inharmonicity, hence irrelevant to piano tuning.
This is an extremely important point that most tuners (and Kees) are missing. These aren't offsets.

How can I miss that point when I bring it up myself???

I guess we are dealing with CHAS logic here?

Kees

Top
#2195102 - 12/09/13 03:44 PM Re: CHAS for Dummies [Re: DoelKees]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Yeah, maybe it's better to talk about these concepts separate from CHAS, since CHAS is such a confused conglomeration of claims and concepts with inappropriate math to describe tuning ideas.

What I meant was that in bringing up the idea of offsets, you weren't understanding the point of the idea Alfredo was trying to express. CHAS is an attempt to explain a whole way of tuning that is antithetical to offsets. More than offsets, I saw the real point as describing a way of tuning.

But who am I to say? It's possible I am reading in some logical idea to CHAS that isn't even there.

Point taken, Withindale. I made the mistake too, in talking to Alfredo.

Anyway, I think the real point here is: CHAS is an unnecessarily complicated and confusing explanation about tuning that is otherwise already available in other forms from various sources.
_________________________
www.tunewerk.com

Unity of tone through applied research.

Top
#2195120 - 12/09/13 04:06 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
pinkfloydhomer, don't worry about not getting CHAS theory, it is best to see it for what it is worth and then move on.

CHAS is in reality a normal 4th/5th based tuning with RBI checks and expansion that is essentially the same as that which tuners have been using for many decades, but re-branded. The difference is that it has been self-promoted in a way that dupes reader into thinking that there is a special mathematical basis that has roots in natural phenomena and the beauty of nature.

Trying to program offsets that represent CHAS theory into an EDT is ludicrous. Offsets are normally based on 12-root 2 semitone spacing, and then, starting from all zero's for ET, ETDs alter or stretch them to accommodate for inharmonicity for the individual piano. To suggest some pre-stretching by altering offsets at the start would defeat the stretch algorithms that the ETD is designed to compute.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2195531 - 12/10/13 12:12 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
CHAS is an equation that describes a well-stretched piano using the balance between a stretched 15th and a narrow 12th. This is what many of us habitually try to tune anyway. It has merit in the way the equation allows you to see what happens to the beatrates of other intervals if this stretch is maintained consistently - specifically the way the 5ths and 4ths behave. If I remember correctly, the fifths reach a minimum beatrate close to pure somewhere below the temperament region (depending on the scaling) and get progressively narrower as you move upwards and downwards from that minimum. This is the consequence of semitones being the size that they are supposed to be in this system. It also has progressive 4ths.

Alfredo's tuning technique attempts to incorporate these progressions into the tuning, but the accuracy required is very high, with diminishing returns.

There's no denying that this size stretch results in a beautiful tuning. But there's a massive disconnect between the theory (which is actually very simple, it just suffers from a lot of obfuscation and bad communication) and the practice, and unfortunately that gap has been filled with alfredo's own tuning philosophy. (I'm not saying your tuning technique is bad, alfredo, it's just separate from the model you have presented, yet you treat it as the same. Slow-pull technique and pin 'charging' is nothing to do with CHAS)

There's also space within his maths for other 'delta' values, amounting to different stretch patterns. I find it an adequate model for a theoretical 'good' tuning on a theoretical piano. I believe if it was programmed into a dedicated ETD then it would produce good results similar to StopperStimmung.
_________________________
Phil Dickson
The Cycling Piano Tuner

Top
#2195540 - 12/10/13 12:37 PM Re: CHAS for Dummies [Re: Phil D]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Phil D
CHAS is an equation that describes a well-stretched piano using the balance between a stretched 15th and a narrow 12th. This is what many of us habitually try to tune anyway. It has merit in the way the equation allows you to see what happens to the beatrates of other intervals if this stretch is maintained consistently - specifically the way the 5ths and 4ths behave. If I remember correctly, the fifths reach a minimum beatrate close to pure somewhere below the temperament region (depending on the scaling) and get progressively narrower as you move upwards and downwards from that minimum.

Not so. Are intervals remain the same size everywhere in chas as chas doesn't take inharmonicity into account at all, hence it has no relevance to piano tuning.

Kees

Top
#2195544 - 12/10/13 12:41 PM Re: CHAS for Dummies [Re: Phil D]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Originally Posted By: Phil D
It has merit in the way the equation allows you to see what happens to the beatrates of other intervals if this stretch is maintained consistently - specifically the way the 5ths and 4ths behave.


Hey Phil, how do you see this?
_________________________
www.tunewerk.com

Unity of tone through applied research.

Top
#2195548 - 12/10/13 12:50 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
It's not in the original paper, Tunewerk, but it came up in the discussions, so it'll be buried somewhere in the many threads. The derivation would be tedious but you can see how it might be done.

Inharmonicity is not taken into account in the equation, Kees, but he compares his values to the railsback curve, which is an idealised inharmonicity model of a piano, and it compares favourably.

As I said, an idealised model for an idealised piano.
_________________________
Phil Dickson
The Cycling Piano Tuner

Top
#2195554 - 12/10/13 01:06 PM Re: CHAS for Dummies [Re: Phil D]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Thanks for the reply, Phil.

No, I don't see how this could be done. Reversal of 5ths and 4ths was an inharmonicity artifact first discovered by Fairchild. No math will predict or model this, unless you are talking about finite element analysis of soundboard loading and scales.

CHAS too easily becomes a Shopsmith talisman for answering everything piano. I think this is a problem that leads to its discredit.
_________________________
www.tunewerk.com

Unity of tone through applied research.

Top
#2195555 - 12/10/13 01:08 PM Re: CHAS for Dummies [Re: Phil D]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Phil D

Inharmonicity is not taken into account in the equation, Kees, but he compares his values to the railsback curve, which is an idealised inharmonicity model of a piano, and it compares favourably.

He just states that it compares favourably, without ever showing the CHAS and Railsback curves together. The CHAS "curve" which is supposed to be like the Railsback curve is actually just a straight line. It does not "compare favourably" at all.

Kees

Top
#2195713 - 12/10/13 06:31 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
erichlof Online   content
Full Member

Registered: 04/26/10
Posts: 369
I've never understood how 4ths and 5ths "reverse". When and where on the keyboard does this supposedly occur? Aren't all 5ths supposed to be narrow and all 4ths wide, no matter the register?

Top
#2195744 - 12/10/13 07:24 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
Well I just took his word for it really, so I'm happy to be corrected.

erichlof, it wasn't that the 5ths become wide, it was that the fifths become less narrow, and then more narrow. So the direction of the change of narrowness reverses.
_________________________
Phil Dickson
The Cycling Piano Tuner

Top
#2195748 - 12/10/13 07:34 PM Re: CHAS for Dummies [Re: erichlof]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Good question, Erichlof. This is something I'd really have to pull out the data for, which I don't have around at the moment.

To the best of my memory, increased soundboard loading causes negative inharmonicity on 3rd partial of most pianos, around the 5th-6th octave. This causes the 5th to be pure with less stretch and, at the same time, the 4th to be pure with more stretch (neg. iH acting on both sides of these complimentary intervals).

Very rarely is there a crossover. It has been documented and is possible with extreme negative iH, but it is rare.

The real world outcome of this effect is you'll notice it is easier to get both 4ths and 5ths pure as you rise out of the temperament region.

This is an excellent point to post here, because tuning models never represent variable partial fields on a real piano. When partial fields fluctuate, the rules of tuning fluctuate.

Phil - glad to hear, and to know that all together we can clear up misinformation! smile


Edited by Tunewerk (12/10/13 07:43 PM)
_________________________
www.tunewerk.com

Unity of tone through applied research.

Top
#2195761 - 12/10/13 08:07 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
erichlof Online   content
Full Member

Registered: 04/26/10
Posts: 369
Ahh... thank you Phil and Tunewerk for the explanations. I think I understand a little better now. I guess it's kind of like in physics when you can have negative acceleration. smile This concept always tripped me up in High School and here I am many years later encountering it again with a completely different system!

Thanks!
-Erich

Top
#2195784 - 12/10/13 09:06 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
rxd Offline
1000 Post Club Member

Registered: 03/11/09
Posts: 1712
Loc: London, England
Many intervals exhibit anomalous behaviour. All aural tuners who use all the test intervals in the whole piano must have noticed them, particularly how single octave size and double octave size change places on several notes in and around the top octave, even in the best pianos..
This is maybe the most readily apparent of them, at least it's the first one I ever noticed as an ardent student of all this. It's only about 30 years ago that I started to choose the single octave to tune to instead of the double octave when the alternatives were too noisy in the smaller intervals. That was the time I started working in more recording studios and spending more time listening to playbacks with other musicians than tuning. (1 hour tuning/3hours listening).

Bass strings exhibit even more random exchanges but that's to be expected even in the largest pianos. Far too random to try to marshal them into some sort of order.

ETD's never pick up on them or pick up on the wrong ones.

A wizened old tuner once told me, don't listen too hard, you'll go crazy. Maybe that's what's happnin'.
_________________________
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



Top
#2196421 - 12/12/13 05:21 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1062
Loc: Sicily - Italy
Hi,

Posted in the "Sample" thread:

Originally Posted By: rxd
Originally Posted By: alfredo capurso
Originally Posted By: rxd
Originally Posted By: bkw58
Does the pianist not have at least something to say about it? It's not like he's poking around on an old Underwood. He takes the best that the tuner can provide with what he has to work with and creates his desire with very specific skills at his finger tips.


I must confess to not listening again, I started to but refused to pick through all the talking but the pianist can do much more than we think.

The sustain varies very subtly from note to note in all pianos. A stage piano doesn't always get the maintenance it should and equality of sustain suffers.
while there are ways of poking through the strings with a long needle to obtain more sustain from the hammer, tuning on the day of a big production like this rarely allows for any refinement.

I have to sincerely question isaacs experience of this kind of work. He claims to know but his comments show a distinct lack of understanding. There's more of self promotion in his nit picking criticism. I would expect sympathy with the situation from a real fellow professional. He sounds to me like a really talented amateur who hangs around the profession and then totally falls apart when the real job has to be done. I've known quite a few.


rxd,

I think that only a boor would direct those words to a technician as Isaac, and I do not see how that style can help to describe our work. I think you ought to apologize.
.


I quite agree and understand fully where you're coming from and the emotional content carried over from other threads. - an all too common occurrence.
Since you raised the issue again, It took a few words in order to address an ongoing problem. A totally unfounded, unnecessary and pretentious criticism of a compressed recording couldn't go unchallenged at the same level.

Am I to assume that you agree with isaacs original "criticism" when he himself posted later an admission that he really couldn't tell the difference between what was the piano and what was the tuning and then delete that post a few hours later?

I suggest you read the complete thread. It's all there and doesn't need the deleted parts to be indefensible.

Constructive criticism-Yes.
Self serving, Ill considered boorish and unfounded carping,- a resounding No.


rxd, when you mention "..the emotional content carried over from other threads..", do you mean this thread? Or is it the "How long should it take?", where you wrote:

Originally Posted By: rxd
[/quote]
........ and I think about art.

Best regards, a.c.
.

In all branches of the arts, phrases like this have long been regarded, rightly or wrongly as the last refuge of a charlatan.

I have read some of your work as presented here and experimented with some of it.

You have just another opinion. It is a different twist on an old problem that has been pondered and discussed by generations of fine mainstream tuners who have had to tune the old designs of smaller grands produced by some of the finest makers. Your solution still doesn't address the basic problems.

When I pondered whether or not to dine with you, one of the issues I considered was whether I would be spending a bright convivial evening with a fellow professional or would I be taken hostage by an intense and over enthusiastic amateur. Most people have relationships. Some take others hostage and think it is a relationship.

I asked you directly of your professional experience and you gave me a brief dismissive and evasive answer. I also answered fully to some of your direct technical and artistic questions of me. Your replies to my answers betrayed that you hadn't the feintest idea what I was talking about. It's all in the archives here.

Now you resort to an attempt to insult us all and in the name of art no less.
Ooooooo get you!!.

Let yourself out when you've finished tuning and switch off the lights. We're going to bed.


What I am saying, rxd, is that your insinuations do not help, and in the Sample thread I was not concerned about me, but Isaac.

Sure, I cannot say I am happy to read that I would be a charlatan, or an amateur, or one that would try to take you hostage, or... crazy, as you last wrote in this thread.

Let me suggest: take it easy, be respectful and filter your thoughts and fantasies three times before you post.

About theoretical and practical/technical contents... later on.
.
_________________________
alfredo

Top
#2196424 - 12/12/13 06:00 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
rxd Offline
1000 Post Club Member

Registered: 03/11/09
Posts: 1712
Loc: London, England
Sorry, everyone, I appear to have picked up another self obsessed stalker in the above post who, not content with insulting us all and being censured for it, has chosen to mix up the content of two different threads for their own ends.

I apologise to you all for any inconvenience or confusion this has caused.
_________________________
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



Top
#2196425 - 12/12/13 06:27 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1062
Loc: Sicily - Italy
IMO, there is little to be sorry about, when we try to be clearer.

You confirm your attitude again, rxd. BTW, do you have a name and surname?
_________________________
alfredo

Top
#2196428 - 12/12/13 06:50 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1062
Loc: Sicily - Italy
Originally Posted By: pinkfloydhomer
I have read the threads about CHAS, and I must admit I don't get it, even if I have a solid mathematical background.

Can someone explain it to me in plain terms? Or at least in mathematically unambiguous terms?

Would it be possible to tune CHAS with TuneLab?


Hi pinkfloydhomer,

Unfortunately I do not know what the user can do with TL, and I am not familiar with recent ETD's; I guess Robert Scott may say, perhaps it is worth a PM?

As for the Chas maths, which is the point you do not get?

Regards, a.c.
.
_________________________
alfredo

Top
#2196430 - 12/12/13 07:11 AM Re: CHAS for Dummies [Re: alfredo capurso]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: alfredo capurso
IMO, there is little to be sorry about, when we try to be clearer.

You confirm your attitude again, rxd. BTW, do you have a name and surname?


No he does not have a real name. He is a robot from a Boy Scout project that went horribly wrong. rxd is just a model number.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2196441 - 12/12/13 07:46 AM Re: CHAS for Dummies [Re: rxd]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Oh no, he found it..

This thread, even though already resolved, is about to become extremely confusing. And long.

Originally Posted By: Alfredo
Let me suggest: take it easy, be respectful and filter your thoughts and fantasies three times before you post.


This is great advice that you should follow yourself, Alfredo.

Originally Posted By: Alfredo
About theoretical and practical/technical contents... later on.


It always is later on, even if unsolicited. And when you do explain, you never do really explain.

Yes, I think it is clear to everyone that CHAS is more about your own personal show than presenting something of worth.
_________________________
www.tunewerk.com

Unity of tone through applied research.

Top
#2196450 - 12/12/13 08:40 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
rxd Offline
1000 Post Club Member

Registered: 03/11/09
Posts: 1712
Loc: London, England
Xd is the original model designation but it all went horribly wrong.
Started to exhibit human traits and developed attitude problems so the R prefix stands for "rebuilt". Now the attitudes are just right.

Some in the piano profession in a few parts of the world know exactly who I am. Some even know who I used to be, still fewer know what I used to be.

Nobody knows why.
_________________________
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



Top
#2196452 - 12/12/13 08:45 AM Re: CHAS for Dummies [Re: rxd]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: rxd
Xd is the original model designation but it all went horribly wrong.
Started to exhibit human traits and developed attitude problems so the R prefix stands for "rebuilt". Now the attitudes are just right.

Some in the piano profession in a few parts of the world know exactly who I am. Some even know who I used to be. still fewer know what I used to be.


And NOBODY, oops, nobody knows what you will become! (Or are you becoming?... naaah)
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2196454 - 12/12/13 08:48 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
rxd Offline
1000 Post Club Member

Registered: 03/11/09
Posts: 1712
Loc: London, England
I am becoming very becoming.

Thanks for a good belly laugh, Jeff

Oh, the original Xd couldn't laugh at itself.
_________________________
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



Top
#2196460 - 12/12/13 09:05 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 212
Loc: Germany
-
_________________________
Bernhard Stopper
www.piano-stopper.de

Salieri: "Mediocrities everywhere, now and to come: I absolve you all! Amen! Amen! Amen!"
(Amadeus, the movie)

Top
#2196465 - 12/12/13 09:11 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
Not meaning to be rude, Mr Stopper, but without any knowledge of your own ideas beyond scraps and vague desriptions and the odd video, your ideas are no better communicated than alfredo's, IMO, and both seem to be wrapped very much in self-promotion (although you do actually have a product to sell, which is fine). You just have the good sense not to try and promote it heavily to the members of this board.
_________________________
Phil Dickson
The Cycling Piano Tuner

Top
#2196553 - 12/12/13 01:10 PM Re: CHAS for Dummies [Re: alfredo capurso]
pinkfloydhomer Offline
Full Member

Registered: 03/07/08
Posts: 228
Originally Posted By: alfredo capurso

Hi pinkfloydhomer,

Unfortunately I do not know what the user can do with TL, and I am not familiar with recent ETD's; I guess Robert Scott may say, perhaps it is worth a PM?

As for the Chas maths, which is the point you do not get?

Regards, a.c.
.


Hi Alfredo, thanks for answering.

What I don't/didn't get about CHAS is/was ... everything smile

I understand the tonal system, I understand various unequal temperaments, I understand equal temperament, I understand the ditonic and the syntonic comma, I understand inharmonicity, I understand what a 6:3 octave is or what a 3:1 twelfth is, I understand what beats are, I understand what equal beating is, I understand what fast and slow beating intervals are, I understand a lot of music theory and I understand the idea behind most aural tuning schemes that I encounter. They all seem to take all of the above into account.

But I didn't understand CHAS since it wasn't precisely described in the threads about it on this forum.

I guess I understand now that CHAS is about equal beating 12ths and 15ths and about a slightly larger semitone ratio than the 12th root of 2? Or is there more to it?

This must be even before we take inharmonicity into account. Taking IH into account, semitone ratio is always greater than the 12th root of 2 on a real piano with positive IH, even if it is tuned in equal temperament. So I guess on a real piano tuned in CHAS, the semitone ratio becomes even greater than the theoretical CHAS semitone because of IH.
_________________________
Amateur pianist working on: Bach. And amateur tuning, regulation and servicing of my own piano.
Piano: Frustrating and cheap Dongbei Nordiska 120CA upright from 2004.

Top
#2196572 - 12/12/13 02:30 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1062
Loc: Sicily - Italy
Originally Posted By: pinkfloydhomer
Originally Posted By: alfredo capurso

Hi pinkfloydhomer,

Unfortunately I do not know what the user can do with TL, and I am not familiar with recent ETD's; I guess Robert Scott may say, perhaps it is worth a PM?

As for the Chas maths, which is the point you do not get?

Regards, a.c.
.


Hi Alfredo, thanks for answering.

What I don't/didn't get about CHAS is/was ... everything smile

I understand the tonal system, I understand various unequal temperaments, I understand equal temperament, I understand the ditonic and the syntonic comma, I understand inharmonicity, I understand what a 6:3 octave is or what a 3:1 twelfth is, I understand what beats are, I understand what equal beating is, I understand what fast and slow beating intervals are, I understand a lot of music theory and I understand the idea behind most aural tuning schemes that I encounter. They all seem to take all of the above into account.

But I didn't understand CHAS since it wasn't precisely described in the threads about it on this forum.

I guess I understand now that CHAS is about equal beating 12ths and 15ths and about a slightly larger semitone ratio than the 12th root of 2? Or is there more to it?

This must be even before we take inharmonicity into account. Taking IH into account, semitone ratio is always greater than the 12th root of 2 on a real piano with positive IH, even if it is tuned in equal temperament. So I guess on a real piano tuned in CHAS, the semitone ratio becomes even greater than the theoretical CHAS semitone because of IH.


Hi pinkfloydhomer,

It is as you say, Chas semitone ratio is slightly larger than the 12th root of 2.

Also the rest is correct: "This must be even before we take inharmonicity into account. Taking IH into account, semitone ratio is always greater than the 12th root of 2 on a real piano with positive IH, even if it is tuned in equal temperament. So I guess on a real piano tuned in CHAS, the semitone ratio becomes even greater than the theoretical CHAS semitone because of IH."

In Chas equation (3-delta)^(1/19)= (4+s*delta)^(1/24)

12ths and 15ths deviate from 3:1 and 4:1 depending on the parameter "s";

for s=1 12ths and 15ths deviate by the same (delta) amount.

That's all.

Cheers, a.c.
.
_________________________
alfredo

Top
#2196629 - 12/12/13 04:47 PM Re: CHAS for Dummies [Re: alfredo capurso]
pinkfloydhomer Offline
Full Member

Registered: 03/07/08
Posts: 228
Okay then, but can you explain to me in short, precise terms why the CHAS semitone ratio is desirable and better than other suggestions (most notable 12th root of 2), and also why equal beating 12ths and 15ths are better than other approaches?

Why isn't CHAS just one more random way to tune? Why is it special? What sets it apart? It must have some kind of fundamental idea binding it together. And idea that it must be possible to express in short and precise terms to an educated audience. An executive summary.
_________________________
Amateur pianist working on: Bach. And amateur tuning, regulation and servicing of my own piano.
Piano: Frustrating and cheap Dongbei Nordiska 120CA upright from 2004.

Top
#2196640 - 12/12/13 05:09 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: pinkfloydhomer
I have read the threads about CHAS, and I must admit I don't get it, even if I have a solid mathematical background.

Can someone explain it to me in plain terms? Or at least in mathematically unambiguous terms?

Would it be possible to tune CHAS with TuneLab?

Going back to your original question, PFH, this thread and the one about Stopper's temperament have shown that it's not possible to tune CHAS with Tunelab.

CHAS is a heuristic method of tuning rather than a deterministic one with offsets you can feed into an ETD.

Alfredo has set out the method in some detail (see this English translation) and explained that he allows for "variable stretch" in his tunings (see his post in the Stopper thread yesterday).

As I see it, you will never know in advance what the values of his "s" variables will be. To achieve the beat rate progression curves he is looking for stretch may swing between pure octaves and pure twelfths; conceivably more I suppose.

No doubt you are familiar with those Railsback diagrams with smooth curves approximating inharmonicity and jagged lines showing actual tunings. A Railsback curve represents a mathematical model which is a figment of the imagination. The jagged line is reality.

Don't get me wrong, I am a great believer in mathematical models. They can do a lot, but I know their limitations.

You will never get CHAS from Alfredo's equations, nor will anyone else. It's the tunings that matter.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2196643 - 12/12/13 05:23 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
This it does not have.

It does not have this because CHAS is a retroactive arithmetical explanation for subjective, qualitative field experience that has led a lot of tuners to believe tuning near the 12th works best on the modern piano.

It works backwards, not forwards. It provides a gum-and-tape explanation for complex interactions. As a result of this, it cannot be used as a model to work forward or predict anything physical in terms of real pianos.

Not only that, but the mathematical model is insufficient and incorrect. It does not model what Alfredo claims it does. I've modelled this in MatLab some time ago.

The positive role this model could have is giving new tuners a more quantitative view for the goal of tuning. Used in general conceptual terms, it could be helpful.

Originally Posted By: Withindale
CHAS is a heuristic method of tuning rather than a deterministic one with offsets you can feed into an ETD.

Alfredo has set out the method in some detail (see this English translation) and explained that he allows for "variable stretch" in his tunings (see his post in the Stopper thread yesterday).

As I see it, you will never know in advance what the values of his "s" variables will be. To achieve the beat rate progression curves he is looking for stretch may swing between pure octaves and pure twelfths; conceivably more I suppose.

No doubt you are familiar with those Railsback diagrams with smooth curves approximating inharmonicity and jagged lines showing actual tunings. A Railsback curve represents a mathematical model which is a figment of the imagination. The jagged line is reality.

Don't get me wrong, I am a great believer in mathematical models. They can do a lot, but I know their limitations.

You will never get CHAS from Alfredo's equations, nor will anyone else. It's the tunings that matter.


+1


Edited by Tunewerk (12/12/13 05:33 PM)
_________________________
www.tunewerk.com

Unity of tone through applied research.

Top
#2197209 - 12/13/13 07:09 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1062
Loc: Sicily - Italy
Originally Posted By: pinkfloydhomer
Okay then, but can you explain to me in short, precise terms why the CHAS semitone ratio is desirable and better than other suggestions (most notable 12th root of 2), and also why equal beating 12ths and 15ths are better than other approaches?

Why isn't CHAS just one more random way to tune? Why is it special? What sets it apart? It must have some kind of fundamental idea binding it together. And idea that it must be possible to express in short and precise terms to an educated audience. An executive summary.


Hi pinkfloydhomer,

Yes, I can try, but at some point we will have to address theory and practice separately, so that we do not get confused.

@ ...why the CHAS semitone ratio is desirable...

Here I can only talk subjectively, I was longing for a ratio (and tuning criteria) that my sense_of_intonation could justify, and that ratio was lacking. That “desire” made me start with my research... on the one hand there was no way to tune pure octaves, on the other hand there was no need to avoid faintly beating octaves... This made me believe that perhaps a better scale_geometry could be found, that it could depend on strict application.

@ ...and better than other suggestions (most notable 12th root of 2)...

There is no way we can put 12th root of two into practice; that ratio favors pure_octaves (2:1), and in doing so it doubles all other intervals deviation values, every other octave; the Chas semitone ratio is “better” in that it spreads deviations amongst all intervals, so that - octave after octave - all intervals can progress together, as part of a whole.

@ ...why equal beating 12ths and 15ths are better than other approaches?...

12ths and 15ths..., because in this way we actually stretch the fourth (4:3 - in between the 12th and the 15th) which is the interval that first closes a circle (we say so, but it is a spiral), enumerating the number (4*3) of semitones.

@ ...Why isn't CHAS just one more random way to tune?...

The Chas model has nothing against “random” tunings, i.e. tunings that may result from any other semitone ratio, that is the meaning of the “s” variable; in fact, this is a fundamental passage: we are expected (and enabled) to modify the ratio in order to set the “desired” semitone progression; on the other hand, s=1 defines the most coherent geometry.

@ ...Why is it special?...

The Chas ratio (with s=1) is special in that it is self-referential: by stretching the fourth (4:3), we determine the constraint for 12ths (3:1) and 15ths (4:1), and s=1 fixes that constraint in 1:1 proportion.

@ ...What sets it apart?

Maximum coherence.

@ ...It must have some kind of fundamental idea binding it together...

No interval needs to be pure;

Deviations define “color”, more than pure intervals;

Deviations need to be ordered in proportion;

We can order scale frequencies and deviations with one ratio;

What we need to consider, represent and aim at, it's a dynamic (beating) whole, then we can set the premises.

@ ...And idea that it must be possible to express in short and precise terms to an educated audience. An executive summary.

I do make use of a PowerPoint with some short phrases and graphs... are you asking for that?

Regards, a.c.
.
_________________________
alfredo

Top
#2208734 - 01/05/14 03:11 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1062
Loc: Sicily - Italy

Hi,

Phil, it is a bit of a shame that my sharings on this board appears as self-promotion, as if I wanted to sell something... Honestly, I do not understand what is giving this impression, if not my mere enthusiasm when I think that, three hundred years ago, these results would have remained the preserve of a few. Anyway, thank you for posting and for pointing that out (and thanks PW for providing this opportunity).

Tunewerk, I hope you will be able to compare the Chas model with other models and soon realize that the tonal scale is now tailored correctly. About maths, try not to confuse notions, for instance what “equality” means, and about tuning in general, try to help other colleagues understand now why the octave needs to be stretched. Oh, it would be great if you could help also Jeff, Chris, Kees and Bill.. :-)

Here is a link to some literature:
http://www.huygens-fokker.org/docs/bibliography.html#C

Ian, thank you for your posts... seeing how other posters mix up notions, concepts and practical issues, I find your lines refreshing.

To All, have a nice Epiphany.
.
_________________________
alfredo

Top
#2273227 - 05/09/14 11:55 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
In keeping with this topic for dummies, I would like to present an imitation CHAS -- for dummies like me.

This is an equal temperament very close to that of CHAS, but one that I will describe in terms with which I am familiar. I am hoping others will see this as a worthy contribution to the topic.

First, mathematical models are useful, in that they identify the target beat rates from which you will depart when actually tuning in the real world. A piano tuned to a 12th root of 2 model will have beat rates as close as possible to that of the 12th root of 2 model.

Pianos are scaled in general so that their beat rates can approach that of the models of equal temperament; this is obviously less true for some pianos than it is for others, but it would have been easy to make pianos that could not be tuned with beat rates that remotely resemble the beat rates of any model.

Modern equal temperaments come in a variety of widths.

The temperament denoted by the 12th root of 2 is 12-tone to the just octave equal temperament. It is characterized by clean octaves, and with 4ths expanded by approximately 2 cents and 5ths contracted by the same approximate 2 cents. The C4-F4 fourth will beat the same as the F4-C5 5th. (If that 4th is faster than that 5th, then the octave is expanded, and the model for the tuning is not the 12th root of 2.) This is considered to be the most narrow equal temperament that is musically useful.

The temperament denoted by the 7th root of 1.5 is 7-tone to the just fifth equal temperament. It is characterized by clean fifths -- and octaves expanded by approximately 3 1/3 cents. The C3-A3 sixth will beat the same as the C3-E4 10th. This is sometimes considered to be the widest equal temperament that is musically useful. However, my PTG Atlanta institute class will demonstrate some equal temperaments that are substantially wider than this.

The temperament denoted by the 19th root of 3 strikes a middle ground in the range of equal temperaments. It is characterized by clean 12ths — and by octaves expanded by approximately 1 1/4 cents and 5ths contracted by the same approximate 1 1/4 cents. The D3-A3 5th will beat the same as the A3-A4 octave. If this temperament is executed evenly across a piano scale, some, including myself, claim that a particularly coherent tuning will result.

The source of the coherence of a tuning with an evenly-executed stretch may be the temperament itself, or perhaps it is that it is unusual for a chosen specific level of stretch to be accurately executed across a whole scale. This appears to still be an open question, because it seems to be reasonable to think that executing a consistent amount of stretch across a scale might contribute to coherence in a tuning. My class will deal extensively with these and related issues.

There are other widths of equal temperament that can be readily identified, including one denoted by the 31st root of 6. It is characterized by clean double-octave 5ths. The C3-C4 octave will beat the same as the C4-G5 12th.

Of particular interest to this PianoWorld topic is the equal temperament denoted by the 43rd root of 12. It is characterized (at least theoretically, in its zero-inharmonicity mathematical form) by clean triple-octave 5ths, and double octaves that are expanded by the same amount in cents (about 1.09 cents) as the 12ths are contracted (again, about 1.09 cents). The C3-G4 12th will beat the same as the G4-G6 double-octave. (I believe equal-beating double octaves and 12ths are claimed in CHAS.)

It would be of interest to me to understand how the 43rd root of 12 ET differs substantially from CHAS. They appear to be so similar that it would be difficult to aurally distinguish one from the other. Perhaps someone could identify for me a specific pair of 12th and double-octave that would be equal-beating in CHAS.?

Thanks.

Top
#2273276 - 05/09/14 02:14 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Mr. Swafford:

I rarely view posts having to do with CHAS, but I made an exception when seeing that you posted to this Topic.

The purpose of CHAS is for Alfredo to promote himself. The model is for 12ths and double octaves with a common note on top bottom to beat at the same speed. This is virtually identical to "mindless octaves". So D3-A4 A2-E3 would beat (3:1 narrow of just intonation) the same as A2-A4 (4:1 wide of just intonation).

I believe pure 12ths to be an exceptional stretch and use it exclusively. I don't want to post about it on this Topic, but here is a current one on the subject: P12 Tuning Sequence

If you respond, I may not get back to you until Monday. I rarely post on weekends.


Edited by UnrightTooner (05/09/14 05:07 PM)
Edit Reason: correct error
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2273361 - 05/09/14 05:48 PM Re: CHAS for Dummies [Re: Kent Swafford]
Mark R. Offline
2000 Post Club Member

Registered: 07/31/09
Posts: 2014
Loc: Pretoria, South Africa
Dear Kent,

You start of by writing:

Originally Posted By: Kent Swafford
In keeping with this topic for dummies, I would like to present an imitation CHAS -- for dummies like me.

This is an equal temperament very close to that of CHAS, but one that I will describe in terms with which I am familiar. I am hoping others will see this as a worthy contribution to the topic.


You then proceed to present various degrees of stretches:

Originally Posted By: Kent Swafford
The temperament denoted by the 12th root of 2

[...]

The temperament denoted by the 7th root of 1.5

[...]

The temperament denoted by the 19th root of 3

[...]

it seems to be reasonable to think that executing a consistent amount of stretch across a scale might contribute to coherence in a tuning.

[...]

There are other widths of equal temperament that can be readily identified, including one denoted by the 31st root of 6.

[...]

Of particular interest to this PianoWorld topic is the equal temperament denoted by the 43rd root of 12.


May I ask: which of these schemes (or widths) is it that you would like to "present as an imitation CHAS"?
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

Top
#2273601 - 05/10/14 10:49 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
In Chas temperament method there is an unique feature that I never find anywhere , that is the installation of future enlarging that is done in an initial not particularely expanded octave (minimally expanded, in my opinion, when comparing with some basic octaves A3 A4 I have seen describe.)

Without that trick you cannot tune with higher ratios than 2:1 without raising a lot the speed of FBI and even the octaves and doubles.

In my opinion





Edited by Olek (05/10/14 10:50 AM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2273716 - 05/10/14 04:09 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford

There are other widths of equal temperament that can be readily identified, including one denoted by the 31st root of 6.

And there is the 55th root of 24, the 61st root of 34, the 67th root of 48, the 74th root of 72, the 79th root of 96, etc. etc. ad infinitum.

These theoretical numbers (relevant to a theoretical zero inharmonicity instrument) differ by such small amounts that these differences are completely washed away by effects caused by inharmonicity in a real piano.

Kees

Top
#2273755 - 05/10/14 06:08 PM Re: CHAS for Dummies [Re: DoelKees]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Kees writes:

"These theoretical numbers (relevant to a theoretical zero inharmonicity instrument) differ by such small amounts that these differences are completely washed away by effects caused by inharmonicity in a real piano."

Of course.

But _my_ point remains that there are various widths of equal temperament that _are_ readily identifiable by their characteristic beat rate patterns, as I detailed. These various ET's can be aurally differentiated from each other.

The ET denoted by the 43rd root of 12 would, I believe, be difficult to aurally distinguish from CHAS.

Since the 43rd root of 12 ET is easily described and CHAS is somewhat difficult to describe, I suggest that the 43rd root of 12 ET might be a good simpler alternative to CHAS.

Top
#2273800 - 05/10/14 10:24 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
Kent, Just a few figures:

If A6 on a typical Yamaha U1 is tuned we get about 1776 or so Hz using a reasonable stretch.

With 12 root 2 the frequency is 1760 Hz
With 19 root 3 the frequency is 1762 Hz
With 7 root 1.5 the frequency is 1767 Hz
With 42 root 12 the frequency is 1820 Hz

Although I have only shown one note, none of these models resembles what a real piano should be given inharmonicity. A particular model may be close for some parts of the scale and some pianos but not others. I think it is pointless trying to characterise CHAS with a model such as these unless it is modified with other coefficients such as what Alfredo does.

12 root 2 is a default model and is fundamental reference for the way we describe tuning systems. It is not used in practice for pianos unless we describe tuning frequencies in terms of cents offsets from 12 root 2. With the other models we will still have to describe actual tuning frequencies in terms of deviations from the theoretical values of the model.


Edited by Chris Leslie (05/10/14 10:42 PM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2273865 - 05/11/14 06:24 AM Re: CHAS for Dummies [Re: Chris Leslie]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: Chris Leslie
Kent, Just a few figures:

If A6 on a typical Yamaha U1 is tuned we get about 1776 or so Hz using a reasonable stretch.

With 12 root 2 the frequency is 1760 Hz
With 19 root 3 the frequency is 1762 Hz
With 7 root 1.5 the frequency is 1767 Hz
With 42 root 12 the frequency is 1820 Hz

Although I have only shown one note, none of these models resembles what a real piano should be given inharmonicity. A particular model may be close for some parts of the scale and some pianos but not others. I think it is pointless trying to characterise CHAS with a model such as these unless it is modified with other coefficients such as what Alfredo does.

12 root 2 is a default model and is fundamental reference for the way we describe tuning systems. It is not used in practice for pianos unless we describe tuning frequencies in terms of cents offsets from 12 root 2. With the other models we will still have to describe actual tuning frequencies in terms of deviations from the theoretical values of the model.


The value I get for A6 using the 43rd root of 12 is more like 1761.11.

Models assume zero inharmonicity, so there is obviously no claim that they "resemble what a real piano should be given inharmonicity".

You use the phrase, "we describe tuning frequencies in terms of cents offsets from 12 root 2". Yes, that is the way models are used in electronic tuning devices.

However, there is another way to use models, as I pointed out in my post. As Daniel Levitan puts it in his text, The Craft of Piano Tuning: "...Piano tuners always prefer to approximate to some extent the theoretical beat rates of equal temperament, purposefully mistuning 1st partials... This is because piano tuners listen, not to 1st partials, but to coincident partials. Through the artful mistuning of 1st partials, tuners strive to create the illusion that there is no inharmonicity in the intervals of a piano."

So, as I said, models provide target beat rates, not frequencies.

Top
#2274033 - 05/11/14 01:46 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford

So, as I said, models provide target beat rates, not frequencies.

Any reasonable model of piano tuning should incorporate a model of inharmonicity, as do all ETD's.

2^(1/12) model is the coarsest model and gives you ballpark figures for beatrates. Any refinement of this model should first deal with inharmonicity, then the various stretching methods can be discussed.

Fooling around with other semitone ratios without modeling inharmonicity seems pointless to me. You can propose any real number close to 2^(1/12) as the basis of a "new tuning", it does not matter if it can be written as the foo root of bar or not.

That's why the whole chas "theory" is pointless.

Kees

Top
#2274055 - 05/11/14 02:34 PM Re: CHAS for Dummies [Re: DoelKees]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: DoelKees
Originally Posted By: Kent Swafford

So, as I said, models provide target beat rates, not frequencies.

Any reasonable model of piano tuning should incorporate a model of inharmonicity, as do all ETD's.

2^(1/12) model is the coarsest model and gives you ballpark figures for beatrates. Any refinement of this model should first deal with inharmonicity, then the various stretching methods can be discussed.

Fooling around with other semitone ratios without modeling inharmonicity seems pointless to me. You can propose any real number close to 2^(1/12) as the basis of a "new tuning", it does not matter if it can be written as the foo root of bar or not.

That's why the whole chas "theory" is pointless.

Kees


<grin>

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.

The chosen width and its associated beat rates are executed across a scale artfully by the piano tech to provide a best-fit, coherent tuning in spite of inharmonicity.

Top
#2274064 - 05/11/14 02:54 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.


I don't see how that is possible. Let's take a semitone of 2^(1/12) and try to use those zero-ih beatrates as guides.

The octaves (and double, and triple, etc) have theoretical beatrates of zero. Problem is that on a real piano a single octave has at least 3 beat rates, 2:1, 4:2, and 6:3, which can not all be zero. What do you now do with your "target beat rate"?

Kees

Top
#2274089 - 05/11/14 03:45 PM Re: CHAS for Dummies [Re: DoelKees]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21536
Loc: Oakland
Originally Posted By: DoelKees
Problem is that on a real piano a single octave has at least 3 beat rates, 2:1, 4:2, and 6:3, which can not all be zero.
Kees


I have asked twice what those different beat rates are supposed to sound like, and I have gotten no response.

Beats occur according to when the maxima and minima of two interfering waves coincide. When the maxima and minima of a piano tone occur is affected by the shape of the wave, which determines the partials, but it does not mean that the maxima and minima of the partials can interfere with each other to the extent that they differ from those of the fundamentals. It just means that the beats will not be nice, clean, regular sine waves themselves, just as the fundamentals are not a nice, clean, regular sine waves.

There are other things that affect how beats sound. There is the difference in volume between any two notes, which is why beats on a piano never approach silence at their minima, and there is the decay which overwhelms the sound of the beat as the intervals come closer to coinciding. These make "beatless" a relative term. I would like someone to demonstrate how octaves can be beatless on a piano. If it is such an important phenomenon, someone should be able to record it so we could listen to it and hear exactly what it is.
_________________________
Semipro Tech

Top
#2274092 - 05/11/14 03:49 PM Re: CHAS for Dummies [Re: DoelKees]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: DoelKees
Originally Posted By: Kent Swafford

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.


I don't see how that is possible. Let's take a semitone of 2^(1/12) and try to use those zero-ih beatrates as guides.

The octaves (and double, and triple, etc) have theoretical beatrates of zero. Problem is that on a real piano a single octave has at least 3 beat rates, 2:1, 4:2, and 6:3, which can not all be zero. What do you now do with your "target beat rate"?

Kees

In addition, the iH is not consistent across the break, and, the lower partials in the bass are anomalous, due to bridge rocking or some other not well researched effects. Any tuning paradigm must include those factors - in the case of aural tuners , they use their ears, in the of ETDs, compromises must be made.

Top
#2274174 - 05/11/14 06:19 PM Re: CHAS for Dummies [Re: Kent Swafford]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
Originally Posted By: Kent Swafford

<grin>

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.

The chosen width and its associated beat rates are executed across a scale artfully by the piano tech to provide a best-fit, coherent tuning in spite of inharmonicity.



OK, go on. Lets suppose that you determine beat rates for a chosen model. Then how do you propose to extend this to actually tuning a piano?
Have you actually tuned a piano like this?
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2274179 - 05/11/14 06:26 PM Re: CHAS for Dummies [Re: Chris Leslie]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Chris Leslie
Originally Posted By: Kent Swafford

<grin>

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.

The chosen width and its associated beat rates are executed across a scale artfully by the piano tech to provide a best-fit, coherent tuning in spite of inharmonicity.



OK, go on. Lets suppose that you determine beat rates for a chosen model. Then how do you propose to extend this to actually tuning a piano?
Have you actually tuned a piano like this?


Unless I am completely wrong, it is not possible to use any size octave other than precisely 2:1 octaves for instruments that do not exhibit iH, such as a pipe organ. As a result, on a piano, the iH is 'a priori', after which a stretch can be imposed.

Top
#2274191 - 05/11/14 06:56 PM Re: CHAS for Dummies [Re: prout]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: prout
.
.
.
.

Unless I am completely wrong, it is not possible to use any size octave other than precisely 2:1 octaves for instruments that do not exhibit iH, such as a pipe organ. As a result, on a piano, the iH is 'a priori', after which a stretch can be imposed.


Well, no.

If I understand, Mr. Capurso designed CHAS to be valid in instruments without iH.

Top
#2274202 - 05/11/14 07:23 PM Re: CHAS for Dummies [Re: DoelKees]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: DoelKees
Originally Posted By: Kent Swafford

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.


I don't see how that is possible. Let's take a semitone of 2^(1/12) and try to use those zero-ih beatrates as guides.

The octaves (and double, and triple, etc) have theoretical beatrates of zero. Problem is that on a real piano a single octave has at least 3 beat rates, 2:1, 4:2, and 6:3, which can not all be zero. What do you now do with your "target beat rate"?

Kees


Fine aural tuning predates a complete understanding of inharmonicity. There was a time when piano techs didn't even know inharmonicity existed and yet they tuned pianos as best they could using the beat rates of the model, because that was all they had.

You say, 2:1, 4:2, and 6:3 can not all be zero, which is obviously true. However, what does that have to do with artfully tuning a clean octave aurally? The whole sound of an octave can have a clean sound. And the octave can be tuned clean while tuning 4ths that beat much the same as 5ths in the 4th-5th test of the 4:2 octave.

Top
#2274211 - 05/11/14 07:38 PM Re: CHAS for Dummies [Re: Gadzar]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Gadzar
Originally Posted By: prout
.
.
.
.

Unless I am completely wrong, it is not possible to use any size octave other than precisely 2:1 octaves for instruments that do not exhibit iH, such as a pipe organ. As a result, on a piano, the iH is 'a priori', after which a stretch can be imposed.


Well, no.

If I understand, Mr. Capurso designed CHAS to be valid in instruments without iH.

Well, that's a problem then.

Take linearly stretched octaves of 2.005 (as I believe is the CHAS model) of say 100 Hz-200.5-402.0025-806.015 on a organ. Because the partials are, in fact, harmonic, you now have the following beating sequence - 100-200-200.5-300-400-401-402.0025-500-600-601.5-700-800-801-802-804.05.

Now, if the octave were precisely 2:1, the sequence would be 100-200-300-400-500-600-700-800.

Which do you think will sound better?

Top
#2274213 - 05/11/14 07:38 PM Re: CHAS for Dummies [Re: Chris Leslie]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: Chris Leslie
Originally Posted By: Kent Swafford

<grin>

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.

The chosen width and its associated beat rates are executed across a scale artfully by the piano tech to provide a best-fit, coherent tuning in spite of inharmonicity.



OK, go on. Lets suppose that you determine beat rates for a chosen model. Then how do you propose to extend this to actually tuning a piano?
Have you actually tuned a piano like this?


Of course I have tuned a piano like this. And I have said how to go about it, by artfully tuning as closely as possible to the beat rates of the model and by doing so, to give the illusion of zero inharmonicity.

For my PTG Atlanta institute class, I have prepared tunings of the Pianoteq modeled piano to demonstrate equal temperaments at various recognizable widths.

As as been mentioned elsewhere on Piano World, Pianoteq supports the Scala tuning protocol, and it even supports 88 note tunings, and so I have used Scala to tune the Pianoteq piano note by note to a high degree of accuracy, and to many different tunings.

Obviously, it would be better to demonstrate these tunings with real pianos and that can be done, but with Pianoteq in a classroom situation, all the tunings will be utterly stable, and will be immediately available and comparable at the click of a trackpad button.

Top
#2274214 - 05/11/14 07:39 PM Re: CHAS for Dummies [Re: Kent Swafford]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Kent Swafford
Originally Posted By: DoelKees
Originally Posted By: Kent Swafford

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.


I don't see how that is possible. Let's take a semitone of 2^(1/12) and try to use those zero-ih beatrates as guides.

The octaves (and double, and triple, etc) have theoretical beatrates of zero. Problem is that on a real piano a single octave has at least 3 beat rates, 2:1, 4:2, and 6:3, which can not all be zero. What do you now do with your "target beat rate"?

Kees


Fine aural tuning predates a complete understanding of inharmonicity. There was a time when piano techs didn't even know inharmonicity existed and yet they tuned pianos as best they could using the beat rates of the model, because that was all they had.

You say, 2:1, 4:2, and 6:3 can not all be zero, which is obviously true. However, what does that have to do with artfully tuning a clean octave aurally? The whole sound of an octave can have a clean sound. And the octave can be tuned clean while tuning 4ths that beat much the same as 5ths in the 4th-5th test of the 4:2 octave.



This works well for a decaying sound envelope. Not so easy with a constant amplitude sound.

Top
#2274216 - 05/11/14 07:41 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
ET forces the existence of a semitone ratio. Usually this ratio is supposed to be 12th root of 2, as the ratio of the octave is 2.

But iH in pianos creates multiple kinds of octaves: 2:1, 4:2, 6:3, 8:4, etc.

Ths the magic octave ratio of 2 is blown off.

In real pianos there are no pure octaves. They beat and they have multiple beat rates, one for each pair of quasi coincident partials.

The same happens for all the intervals, they all have multiple simultaneous beat rates. In P5s for example we have two distinctive beat rates namely 3:2 and 6:4
Theoretically there is an infinite number of quasi coincident partials for each kind of interval. Thus for the P4 we have 4:3, 8:6, 16:12, etc... In the real world only 2 or 3 pair of quasi coincident partials are audible at some specific locations of the piano's scale.

IMO there is no fixed ratio for the semitone that can be taken to tune a puano from A0 to C8.

The iH of a piano is not constant across the scale, it's curve has "hokey stick" shape.

Thus, I think the size of the semitone can not be constant but it must change from A0 to C8.

The fact here is that we can no more talk about an Equal Temperament.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2274235 - 05/11/14 08:07 PM Re: CHAS for Dummies [Re: Gadzar]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Gadzar wrote:

"The fact here is that we can no more talk about an Equal Temperament."

Beat rates. Define equal temperament in terms of beat rates.

For me, the recently passed Bill Garlick provided the best definition of equal temperament for the modern world.

"In equal temperament on the modern piano there is not a single interval which is tuned just or perfect -- even including the octave. Due to the Comma of Pythagoras and inharmonicity all intervals must be contracted or expanded from perfect and will therefore beat... All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically. It should be noted that such chromatically ascending progressions, particularly of M3rds and M6ths is a characteristic unique to equal temperament and distinguishes it from any other temperament."

-- Bill Garlick

Top
#2274258 - 05/11/14 08:37 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford
Originally Posted By: DoelKees
Originally Posted By: Kent Swafford

There is a way of tuning in which one can pick a stretch level by choosing a width of equal temperament and using the beat rates of that width of ET to provide the target beat rates for a tuning, regardless of inharmonicity.


I don't see how that is possible. Let's take a semitone of 2^(1/12) and try to use those zero-ih beatrates as guides.

The octaves (and double, and triple, etc) have theoretical beatrates of zero. Problem is that on a real piano a single octave has at least 3 beat rates, 2:1, 4:2, and 6:3, which can not all be zero. What do you now do with your "target beat rate"?

Kees


Fine aural tuning predates a complete understanding of inharmonicity. There was a time when piano techs didn't even know inharmonicity existed and yet they tuned pianos as best they could using the beat rates of the model, because that was all they had.

You say, 2:1, 4:2, and 6:3 can not all be zero, which is obviously true. However, what does that have to do with artfully tuning a clean octave aurally? The whole sound of an octave can have a clean sound. And the octave can be tuned clean while tuning 4ths that beat much the same as 5ths in the 4th-5th test of the 4:2 octave.


Of course, but what does that have to do with exotic zero-ih models with weird roots?

Kees

Top
#2274267 - 05/11/14 08:54 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
"Of course, but what does that have to do with exotic zero-ih models with weird roots?"

Kees

I'm not so sure they are so weird.

They provide a good way of quantifying stretch, and executing their characteristic beat rate patterns evenly across the scale can promote coherent-sounding tunings.

Top
#2274270 - 05/11/14 09:03 PM Re: CHAS for Dummies [Re: Kent Swafford]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: Kent Swafford
Gadzar wrote:

"The fact here is that we can no more talk about an Equal Temperament."

Beat rates. Define equal temperament in terms of beat rates.
.
.
.
"All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically."
-- Bill Garlick


It's impossible.

You can tune M3s in an even progression.
Or you can tune P5s in an even progression.

But in a real piano there are iH jumps in the scale and you can not tune an even progression of M3s and P5s.

You have a jump at the break, you have a jump when passing from wound strings to plain strings and you have a jump each time the diameter of plain strins changes.

So it is impossible to tune all intervals in even progressions of beat rates.


Edited by Gadzar (05/11/14 09:08 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2274319 - 05/11/14 10:21 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford
"Of course, but what does that have to do with exotic zero-ih models with weird roots?"

Kees

I'm not so sure they are so weird.

They provide a good way of quantifying stretch, and executing their characteristic beat rate patterns evenly across the scale can promote coherent-sounding tunings.


It sounds good in a vague sentence, but how do you propose to "execute their characteristic beat rate patterns evenly across the scale" exactly? Beat rates of which intervals?

Kees

Top
#2274323 - 05/11/14 10:22 PM Re: CHAS for Dummies [Re: Gadzar]
Ed Foote Offline
1000 Post Club Member

Registered: 05/03/03
Posts: 1165
Loc: Tennessee
Originally Posted By: Gadzar
Originally Posted By: Kent Swafford

"All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically."
-- Bill Garlick


It's impossible.

You can tune M3s in an even progression.
Or you can tune P5s in an even progression.
But in a real piano there are iH jumps in the scale and you can not tune an even progression of M3s and P5s.
You have a jump at the break, you have a jump when passing from wound strings to plain strings and you have a jump each time the diameter of plain strins changes.
So it is impossible to tune all intervals in even progressions of beat rates.


Greetings,
I am going to guess that you never heard Bill Garlick tune a piano. He varied the sizes of his octaves as he got to them, after making an initial decision when he tempered the temperament octave, itself. It may be impossible for ideals to be met on paper, since the numbers are obviously indicating unevenness. However, in the real world,( where evenness is being measured sensually i.e., by listening), tuning can be perfected to the point where any inequity in the division of the octave is not discernible. This is assuming a reasonably scaled larger piano. It is possible to hide the errors in such a way that a clinical environment is needed to find them, but it is a rare ear that does this.

We spend a lot of time judging the evenness and accuracy of the tunings, but that last 1% is of little import to the musical world. ET has such a busy background that things have to be pretty uneven to be noticed in a musical setting. Even given that the thirds are in control of the tonal value of the triad, unless one is playing chromatic thirds and comparing them, equally tempered ones pass as identical if they are within a cent of each other. I use a lot of UT's, and the 12 or 15 cent thirds are never commented on. The 5 cent and 18 cent thirds, yes, but not those that vary by a cent.
Regards,

Top
#2274329 - 05/11/14 10:29 PM Re: CHAS for Dummies [Re: Gadzar]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Gadzar
Originally Posted By: Kent Swafford
Gadzar wrote:

"The fact here is that we can no more talk about an Equal Temperament."

Beat rates. Define equal temperament in terms of beat rates.
.
.
.
"All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically."
-- Bill Garlick


It's impossible.

You can tune M3s in an even progression.
Or you can tune P5s in an even progression.

But in a real piano there are iH jumps in the scale and you can not tune an even progression of M3s and P5s.

You have a jump at the break, you have a jump when passing from wound strings to plain strings and you have a jump each time the diameter of plain strins changes.

So it is impossible to tune all intervals in even progressions of beat rates.


This is so true. A simple spreadsheet using 12-ET, which includes the measured iH of a given piano, will immediately reveal the variations in beat progressions. You can choose one interval to be monotonically increasing, but the others will then not be monotonic. Any theoretical ET model which does not involve iH will have all intervals increasing monotonically.

Top
#2274338 - 05/11/14 10:35 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford

"In equal temperament on the modern piano there is not a single interval which is tuned just or perfect -- even including the octave. Due to the Comma of Pythagoras and inharmonicity all intervals must be contracted or expanded from perfect and will therefore beat... All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically. It should be noted that such chromatically ascending progressions, particularly of M3rds and M6ths is a characteristic unique to equal temperament and distinguishes it from any other temperament."

-- Bill Garlick

We had a long thread (or threads) on this subject a while ago which you may want to look up if you're interested. At some point it was proposed to relax these conditions to progressive M3 and M6 only. As it turned out nobody was able to actually tune a temperament octave with strictly progressive M3's, with the exception of Bernhard Stopper with a modified OnlyPure ETD.

Another remark I have is that that definition is incomplete, at least when taken to define what we commonly call ET. You have to put some restrictions on the octaves. Otherwise a semitone ratio of 2 would be ET according to this definition.

Finally the part "and inharmonicity" does not belong in the definition. Organs can also be tuned in ET>

Kees

Top
#2274361 - 05/11/14 10:45 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Hi Ed,

Greetings.

I agree in all yo say. 100%.

And you guessed right, unfortunately I never heard Bill Garlick tune a piano.

Tuning a piano in ET is all about compromises. You compromise the progression of one interval to favor another one, and it is the balancing of these compromises that characterises a good tuning.

As you said the octaves are not the same size all along the scale of the piano and it is in that sense that I say ET does not exist. There are different sizes of the same interval in different places of the scale.


Edited by Gadzar (05/11/14 10:46 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2274446 - 05/11/14 11:43 PM Re: CHAS for Dummies [Re: BDB]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: BDB

I have asked twice what those different beat rates are supposed to sound like, and I have gotten no response.

Here you go.

2:1
4:2
6:3
Equal beating 6:3 4:2

Inharmonicity according to measurements of Hellas Helsinki upright.

Kees

Top
#2274514 - 05/12/14 01:08 AM Re: CHAS for Dummies [Re: prout]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: prout
Originally Posted By: Gadzar
Originally Posted By: prout
.
.
.
.

Unless I am completely wrong, it is not possible to use any size octave other than precisely 2:1 octaves for instruments that do not exhibit iH, such as a pipe organ. As a result, on a piano, the iH is 'a priori', after which a stretch can be imposed.


Well, no.

If I understand, Mr. Capurso designed CHAS to be valid in instruments without iH.

Well, that's a problem then.

Take linearly stretched octaves of 2.005 (as I believe is the CHAS model) of say 100 Hz-200.5-402.0025-806.015 on a organ. Because the partials are, in fact, harmonic, you now have the following beating sequence - 100-200-200.5-300-400-401-402.0025-500-600-601.5-700-800-801-802-804.05.

Now, if the octave were precisely 2:1, the sequence would be 100-200-300-400-500-600-700-800.

Which do you think will sound better?


I really don't know. I never play organ, I've never tuned one. I guess if you ask Mr. Capurso he will say CHAS is better.

For me all I can say is that if I tune the high treble of a piano with clean 2:1 octaves, it sounds flat to me, I wonder if an organ will have the same flatness when tuned with exact theoretical harmonic frequences.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2274524 - 05/12/14 01:44 AM Re: CHAS for Dummies [Re: DoelKees]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21536
Loc: Oakland
Originally Posted By: DoelKees
Originally Posted By: BDB

I have asked twice what those different beat rates are supposed to sound like, and I have gotten no response.

Here you go.

2:1
4:2
6:3
Equal beating 6:3 4:2

Inharmonicity according to measurements of Hellas Helsinki upright.

Kees


Those are not from a piano; those are just some sounds you have put together.
_________________________
Semipro Tech

Top
#2274563 - 05/12/14 04:13 AM Re: CHAS for Dummies [Re: Kent Swafford]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
Originally Posted By: Kent Swafford

Of course I have tuned a piano like this. And I have said how to go about it, by artfully tuning as closely as possible to the beat rates of the model and by doing so, to give the illusion of zero inharmonicity.
..........
Obviously, it would be better to demonstrate these tunings with real pianos and that can be done, but with Pianoteq in a classroom situation, all the tunings will be utterly stable, and will be immediately available and comparable at the click of a trackpad button.


In order to calculate the beat rates you must first know the inharmonicity constants for every note for the particular piano. So, how do you know what inharmonicity to use? If you use a zero-inharmonicity 42-ET model with the hope that the beat rates are correct, it will only be correct for one fictitious piano. How do you know it will work on both a grand piano and a spinet?

Also, lets suppose that you have a calculated beat rate spreadsheet. How do you then tune a note so that the beat rate is correct? What technique do you have to say that your beat rate is precise?

Like Gadzar, I don't believe that all ET semitones for a real piano are the same across the range of a real piano tuned either aurally or with an ETD.

Kent, you need to be more precise with real techniques and evidence if I am to take you seriously.


Edited by Chris Leslie (05/12/14 04:18 AM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2274600 - 05/12/14 06:40 AM Re: CHAS for Dummies [Re: Chris Leslie]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: Chris Leslie
Originally Posted By: Kent Swafford

Of course I have tuned a piano like this. And I have said how to go about it, by artfully tuning as closely as possible to the beat rates of the model and by doing so, to give the illusion of zero inharmonicity.
..........
Obviously, it would be better to demonstrate these tunings with real pianos and that can be done, but with Pianoteq in a classroom situation, all the tunings will be utterly stable, and will be immediately available and comparable at the click of a trackpad button.


In order to calculate the beat rates you must first know the inharmonicity constants for every note for the particular piano. So, how do you know what inharmonicity to use? If you use a zero-inharmonicity 42-ET model with the hope that the beat rates are correct, it will only be correct for one fictitious piano. How do you know it will work on both a grand piano and a spinet?

Also, lets suppose that you have a calculated beat rate spreadsheet. How do you then tune a note so that the beat rate is correct? What technique do you have to say that your beat rate is precise?

Like Gadzar, I don't believe that all ET semitones for a real piano are the same across the range of a real piano tuned either aurally or with an ETD.

Kent, you need to be more precise with real techniques and evidence if I am to take you seriously.


Thanks, this has been fun. This has gone about how I suspected it would. 8^)

In a world where our understanding of inharmonicity is complete, and we actually have the ability to measure inharmonicity for each note and calculate a tuning that takes into consideration each note's individual inharmonicity, then it is obvious that equal temperament is impossible.

And yet, I am employed every day to tune equal temperament, and other techs have been so employed at least since Montal a century and a half ago.

The concept that Virgil Smith called the "whole sound", and Brian Capleton calls the whole "soundscape" includes some effects that are not taken into consideration when one looks only at individual partials of individual notes.

I have spent the last year studying the tuning literature to see if I could deepen my understanding of tuning. I will present what I have found in a class in July. Presenting a class such as this is the only way I have after 35 years of tuning for me to have any chance of learning something new about the art/craft of tuning.

I would have thought that one event here would have been a tip-off that there is more to tuning than can be accounted for with individual partials: Kees wrote, "As it turned out nobody was able to actually tune a temperament octave with strictly progressive M3's, with the exception of Bernhard Stopper..." I doubt that it was an accident that Bernhard Stopper was able to do this.

I can hear people now, "How can there be 'more than individual partials'? That is impossible!"

Or maybe we just have more to learn about tuning. I gotta go work on my class, and then go tune some pianos in equal temperament!

Top
#2274628 - 05/12/14 07:45 AM Re: CHAS for Dummies [Re: Kent Swafford]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: Kent Swafford


The concept that Virgil Smith called the "whole sound", and Brian Capleton calls the whole "soundscape" includes some effects that are not taken into consideration when one looks only at individual partials of individual notes.




I like that. partials only are ( often ?) a little off what we want.

We look for an optimal bloom in octaves, that mean depending where in the piano , different "sizes" will be used, but no partial is left aside doing so, we try to have all them right and do not cry if the octave have some activity, as long it sound as a pure interval.
I seem to use 2:1 and 4:2 more than a directly tuned 6:3 , that sound off to me.

2:1 , 4:2 6:3 are all tuneable directly by ear.

Checking with beat rates of different intervals is not as precise I thought for a long time, they are tools, mostly learning tools or control tools. Due to the fluctuation in beats strength and speed, how can I compare them precisely ? I just persuade myself they beat the same, a little faster:slower can be heard but not very little speed differences.





Edited by Olek (05/12/14 11:18 AM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2274635 - 05/12/14 07:56 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
All:

I think we are missing the forest for the trees.

Pick an ET model, see what pure or equal beating intervals define it, apply those intervals to a tuning of an instrument with iH and the result will be a certain amount of stretch. For instance:

12th root of two is understood to be 2:1 octaves.

19th root of three is understood to be 3:1 twelfths.

24th root of 4 is understood to be 4:1 double-octaves.

and so on.

A mathematical model when applied to a real piano is just a way of saying what intervals are pure or equal beating.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2274644 - 05/12/14 08:12 AM Re: CHAS for Dummies [Re: Kent Swafford]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Kent Swafford
Gadzar wrote:

"The fact here is that we can no more talk about an Equal Temperament."

Beat rates. Define equal temperament in terms of beat rates.

For me, the recently passed Bill Garlick provided the best definition of equal temperament for the modern world.

"In equal temperament on the modern piano there is not a single interval which is tuned just or perfect -- even including the octave. Due to the Comma of Pythagoras and inharmonicity all intervals must be contracted or expanded from perfect and will therefore beat... All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically. It should be noted that such chromatically ascending progressions, particularly of M3rds and M6ths is a characteristic unique to equal temperament and distinguishes it from any other temperament."

-- Bill Garlick


I don't quite agree with Mr. Garlick. A piano can be tuned with pure 2:1 octaves or pure 4:2 octaves if it is recognized that these are actually two different intervals. And I think we must view multiple partial matches as different intervals, otherwise there is the possibility of an interval both increasing and decreasing in beatspeed at the same time. (Or being both wide and narrow at the same time. It would not always be possible to say whether multi-partial intervals are progressive or not.)

And in cases where a pure interval is tuned, an optimum way of dealing with jumps in iH is offered. For instance if a 4:2 pure octave definition of ET is used, which also means that stacked 4ths and 5ths beat equally, then 4ths and 5ths should be tuned to be as progressive as possible across a break. Without going into detail, this only holds true for test intervals that are wholly within the defined interval. The M3-M10 test for 4:2 octaves wouldn't work. "Making the M3s and M10s as progressive as possible across a break wouldn't work as well."
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2274651 - 05/12/14 08:24 AM Re: CHAS for Dummies [Re: prout]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: prout
Originally Posted By: Gadzar
Originally Posted By: Kent Swafford
Gadzar wrote:

"The fact here is that we can no more talk about an Equal Temperament."

Beat rates. Define equal temperament in terms of beat rates.
.
.
.
"All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically."
-- Bill Garlick


It's impossible.

You can tune M3s in an even progression.
Or you can tune P5s in an even progression.

But in a real piano there are iH jumps in the scale and you can not tune an even progression of M3s and P5s.

You have a jump at the break, you have a jump when passing from wound strings to plain strings and you have a jump each time the diameter of plain strins changes.

So it is impossible to tune all intervals in even progressions of beat rates.


This is so true. A simple spreadsheet using 12-ET, which includes the measured iH of a given piano, will immediately reveal the variations in beat progressions. You can choose one interval to be monotonically increasing, but the others will then not be monotonic. Any theoretical ET model which does not involve iH will have all intervals increasing monotonically.

Do you mean the spreadsheet shows the odd interval beating slower as you ascend chromatically?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2274695 - 05/12/14 09:47 AM Re: CHAS for Dummies [Re: Withindale]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Withindale
Originally Posted By: prout
Originally Posted By: Gadzar
Originally Posted By: Kent Swafford
Gadzar wrote:

"The fact here is that we can no more talk about an Equal Temperament."

Beat rates. Define equal temperament in terms of beat rates.
.
.
.
"All the tempered intervals of equal temperament should gradually increase in beat speed evenly, ascending chromatically."
-- Bill Garlick


It's impossible.

You can tune M3s in an even progression.
Or you can tune P5s in an even progression.

But in a real piano there are iH jumps in the scale and you can not tune an even progression of M3s and P5s.

You have a jump at the break, you have a jump when passing from wound strings to plain strings and you have a jump each time the diameter of plain strins changes.

So it is impossible to tune all intervals in even progressions of beat rates.


This is so true. A simple spreadsheet using 12-ET, which includes the measured iH of a given piano, will immediately reveal the variations in beat progressions. You can choose one interval to be monotonically increasing, but the others will then not be monotonic. Any theoretical ET model which does not involve iH will have all intervals increasing monotonically.

Do you mean the spreadsheet shows the odd interval beating slower as you ascend chromatically?


Yes. Here is my M&H BB tuning prediction based on its own iH.
Note that the M3s are progressive, but the P5s and P4s are not.
I should also note that the octaves from C3-E4 are basically 4:2 transitioning to 2:1 at C5. This is a test only. The stretch at C5 is +0.6 cents.



Edited by prout (05/12/14 10:54 AM)

Top
#2274748 - 05/12/14 11:17 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
An interval is produced when we play simultaneously 2 keys in the piano. For example if we play C4G4 the intervel is a P5. In this interval we have two distinct beat rates namely 3:2 and 6:4. Some may say these are two different intervals but the truth is that there is only one interval with two different beat rates coming from two pairs of almost coincident partials. There is no way to play a 6:4 fifth without its corresponding 3:2 fifth.

When ascending chromatically we can ttune in a way to have one beat rate progressing evenly faster but we have no control over the secpnd beat rate. In a well scaled piano normally the second will follow the first one but when there are jumps in the iH then disruptions in the progression can not be avoided.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2274754 - 05/12/14 11:21 AM Re: CHAS for Dummies [Re: Gadzar]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: Gadzar
An interval is produced when we play simultaneously 2 keys in the piano. For example if we play C4G4 the intervel is a P5. In this interval we have two distinct beat rates namely 3:2 and 6:4. Some may say these are two different intervals but the truth is that there is only one interval with two different beat rates coming from two pairs of almost coincident partials. There is no way to play a 6:4 fifth without its corresponding 3:2 fifth.

When ascending chromatically we can ttune in a way to have one beat rate progressing evenly faster but we have no control over the secpnd beat rate. In a well scaled piano normally the second will follow the first one but when there are jumps in the iH then disruptions in the progression can not be avoided.


Plus a beat created by the rubbing between partials.

I have a nice table of those "phantom beats" they obviously interfere with the most prominent ones.

a 3!2 or a 6:4 fifth is not something with a meaning, to me, this is not even a 5th . A fifth is an interval with a slow beat.

A beat is periodic energy fluctuation whatever the number of composites it contains.



Edited by Olek (05/12/14 11:22 AM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2274760 - 05/12/14 11:25 AM Re: CHAS for Dummies [Re: BDB]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: BDB
Originally Posted By: DoelKees
Originally Posted By: BDB

I have asked twice what those different beat rates are supposed to sound like, and I have gotten no response.

Here you go.

2:1
4:2
6:3
Equal beating 6:3 4:2

Inharmonicity according to measurements of Hellas Helsinki upright.

Kees


Those are not from a piano; those are just some sounds you have put together.

To hear them on a piano, go to a piano, tune a 2;1 octave (or hire somebody else if you don't know how), then listen (with your ears). For the 4:2 and other octave follow the same procedure.

Kees

Top
#2274766 - 05/12/14 11:30 AM Re: CHAS for Dummies [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
All:

I think we are missing the forest for the trees.

Pick an ET model, see what pure or equal beating intervals define it, apply those intervals to a tuning of an instrument with iH and the result will be a certain amount of stretch. For instance:

12th root of two is understood to be 2:1 octaves.

19th root of three is understood to be 3:1 twelfths.

24th root of 4 is understood to be 4:1 double-octaves.

and so on.

A mathematical model when applied to a real piano is just a way of saying what intervals are pure or equal beating.


2^(1/12) = 4^(1/24).

Kees

Top
#2274768 - 05/12/14 11:35 AM Re: CHAS for Dummies [Re: UnrightTooner]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: UnrightTooner
... For instance if a 4:2 pure octave definition of ET is used, which also means that stacked 4ths and 5ths beat equally, then 4ths and 5ths should be tuned to be as progressive as possible across a break. Without going into detail, this only holds true for test intervals that are wholly within the defined interval. The M3-M10 test for 4:2 octaves wouldn't work.


I don't follow you. If you tune pure 4:2 octaves then both tests P4P5 and M3M10 will show the 4:2 octaves are pure.

Maybe you mean that P4 will progress evenly while there will be a jump in the progression of M3s, don't you?
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2274770 - 05/12/14 11:38 AM Re: CHAS for Dummies [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: DoelKees
Originally Posted By: BDB
Originally Posted By: DoelKees
Originally Posted By: BDB

I have asked twice what those different beat rates are supposed to sound like, and I have gotten no response.

Here you go.

2:1
4:2
6:3
Equal beating 6:3 4:2

Inharmonicity according to measurements of Hellas Helsinki upright.

Kees


Those are not from a piano; those are just some sounds you have put together.

To hear them on a piano, go to a piano, tune a 2;1 octave (or hire somebody else if you don't know how), then listen (with your ears). For the 4:2 and other octave follow the same procedure.

Kees


Good demo with very audible beats, I believe they can be hidden in a sort of bloom. for instance 4:2 2:1 balance gives a sort of platform where the 6:3 can be hidden (I believe it is an energy question)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2274782 - 05/12/14 11:59 AM Re: CHAS for Dummies [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
All:

I think we are missing the forest for the trees.

Pick an ET model, see what pure or equal beating intervals define it, apply those intervals to a tuning of an instrument with iH and the result will be a certain amount of stretch. For instance:

12th root of two is understood to be 2:1 octaves.

19th root of three is understood to be 3:1 twelfths.

24th root of 4 is understood to be 4:1 double-octaves.

and so on.

A mathematical model when applied to a real piano is just a way of saying what intervals are pure or equal beating.


2^(1/12) = 4^(1/24).

Kees


Yep, I know. The one implies, and should be understood as, the octave being what is divided up into 12 parts, the other the double octave being divided up into 24 parts. that is how we can go from a mathematical, non-iH, model to an actual tuning on a real piano.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2274785 - 05/12/14 12:03 PM Re: CHAS for Dummies [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Gadzar
Originally Posted By: UnrightTooner
... For instance if a 4:2 pure octave definition of ET is used, which also means that stacked 4ths and 5ths beat equally, then 4ths and 5ths should be tuned to be as progressive as possible across a break. Without going into detail, this only holds true for test intervals that are wholly within the defined interval. The M3-M10 test for 4:2 octaves wouldn't work.


I don't follow you. If you tune pure 4:2 octaves then both tests P4P5 and M3M10 will show the 4:2 octaves are pure.

Maybe you mean that P4 will progress evenly while there will be a jump in the progression of M3s, don't you?


Yes, thank you, I my post was confusing. I should have said "Making the M3s and M10s as progressive as possible across a break wouldn't work as well." I will correct it.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2274791 - 05/12/14 12:15 PM Re: CHAS for Dummies [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
All:

I think we are missing the forest for the trees.

Pick an ET model, see what pure or equal beating intervals define it, apply those intervals to a tuning of an instrument with iH and the result will be a certain amount of stretch. For instance:

12th root of two is understood to be 2:1 octaves.

19th root of three is understood to be 3:1 twelfths.

24th root of 4 is understood to be 4:1 double-octaves.

and so on.

A mathematical model when applied to a real piano is just a way of saying what intervals are pure or equal beating.


2^(1/12) = 4^(1/24).

Kees


Yep, I know. The one implies, and should be understood as, the octave being what is divided up into 12 parts, the other the double octave being divided up into 24 parts. that is how we can go from a mathematical, non-iH, model to an actual tuning on a real piano.


(2^(22/3))^(1/88) then? smile

Kees

Top
#2274818 - 05/12/14 01:06 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Human ear :

distortion approx : plus 1/4 tone on a 3 octave span, in soprano region.

There iH is helping us to hear that a piano is in tune wink



Edited by Olek (05/12/14 01:06 PM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2274886 - 05/12/14 02:48 PM Re: CHAS for Dummies [Re: UnrightTooner]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: UnrightTooner
All:

I think we are missing the forest for the trees.

Pick an ET model, see what pure or equal beating intervals define it, apply those intervals to a tuning of an instrument with iH and the result will be a certain amount of stretch. For instance:

12th root of two is understood to be 2:1 octaves.

19th root of three is understood to be 3:1 twelfths.

24th root of 4 is understood to be 4:1 double-octaves.

and so on.

A mathematical model when applied to a real piano is just a way of saying what intervals are pure or equal beating.


No. Please note that the 12th root of 2 and the 24th root of 4 are the same number, so they cannot be used to differentiate between 2:1 and 4:1.

Top
#2275118 - 05/12/14 10:47 PM Re: CHAS for Dummies [Re: Olek]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Olek
Originally Posted By: DoelKees
Originally Posted By: BDB
Originally Posted By: DoelKees
Originally Posted By: BDB

I have asked twice what those different beat rates are supposed to sound like, and I have gotten no response.

Here you go.

2:1
4:2
6:3
Equal beating 6:3 4:2

Inharmonicity according to measurements of Hellas Helsinki upright.

Kees


Those are not from a piano; those are just some sounds you have put together.

To hear them on a piano, go to a piano, tune a 2;1 octave (or hire somebody else if you don't know how), then listen (with your ears). For the 4:2 and other octave follow the same procedure.

Kees


Good demo with very audible beats, I believe they can be hidden in a sort of bloom. for instance 4:2 2:1 balance gives a sort of platform where the 6:3 can be hidden (I believe it is an energy question)


Thanks. I added the 2:1/4:2 mix to the demo list. Can you still hear the 6:3 beats?

2:1
4:2
6:3
Equal beating 6:3 4:2
Equal beating 2:1 4:2

Kees

Top
#2275261 - 05/13/14 05:10 AM Re: CHAS for Dummies [Re: Kent Swafford]
Mark R. Offline
2000 Post Club Member

Registered: 07/31/09
Posts: 2014
Loc: Pretoria, South Africa
Originally Posted By: UnrightTooner
All:

I think we are missing the forest for the trees.

Pick an ET model, see what pure or equal beating intervals define it, apply those intervals to a tuning of an instrument with iH and the result will be a certain amount of stretch. For instance:

12th root of two is understood to be 2:1 octaves.

19th root of three is understood to be 3:1 twelfths.

24th root of 4 is understood to be 4:1 double-octaves.

and so on.

A mathematical model when applied to a real piano is just a way of saying what intervals are pure or equal beating.


Jeff, I can see where you're going (I think): People are getting caught up in the numbers. Of course, purely mathematically, 2^(1/12) = 4^(1/24). But you're making a different point (I think).

"Pick an ET model, see what pure or equal beating intervals define it, apply those intervals to a tuning of an instrument with iH and the result will be a certain amount of stretch."

For example, if you decide to tune an ET inside a pure 3:1 P12, you tune a real, inharmonic, pure 3:1 P12 on this piano, and divide it into 19 equal (progressive) parts. This temperament would be called a "19th root of 3" ET for this specific piano, because the 3:1 P12 is beatless on this specific piano.

However, I see one problem. This notation only works for n:1 invertals, i.e. 2:1 octave, 3:1 P12, 4:1 double octave, etc.

How would you express an ET inside a 4:2 temperament octave or 6:3 temperament octave, or a 4:2/6:3 compromise? 12th root of {what}?
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

Top
#2275333 - 05/13/14 08:37 AM Re: CHAS for Dummies [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: DoelKees

Thanks. I added the 2:1/4:2 mix to the demo list. Can you still hear the 6:3 beats?

2:1
4:2
6:3
Equal beating 6:3 4:2
Equal beating 2:1 4:2


You got it, I think !!!

With the huge advantage they are easy to tune and they give you direct access to the 12th -

Can be confused with 6:3

funny that double conversation wink

Thanks for the recordings


Edited by Olek (05/14/14 06:25 AM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2275417 - 05/13/14 11:11 AM Re: CHAS for Dummies [Re: prout]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: prout
Originally Posted By: Withindale
Do you mean the spreadsheet shows the odd interval beating slower as you ascend chromatically?

Yes. Here is my M&H BB tuning prediction based on its own iH.
Note that the M3s are progressive, but the P5s and P4s are not.


Thanks for posting your figures. Is there a way you can vary your calculation to make all intervals progressive, or do the variations in iH preclude that?

I think you have already indicated you can't but can you give an example of iH values causing problems away from the break?


Edited by Withindale (05/13/14 11:35 AM)
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2275434 - 05/13/14 11:40 AM Re: CHAS for Dummies [Re: Withindale]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Withindale
Originally Posted By: prout
Originally Posted By: Withindale
Do you mean the spreadsheet shows the odd interval beating slower as you ascend chromatically?

Yes. Here is my M&H BB tuning prediction based on its own iH.
Note that the M3s are progressive, but the P5s and P4s are not.


Thanks for posting your figures. Is there a way you can vary your calculation to make all intervals progressive, or do the variations in iH preclude that?

I you have already indicated you can't but can you give an example of iH values causing problems away from the break?


The iH seems to preclude the possibility of fully progressive intervals. I am running a test using progressive narrow fifths at the moment and it is proving difficult. I will post my results and the iH values as well.

I must add that I am using the classic iH formula with corrections for the lower six partials from A0 to about E4. I am working on a test using Robert Scott's modified iH formula as well. It shows great promise and may end up being the best fit for a generic iH formula that does not take into considerations bridge anomalies.

The classic formula iH curve is about as perfect as one can get above the bass bridge break - essentially straight, though on very close inspection you can see the string diameter change points across the compass.

Cheers

Top
#2275596 - 05/13/14 05:25 PM Re: CHAS for Dummies [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: DoelKees
Originally Posted By: Olek
Originally Posted By: DoelKees
Originally Posted By: BDB
Originally Posted By: DoelKees
Originally Posted By: BDB

I have asked twice what those different beat rates are supposed to sound like, and I have gotten no response.

Here you go.

2:1
4:2
6:3
Equal beating 6:3 4:2

Inharmonicity according to measurements of Hellas Helsinki upright.

Kees


Those are not from a piano; those are just some sounds you have put together.

To hear them on a piano, go to a piano, tune a 2;1 octave (or hire somebody else if you don't know how), then listen (with your ears). For the 4:2 and other octave follow the same procedure.

Kees


Good demo with very audible beats, I believe they can be hidden in a sort of bloom. for instance 4:2 2:1 balance gives a sort of platform where the 6:3 can be hidden (I believe it is an energy question)


Thanks. I added the 2:1/4:2 mix to the demo list. Can you still hear the 6:3 beats?

2:1
4:2
6:3
Equal beating 6:3 4:2
Equal beating 2:1 4:2

Kees


It will probably pass unnoticed because it is a little OT of the thread wink
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2275617 - 05/13/14 05:59 PM Re: CHAS for Dummies [Re: Mark R.]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Mark R.
...

However, I see one problem. This notation only works for n:1 invertals, i.e. 2:1 octave, 3:1 P12, 4:1 double octave, etc.

How would you express an ET inside a 4:2 temperament octave or 6:3 temperament octave, or a 4:2/6:3 compromise? 12th root of {what}?


How about the 36th root of 6 divided by the 19th root of 3 or something. (Or something... I'm not thinking clear today - Dentist. I just might win the Jack-o-Lantern look alike contest this fall!)
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2275646 - 05/13/14 07:13 PM Re: CHAS for Dummies [Re: UnrightTooner]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
Originally Posted By: UnrightTooner
All:

I think we are missing the forest for the trees.

_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2275654 - 05/13/14 07:37 PM Re: CHAS for Dummies [Re: Withindale]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Withindale
Originally Posted By: prout
Originally Posted By: Withindale
Do you mean the spreadsheet shows the odd interval beating slower as you ascend chromatically?

Yes. Here is my M&H BB tuning prediction based on its own iH.
Note that the M3s are progressive, but the P5s and P4s are not.


Thanks for posting your figures. Is there a way you can vary your calculation to make all intervals progressive, or do the variations in iH preclude that?

I think you have already indicated you can't but can you give an example of iH values causing problems away from the break?


Here is an example using progressive P5s:



Note that I was able to create precise matches to the theoretical P5s. However, it is important to understand that the iH shown has been corrected for anomalies in the first six partials for most of the notes. If you were to use the data indicated without those corrections, the beat rates would be different.

Note also that the M3s are not progressive, but actually still a pretty good fit. The P4s are not even close.

This is only one of an infinite number of progressive P5 tunings, but it seems to show promise.

I have more trouble getting a coherent sound using progressive M3s than using progressive P5s. This may come from my tuning mostly UTs in the past, where I am listening to the P5s and taking whatever M3s result.

Top
#2275848 - 05/14/14 06:57 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Beats are slowing audibly. I am not sure I understand how you compute. It is only one level of partial match .?

i was said the best way to use credible partials was yo examiné each string and use the most accurate one for the display (etd)


Edited by Olek (05/14/14 06:59 AM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2275852 - 05/14/14 07:03 AM Re: CHAS for Dummies [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: UnrightTooner
Originally Posted By: Mark R.
...

However, I see one problem. This notation only works for n:1 invertals, i.e. 2:1 octave, 3:1 P12, 4:1 double octave, etc.

How would you express an ET inside a 4:2 temperament octave or 6:3 temperament octave, or a 4:2/6:3 compromise? 12th root of {what}?


How about the 36th root of 6 divided by the 19th root of 3 or something. (Or something... I'm not thinking clear today - Dentist. I just might win the Jack-o-Lantern look alike contest this fall!)


Doh!

(2/1)^(1/12), 2:1 octaves
(4/2)^(1/12), 4:2 octaves
(6/3)^(1/12), 6:3 octaves
(((4/2)+(6/3))/2)^(1/12), equal beating 4:2, 6:3 octaves
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2275858 - 05/14/14 07:30 AM Re: CHAS for Dummies [Re: prout]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: prout
Originally Posted By: Withindale
Originally Posted By: prout
Originally Posted By: Withindale
Do you mean the spreadsheet shows the odd interval beating slower as you ascend chromatically?

Yes. Here is my M&H BB tuning prediction based on its own iH.
Note that the M3s are progressive, but the P5s and P4s are not.


Thanks for posting your figures. Is there a way you can vary your calculation to make all intervals progressive, or do the variations in iH preclude that?

I think you have already indicated you can't but can you give an example of iH values causing problems away from the break?


Here is an example using progressive P5s:



Note that I was able to create precise matches to the theoretical P5s. However, it is important to understand that the iH shown has been corrected for anomalies in the first six partials for most of the notes. If you were to use the data indicated without those corrections, the beat rates would be different.

Note also that the M3s are not progressive, but actually still a pretty good fit. The P4s are not even close.

This is only one of an infinite number of progressive P5 tunings, but it seems to show promise.

I have more trouble getting a coherent sound using progressive M3s than using progressive P5s. This may come from my tuning mostly UTs in the past, where I am listening to the P5s and taking whatever M3s result.


Prout:

Something seems wrong. Maybe it has to do with: "the iH shown has been corrected for anomalies in the first six partials for most of the notes."

First, since the iH is progressive, I would expect that it is possible to have all RBIs progressive if not the SBIs as well.

When I use your iH and offsets for A3 and A4 I get an octave wider than 6:3. But according to you table, both the A3-D4 P4 and the D4-A4 P5 have identical beatrates of 0.99; the octave must be a pure 4:2.

Any explanation? Is it that the individual partials are that whacky?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2275892 - 05/14/14 09:38 AM Re: CHAS for Dummies [Re: UnrightTooner]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Jeff:
Yes, the individual partials are wacky, which gives a pure, beatless 2:1 and 4:2 A3-A4 octave with a narrow 6:3 A3-A4 by 1.4 bps.

For that test I chose to use the theoretical values of the P5 and P4 on A3-D4-A4 as a starting point which resulted in the above data.

I could have compromised and stretched the octave a bit to create a 0.5bps wide 4:2 and a 0.5bps narrow 6:3 which yields a slower P5 by 0.3bps and a faster P4 by 0.3bps, but when I start doing that the tuning tends toward Reverse Well.

Keep those fifths narrow. laugh

Top
#2275896 - 05/14/14 09:51 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Prout:

Then you are demonstrating what non-typical partials do to beatrate progressions. I don't see the point. You are not showing how iH affects beatrate progressions, just what "background noise" does. Is that your point? It may be a good one.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2275899 - 05/14/14 10:11 AM Re: CHAS for Dummies [Re: UnrightTooner]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: UnrightTooner
Prout:

Then you are demonstrating what non-typical partials do to beatrate progressions. I don't see the point. You are not showing how iH affects beatrate progressions, just what "background noise" does. Is that your point? It may be a good one.


In a way, I guess that is my point. Unless my methodology for measuring the individual partials is wrong, it seems that there are statistically significant departures of the various partials from the theoretical values when using either the standard iH formula or R. Scott's formula. Those anomalies force the tuner to make a decision about how to tune a particular piano.

So the question still is, as has been discussed on this forum so many times, what is the best way to tune an ET that is consistent across the compass and also coherent?

Coherence, to me, as a pianist, seems to come mostly from the interaction of octaves and fifths, especially when using the damper pedal. A single note played with the damper lifted, needs to have the rest of the piano helping it. Having tuned various temperaments on my piano, each one still had to have the octaves and fifths sounding well together.

Cheers.

Top
#2275906 - 05/14/14 10:36 AM Re: CHAS for Dummies [Re: prout]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: prout
.....

So the question still is, as has been discussed on this forum so many times, what is the best way to tune an ET that is consistent across the compass and also coherent?

Coherence, to me, as a pianist, seems to come mostly from the interaction of octaves and fifths, especially when using the damper pedal. A single note played with the damper lifted, needs to have the rest of the piano helping it. Having tuned various temperaments on my piano, each one still had to have the octaves and fifths sounding well together.

Cheers.



I would call that resonance. I think a piano resonates more when the strongest partials are near to equal beating. The lowest partials are of course the strongest, until you get low enough in the scale that the soundboard does not vibrate that slow. Then the strongest partials are higher ones.

My answer to your question is pure 12ths with prioritizing the P5 across the breaks. And including the octave above the lower note when tuning wound strings. Others have other answers.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2275910 - 05/14/14 10:51 AM Re: CHAS for Dummies [Re: UnrightTooner]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: UnrightTooner
Originally Posted By: prout
.....

So the question still is, as has been discussed on this forum so many times, what is the best way to tune an ET that is consistent across the compass and also coherent?

Coherence, to me, as a pianist, seems to come mostly from the interaction of octaves and fifths, especially when using the damper pedal. A single note played with the damper lifted, needs to have the rest of the piano helping it. Having tuned various temperaments on my piano, each one still had to have the octaves and fifths sounding well together.

Cheers.



I would call that resonance. I think a piano resonates more when the strongest partials are near to equal beating. The lowest partials are of course the strongest, until you get low enough in the scale that the soundboard does not vibrate that slow. Then the strongest partials are higher ones.

My answer to your question is pure 12ths with prioritizing the P5 across the breaks. And including the octave above the lower note when tuning wound strings. Others have other answers.



Good word - 'Resonance'

I would like to think that everything comes into 'tune', but, in reality, it is the calm 'airiness' of the piano that is so satisfying when well tuned.

Thanks for your thoughts.

Top
#2275975 - 05/14/14 02:52 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
For me the problem when dealing with a jump in the iH is that the relative distance between partials changes abruptly. If we pass from wound to plain to strings the higher iH in the plain string makes its partials be more distant to each other. If we chose to tune based on the 4th partial we split in two the deviation of partial 5 (M3s) and partial 3 (P5s).

Prout, haven't you cosidered a tuning based on a smoth progresdion of 4:2 octaves or 4:3 fourths?

IMO, such a tuning will give more coherent M3s and good P5s.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2276064 - 05/14/14 06:37 PM Re: CHAS for Dummies [Re: prout]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
prout, how did you get those figures for those tables? Did you measure them on your piano with your software? Are they repeatable?

Also, I suppose you derived the iH values from the partial data. If so then they will be subject to an error term.

I would be interested in seeing similar figures comparing chromatic M6th given evenly progressive M3rds.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2276065 - 05/14/14 06:39 PM Re: CHAS for Dummies [Re: Gadzar]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Gadzar
For me the problem when dealing with a jump in the iH is that the relative distance between partials changes abruptly. If we pass from wound to plain to strings the higher iH in the plain string makes its partials be more distant to each other. If we chose to tune based on the 4th partial we split in two the deviation of partial 5 (M3s) and partial 3 (P5s).

Prout, haven't you cosidered a tuning based on a smoth progresdion of 4:2 octaves or 4:3 fourths?

IMO, such a tuning will give more coherent M3s and good P5s.


How far up do you usually take the 4:2 octaves?

I usually start with 6:3 on A0 transitioning smoothly to 4:2 by A2 and then transitioning to 2:1 above A4. Even with that conservative treble stretch I am 26 cents sharp at C8.

Top
#2276086 - 05/14/14 07:31 PM Re: CHAS for Dummies [Re: Chris Leslie]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Chris Leslie
prout, how did you get those figures for those tables? Did you measure them on your piano with your software? Are they repeatable?

Also, I suppose you derived the iH values from the partial data. If so then they will be subject to an error term.

I would be interested in seeing similar figures comparing chromatic M6th given evenly progressive M3rds.


The table figures are calculated based on the iH data. Early on in my experiments, I calculated the tuning values, tuned them, and then measured the resultant beat rates against my predicted beat rates. They were accurate within the limits of my measurement capability, but not good enough. I have now refined the accuracy of the iH values, and, using the correction deltas for the lower six partials, feel that the predictions are much more accurate. However, I have not had time to tune using the latest data, measure the resultant beat rates and do the analysis. (Too much concertizing and practicing at the moment.) I hope to eventually show the results, good or bad, for you all to see.

Top
#2276101 - 05/14/14 07:48 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
So how did you get the iH data in the first place? They have to be very accurate or else the rest of the data will be not very valid.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2276124 - 05/14/14 08:18 PM Re: CHAS for Dummies [Re: Chris Leslie]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Chris Leslie
So how did you get the iH data in the first place? They have to be very accurate or else the rest of the data will be not very valid.


The iH data collection has been the most time consuming. I have collected multiple samples of each note (between ten and twenty) in wave files at 24 bit 48kHz using a flat reference microphone. I export the sample (decimated to the Nyquist Freq for the upper partial that I am looking at, which requires multiples runs per note in order to get all the partials) then load each sample of each note into a java programme that does a FFT analysis on the sample, does bin interpolation and converges on the individual partial frequency. That data is exported to an Excel spreadsheet, and averaged with all the other data for that particular partial for that particular note. Once sufficient data has been collected and averaged, I run LINEST function to determine the slope (iH) and the y-intercept (f0). The iH is used to calculate the partials for each note, a delta is determined for the lower six partials for all notes from A0 through C4 and this data is used to produce a basic tuning template for trial stretches and temperament.

Top
#2276132 - 05/14/14 08:47 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
Thanks prout. I was wondering if after that process you are able to determine error terms for the iH values, and then use the variance to look at significant variance in the beat rate figures which helps me to interpret your data.

Sorry, I hope I don't sound too interrogative. I just have a thing about statistical rigour at times.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2276324 - 05/15/14 03:31 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
I was not talking about that.

In the table you posted you have tuned a
quasi perfect progression of 5ths. The result is jumping major thirds.

I ask you if you can try to make a tuning with a quasi perfect progression of fourths, I guess you'll have better major thirds and good fifths.

About what I tune, I start with 4:2 octaves at the temperament (F3-A4). In large pianos I tune 4:2+ octaves and in small pianos I tune 4:2- octaves.

For the treble I tune mindless octaves (4:1+/3:1-) and pure triple octaves at the high treble (8:1).

Some days ago I tried the tuning of pure 19ths, double octave + fifth, 6:1, as suggested by Mark Cerisano and I liked the bright sound it produces.

In the basse I tune 6:3 octaves or even wider octaves, stretching as much as the piano allows. I usually check the tuning of bass notes with notes in the temperament area F3-A4.

For me ET is only an ideal from where we start when setting the temperament octave. From there the notion of equality disappears as we stretch intervals to accomodate for the iH.

The tuning we get is ET in the sense that all the intervals sound equal tempered but in fact they are more stretched at the extremes of the scale: remember Railsback?

A model as CHAS with a fixed ratio and a constant stretch for all the notes from A0 to C8 is not a valid piano tuning model, because it doesn' follow the Railsback curve.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2276360 - 05/15/14 07:05 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Raphael. As long as the model follow an acoustical shape it is driven by the iH.
The fact is that some of the iH is annhilated with Chas because it use a strong resonant node.
a little like you when using small 4:2 octaves. The twelve beat is hidden then.

Regards
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2276377 - 05/15/14 08:43 AM Re: CHAS for Dummies [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Gadzar
.....

The tuning we get is ET in the sense that all the intervals sound equal tempered but in fact they are more stretched at the extremes of the scale: remember Railsback?

A model as CHAS with a fixed ratio and a constant stretch for all the notes from A0 to C8 is not a valid piano tuning model, because it doesn' follow the Railsback curve.


So then a M3 that beats at 3 bps would sound equally tempered to one two octaves higher at 12 bps?

But if we say a tuning model that has equally beating 12ths and 15ths with a common note on bottom (such as CHAS), then that definition does produce a railsback curve on a piano with iH. It just happens that if a piano does not have iH, then the result is the fixed ratio in the model.

The Railsback curve is an "artifact" of tuning to beatrates (aurally or electronically) rather than to a fixed ratio. We need not include it, or any frequency ratios, in a tuning model at all. We can just model with beatrates, which will result in different tunings on different pianos.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2276473 - 05/15/14 12:20 PM Re: CHAS for Dummies [Re: Chris Leslie]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Chris Leslie
Thanks prout. I was wondering if after that process you are able to determine error terms for the iH values, and then use the variance to look at significant variance in the beat rate figures which helps me to interpret your data.

Sorry, I hope I don't sound too interrogative. I just have a thing about statistical rigour at times.


I don't mind the questions at all.

The LINEST function for iH gives me R^2 values that range from 0.9998, mostly 0.999+, to a single low of 0.9974 on D#7 and the +- values are better than 1% up to C7 slowly increasing to 2% at C8. This implies that my published iH values are accurate to 3 significant figures.

I had to make a decision regarding the inclusion of the lower partials in the iH calculation for the bass bridge and lower tenor strings. After much testing I found that removing the lower three or four anomalous partials from the first 32 partials used to calculate the iH, gave a much more accurate result. I continue to use the deviant partials in the beat rate calculations as an offset which can be as much as -6.7 cents. Including the anomalous partials in the iH calculation still gave a usable iH value, but really disturbed the f0 number and still required the inclusion of offsets in the partial calculations for tuning.

Here is the iH graph shown in terms that most ETDs would use:


Top
#2276632 - 05/15/14 06:45 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
Ok prout, I see now, I think! You are somehow measuring partial data using your FFT program. Then you are regressing the partial data for each note and determining the veracity of the data by the examining R^2. I am happy with 3 significant figures if that is what you get. But your beat rates are derived from the measured partial data, right, and not back from the calculated iH data?

I am not sure how the anomalous lower partials will upset your f0. Do you mean P0? If so, shouldn't P0 be a starting point for any calculations rather than a result?


Edited by Chris Leslie (05/15/14 07:03 PM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2276747 - 05/15/14 10:41 PM Re: CHAS for Dummies [Re: UnrightTooner]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: UnrightTooner
Originally Posted By: Gadzar
.....

The tuning we get is ET in the sense that all the intervals sound equal tempered but in fact they are more stretched at the extremes of the scale: remember Railsback?

A model as CHAS with a fixed ratio and a constant stretch for all the notes from A0 to C8 is not a valid piano tuning model, because it doesn' follow the Railsback curve.


So then a M3 that beats at 3 bps would sound equally tempered to one two octaves higher at 12 bps?

But if we say a tuning model that has equally beating 12ths and 15ths with a common note on bottom (such as CHAS), then that definition does produce a railsback curve on a piano with iH. It just happens that if a piano does not have iH, then the result is the fixed ratio in the model.

The Railsback curve is an "artifact" of tuning to beatrates (aurally or electronically) rather than to a fixed ratio. We need not include it, or any frequency ratios, in a tuning model at all. We can just model with beatrates, which will result in different tunings on different pianos.


I guess yes. The question is, as always, what beats are you going to listen to in a given point of the scale and how they will progress?

I have not found a single beat rate that can be tuned from A0 to C8.

For the first part of yor comment I really can not imagine how to tune CHAS with iH. I think equal beating 12ths and 15ths is wrong. That is not CHAS. I understand that CHAS is the geometric mean between pure 12th and and pure 15th. More precisely partials 4 and 3.

There are regions on the piano scale with two audible beat rates for the 12th 3:1 and 6:2 and even a third one in the low bass 9:3. The same happens with 10:5, 8:4, 6:3 4:2, and2:1 octaves. Then how are the CHAS P12/P15 to be tuned there, where several audible beats rates?

And what is for you a piano without iH? You speak of it as if it was a tunable instrument and not a mathematical abstraction.


Edited by Gadzar (05/15/14 11:14 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2276880 - 05/16/14 07:43 AM Re: CHAS for Dummies [Re: Chris Leslie]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Chris Leslie
Ok prout, I see now, I think! You are somehow measuring partial data using your FFT program. Then you are regressing the partial data for each note and determining the veracity of the data by the examining R^2. I am happy with 3 significant figures if that is what you get. But your beat rates are derived from the measured partial data, right, and not back from the calculated iH data?

I am not sure how the anomalous lower partials will upset your f0. Do you mean P0? If so, shouldn't P0 be a starting point for any calculations rather than a result?


It would be best to replace the word 'calculated' with 'predicted'. The 'calc' beat rates shown in the tables are derived from my math. I will run a few test M3s today and show the theoretical, calculated, and actual beat rates.

The f0 I refer to is the base frequency from which all the partials, including the first, are calculated. In theory, it is always lower, due to iH, than the first partial. What is P0?

Top
#2276885 - 05/16/14 07:57 AM Re: CHAS for Dummies [Re: Olek]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Olek
[
a 3!2 or a 6:4 fifth is not something with a meaning, to me, this is not even a 5th . A fifth is an interval with a slow beat.

A beat is periodic energy fluctuation whatever the number of composites it contains.



Isaac, I like that last sentence of yours. When you tune an interval, do you aim for the most calm sound, or the most energy in the sound, or the best colour in the sound? Or, do you tune the interval differently in different places on the keyboard?

Top
#2276887 - 05/16/14 08:01 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Raphael,

Thank you for your ideas on octave sizes when tuning.

I produced a table of perfect P4s and it contains the same type of jumps and variations in the M3s and P5s as the the perfect P5 table I posted. I am working on a quasi-perfect P4 table as you suggested and it shows promise.

Top
#2276911 - 05/16/14 08:55 AM Re: CHAS for Dummies [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Gadzar
Originally Posted By: UnrightTooner
Originally Posted By: Gadzar
.....

The tuning we get is ET in the sense that all the intervals sound equal tempered but in fact they are more stretched at the extremes of the scale: remember Railsback?

A model as CHAS with a fixed ratio and a constant stretch for all the notes from A0 to C8 is not a valid piano tuning model, because it doesn' follow the Railsback curve.


So then a M3 that beats at 3 bps would sound equally tempered to one two octaves higher at 12 bps?

But if we say a tuning model that has equally beating 12ths and 15ths with a common note on bottom (such as CHAS), then that definition does produce a railsback curve on a piano with iH. It just happens that if a piano does not have iH, then the result is the fixed ratio in the model.

The Railsback curve is an "artifact" of tuning to beatrates (aurally or electronically) rather than to a fixed ratio. We need not include it, or any frequency ratios, in a tuning model at all. We can just model with beatrates, which will result in different tunings on different pianos.


I guess yes. The question is, as always, what beats are you going to listen to in a given point of the scale and how they will progress?

I have not found a single beat rate that can be tuned from A0 to C8.

For the first part of yor comment I really can not imagine how to tune CHAS with iH. I think equal beating 12ths and 15ths is wrong. That is not CHAS. I understand that CHAS is the geometric mean between pure 12th and and pure 15th. More precisely partials 4 and 3.

There are regions on the piano scale with two audible beat rates for the 12th 3:1 and 6:2 and even a third one in the low bass 9:3. The same happens with 10:5, 8:4, 6:3 4:2, and2:1 octaves. Then how are the CHAS P12/P15 to be tuned there, where several audible beats rates?

And what is for you a piano without iH? You speak of it as if it was a tunable instrument and not a mathematical abstraction.


"I have not found a single beat rate that can be tuned from A0 to C8."

I have. A pure 3:1 12ths. On an idealized studio it give A0 -9 cents and C8 +28 cents.

As far as defining CHAS, well, Alfredo makes that a "moving target".

Electronic pianos can have no iH. I was using this as a comparison.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2276943 - 05/16/14 10:35 AM Re: CHAS for Dummies [Re: UnrightTooner]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 186
Loc: Montreal
Originally Posted By: UnrightTooner
[quote=Gadzar][quote=UnrightTooner][
Electronic pianos can have no iH. I was using this as a comparison.



That's not true. All digital pianos that sample from real pianos also have the iH sampled in. And digital pianos that use physical modeling (such as Pianoteq) most certainly have iH. I have a Yamaha P120 (1998 vintage) and the piano samples not only have iH but also stretch - this is easy to hear when playing simultaneously with the voices that don't have stretch and iH (e.g. Vibraphone or pipe organ). The M3 rates are pretty progressive too - thought the overall stretch is a bit tame, probably so as to harmonize better with the non-stretched voices.

Paul.

Top
#2277038 - 05/16/14 02:02 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Jeff,

3:1 from A0 to C8 means that you tune the 3rd partial of A0 to the first partial of E2, which is not audible, not even measurable with an ETD!

I've measured the Melodygrand console with Tunelab Pro and the first partial is not present in the spectrum of the notes A#2 down to A0.

So how can one tune a note to a partial that is not audible? And neither measurable?

If you hear any beats in the P12 A0E2 then you are surely hearing 9:3 or 6:2 beatings, but surely not 3:1.

And when you have jumps in iH, it has been proven here that if you tune pure 3:1 P12s, where audible, then you'll have unacceptable jumps (even inversions) in the progression of M3s and all the others RBIs.

Rick Baldassin, in his book "On Pitch", has demonstrated that different sizes of octaves are to be tuned in different places of the piano scale. Different sizes of octaves means different sizes of all other intervals, 3:1 P12s included.

Don't you agree?


Edited by Gadzar (05/16/14 04:20 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2277085 - 05/16/14 03:44 PM Re: CHAS for Dummies [Re: Gadzar]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Gadzar
Jeff,

3:1 from A0 to C8 means that you tune the 3rd partial of A0 to the first partial of E2, which is not audible, not even measurable with an ETD!

I've measured the Melodygrand console with Tunelab Pro and the first partial is not present in the spectrum of the notes A#2 down to A0.

So how can one tune a note to a partial that is not audible? And neither measurable?

If you hear any beats in the P12 A0E2 then you are surely hearing 9:3 or 6:2 beatings, but surely not 3:1.

And when you have jumps in iH, it has been proven here that if you tune pure 3:1 P12s, where audible, then you'll have unacceptable jumps (even inversions) in the progression of M3s and all the others RBIs.

Rick Baldassin, in his book "On Pitch", has demonstrated that different sizes of octaves are to be tuned in different places of the piano scale. Different sizes of octaves means different sizes of all other intervals.

Don't you agree?


Actually, on some pianos (mine in particular), the 3rd partial of A0 is as strong as the first partial of E2, as seen below. Both sounds were recorded at very low volume.

Here is A0 with a -75db third partial



Here is E2 with a -75db first partial


Top
#2277108 - 05/16/14 04:27 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Prout,

You don't have a spinet, do you? Lol!
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2277123 - 05/16/14 05:05 PM Re: CHAS for Dummies [Re: Gadzar]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Gadzar
Prout,

You don't have a spinet, do you? Lol!


Back in 1959 - Yes!

Top
#2277147 - 05/16/14 05:48 PM Re: CHAS for Dummies [Re: prout]
Chris Storch Offline
Full Member

Registered: 08/13/09
Posts: 200
Loc: Massachusetts
Originally Posted By: prout

Actually, on some pianos (mine in particular), the 3rd partial of A0 is as strong as the first partial of E2, as seen below. Both sounds were recorded at very low volume.

Here is A0 with a -75db third partial

Huh. I read a relative level of about -65dB for the third partial in that first plot. Do I need glasses?
_________________________
Chris Storch
Acoustician / Piano Technician

Top
#2277207 - 05/16/14 07:49 PM Re: CHAS for Dummies [Re: Chris Storch]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Chris Storch
Originally Posted By: prout

Actually, on some pianos (mine in particular), the 3rd partial of A0 is as strong as the first partial of E2, as seen below. Both sounds were recorded at very low volume.

Here is A0 with a -75db third partial

Huh. I read a relative level of about -65dB for the third partial in that first plot. Do I need glasses?

Nope. I do. whistle

Top
#2277331 - 05/17/14 04:01 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Here are the notes measured in the Melodigrand. As you can see the first partial of the lower notes is not audible. Thus it is not possible to tune 3:1 P12s in the bass.

iH Melodigrand
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2277360 - 05/17/14 07:37 AM Re: CHAS for Dummies [Re: prout]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: prout
Originally Posted By: Olek
[
a 3!2 or a 6:4 fifth is not something with a meaning, to me, this is not even a 5th . A fifth is an interval with a slow beat.

A beat is periodic energy fluctuation whatever the number of composites it contains.



Isaac, I like that last sentence of yours. When you tune an interval, do you aim for the most calm sound, or the most energy in the sound, or the best colour in the sound? Or, do you tune the interval differently in different places on the keyboard?


Hello thanks, I am sorry not to have a decent explanation.
Since I stopped almost totally to use the standard tests, I replaced them by listening to consonance, activityu, color may be.

WHat I believe is that thos partial match tests are always in a closee ballpark, but they do not really prove us the interval is nicely tuned.

I stick with progressive large intervals of course, wanting mostly none of them to be aggressively shrilling.

But that is also an unison question at that point.

You may know the freeom sensation that it gives to be tuning by musical output.

I think I take the consonance level, and that is that part that I temper, not some beats speed difference, and anyway it can be so small difference I dont believe the ear can really precisely denote it.

Regards
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2277380 - 05/17/14 08:37 AM Re: CHAS for Dummies [Re: Gadzar]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Gadzar
Here are the notes measured in the Melodigrand. As you can see the first partial of the lower notes is not audible. Thus it is not possible to tune 3:1 P12s in the bass.

iH Melodigrand



Yes, I see your point.

Top
#2277381 - 05/17/14 08:51 AM Re: CHAS for Dummies [Re: Olek]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Olek
Originally Posted By: prout
Originally Posted By: Olek
[
a 3!2 or a 6:4 fifth is not something with a meaning, to me, this is not even a 5th . A fifth is an interval with a slow beat.

A beat is periodic energy fluctuation whatever the number of composites it contains.



Isaac, I like that last sentence of yours. When you tune an interval, do you aim for the most calm sound, or the most energy in the sound, or the best colour in the sound? Or, do you tune the interval differently in different places on the keyboard?


I think I take the consonance level, and that is that part that I temper, not some beats speed difference, and anyway it can be so small difference I dont believe the ear can really precisely denote it.

Regards


I am finding that the tempering (stretch) required for ET to have consonance in the multiple octaves/fifths (I am thinking of arpeggios) is different from the stretch needed in another temperament (Young in my case) since the fifths are of different sizes.

Top
#2277408 - 05/17/14 10:44 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
YEs I think a differnt range of consonances.

Tuning by Young or WT temperament is an appreciable experiment for the one used to the ET compromizing.

That is what I mean saying one may experience some freedom doing so.

ANd then I would suppose that kind of freedom can be taken for use when tuning ET (within margins of course)


yes consonance in ET is very strong betwween octaves twelves and all the doublings. That may be how I can precisely tune a 6th octave pure nd lining well just by listening to the tone quality of the note. I just refrain to "raise in turns" in some extreme stretch. Then 3 or 4 octaves span are just in place.

I was surprised to discover that the octave can be so much a good tool for tuning. But the habit of listening to the partials coupling "purity" helps for that of course.

in arpeggios, top note can have a somehow "tempezred" venue, but it does not sound flat as I could notice beforethen.

I believe that the initial mediums octave allow the room for that large span. Enlarging the mediums gives some security in regard of beats progression 'and settling) But it can make the harmony more "static" or "straight" .
Thze fact that low 4:2 and high 2:1 together seem to rule the twelve in a "tempered " feeking is for me an excellent foundation.

Best regards

BTW Gadzar, you did send a sample of very nicely tuned intervals a few years ago. DO you think using an ETD did change a little then way you listen now ?
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2277422 - 05/17/14 11:26 AM Re: CHAS for Dummies [Re: Olek]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Olek


in arpeggios, top note can have a somehow "tempezred" venue, but it does not sound flat as I could notice before then.



This is an interesting psycho-acoustic phenomenon I hear all the time. A full range arpeggio A0-A7 for example) makes the top note sound in tune to me, but playing a small range arpeggio (A4-A7) makes the same top note sound flat to me. Do other people hear this a well?

Top
#2277482 - 05/17/14 01:44 PM Re: CHAS for Dummies [Re: Olek]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: Olek
BTW Gadzar, you did send a sample of very nicely tuned intervals a few years ago. DO you think using an ETD did change a little then way you listen now ?


Thank you Isaac. For me the ETD has been an obstacle in developping my hearing skills and a tool to make money.

The more I use the ETD the less I hear.

I use it to quickly tune the first pass, mostly pitch raises, and then, if I have the time and the mood, I do aurally the fine tuning.

But definitely the ETD has shown me how a given interval should sound. For example if I want to hear the difference between a 6:3 octave and a 4:2. With the ETD they are really easy to tune and then carefully listen to the differences.

It helps also to study the amount of stretch needed by a given piano. Auraly speaking iH is transparent or invisible. When you tune by ear you can only hear if a interval is pure or tempered, if you measure a pure sounding interval you find out that it is actually stretched and you see by how much.

In particular for the tuning of the initial A3A4 octave, if I tune this octave as clean as possible and then I measure it with the ETD, I've found that in small pianos it is often a 2:1/4:2 balance. And in large pianos it is a 4:2/6:3.

But the ETD has a great disadvantage in that you can tune en entire piano without listening except for the unisons.

If I'd never used an ETD I bet my hearing skills had developed more in less time.

Another important issue is that the tuning hammer technique is different for aural tuning than for visual tuning. In particular I am more conscient of what is happening in the NSL when I tune by ear.

When tuning with the ETD I seldom have to shim o crak a unison. This is an almost "by ear" resource.

But what I see as the most valuable advantage of the ETD is that you can use it to learn to set the pitch and tune the temperament by ear. It is a good, objectif, impartial, consistent and reliable judge that tells you how well or bad you are doing it.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2277851 - 05/18/14 10:45 AM Re: CHAS for Dummies [Re: prout]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: prout
Originally Posted By: Olek


in arpeggios, top note can have a somehow "tempezred" venue, but it does not sound flat as I could notice before then.



This is an interesting psycho-acoustic phenomenon I hear all the time. A full range arpeggio A0-A7 for example) makes the top note sound in tune to me, but playing a small range arpeggio (A4-A7) makes the same top note sound flat to me. Do other people hear this a well?


I believe that tuning with open unison (a term visibly not mùany understand here) allows the piano to be more reactive to its own iH. I see no other reason why I have no real justness problems between basses and treble.

NOt anymore anyway since I worked CHAS tuning.

WHenever I test resonance of unplayed notes both directions (ghosting) , I find them very immediate very active and if beating it is slow enough or discrete enough not to be boithering.



Trying to tune pianos as if they had 2 strings is very frustrating. I believe that is why Well tunings are appreciated, as they reinstall some resonance where it is reduced with too straight tuning (unless it have been done with a very precise structure, in that case they color the tuning with a strong but dry attack mode)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2278263 - 05/19/14 07:13 AM Re: CHAS for Dummies [Re: prout]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: prout
Originally Posted By: Olek


in arpeggios, top note can have a somehow "tempezred" venue, but it does not sound flat as I could notice before then.



This is an interesting psycho-acoustic phenomenon I hear all the time. A full range arpeggio A0-A7 for example) makes the top note sound in tune to me, but playing a small range arpeggio (A4-A7) makes the same top note sound flat to me. Do other people hear this a well?


What I notice is that A7 sounds very different when playing an upward, A0-A7, arpeggio than playing a downward A7-A0 arpeggio and then repeating A7. If you tune aurally pure octaves, A#7 sounds much better than A7 after a A7-A0 arpeggio. But on most pianos, it is best to go no lower than A1, and for that matter skip C#2.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2278267 - 05/19/14 07:23 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Mark R. Offline
2000 Post Club Member

Registered: 07/31/09
Posts: 2014
Loc: Pretoria, South Africa
Jeff and prout,

I'd like to try this ascending/descending effect. Do you hold the respective arpeggio with the pedal?
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

Top
#2278294 - 05/19/14 08:31 AM Re: CHAS for Dummies [Re: Mark R.]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Mark R.
Jeff and prout,

I'd like to try this ascending/descending effect. Do you hold the respective arpeggio with the pedal?


I only did so only once. The piano then vomited walrus sputum all over a genuine 17th century persian rug. wink

I use the pedal. It might make a difference. I don't know.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2278639 - 05/19/14 11:47 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Well, I wonder if this post belongs here or to the thread on P12s tuning, anyway here it is:

I tuned the Melodigrand with pure 3:1 P12s by ear, so I guess in the lower part of the scale I actually tuned 6:2 P12s. The only check I did was hearing the 4:1 double octave, which must be wide. Example tune E3 to B4 from sharp to in tune, while checking E3E5 remains wide. Aiming to tune a pure 3:1 and not a 6:2 P12.

And the result was beating narrow octaves from E3 down to C#2. From C2 down to A0 octaves were less narrow. At some point they became acceptable.

From A0 to C2 there are monochords with double wound strings.

From C#2 up to G#3 there are bichords with single wound strings.

I liked the treble. Though, the high treble was a little flat to my taste.


Edited by Gadzar (05/20/14 12:33 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2278728 - 05/20/14 08:28 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Rafael:

You will probably agree with me that wound strings are a special case in any tuning method. The reason there are wound strings at all is because we don't build 20+ foot long pianos very often. Wound strings are a compromise, and should be tuned with some sort of compromise. Do you agree with this Rafael?

The compromise I use when tuning pure 12ths is to include the octave above the lower note when expanding the temperament downward and strive for the most resonant sound.

Btw, how did your RBIs across the break turn out?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2278741 - 05/20/14 08:52 AM Re: CHAS for Dummies [Re: Mark R.]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Mark R.
Jeff and prout,

I'd like to try this ascending/descending effect. Do you hold the respective arpeggio with the pedal?


For me, it is most noticeable with the dampers lifted. On the short arpeggios, the upper note can sound as much as a semitone flat. On the full arpeggio, it sounds correctly placed with the rest of the notes. I wonder if the upper partials from the lower notes are masking/reinforcing the perceived pitch?

Top
#2278903 - 05/20/14 04:03 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
SOmeone make a recording please ?
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2279105 - 05/21/14 06:15 AM Re: CHAS for Dummies [Re: UnrightTooner]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: UnrightTooner

Originally Posted By: Gadzar

I have not found a single beat rate that can be tuned from A0 to C8.


"I have not found a single beat rate that can be tuned from A0 to C8."

I have. A pure 3:1 12ths. On an idealized studio it give A0 -9 cents and C8 +28 cents.


I gave it a try and I got what I suspected: too narrow bass and high treble. And you say:

Originally Posted By: UnrightTooner
Rafael:

You will probably agree with me that wound strings are a special case in any tuning method. The reason there are wound strings at all is because we don't build 20+ foot long pianos very often. Wound strings are a compromise, and should be tuned with some sort of compromise. Do you agree with this Rafael?

The compromise I use....




You said first that 3:1 P12s can be used to tune from A0 to C8.

Now you say that compromises must be made for tuning wound strings.


Is it kind of a joke?

I have the impression you are turning around going nowhere. Studying idealized pianos without iH,, that do not exist, tuning imaginary intervals that can not be heard. I realy don't follow you.

Because of iH, tuning a piano is a matter of compromises, different compromises at different points of the scale, so you can not therefore tune it using one unique interval from A0 to C8.

Baldassin has written a complete book explaining all this stuff, with details of the intervals and ranges of the scale, tests for each interval, aural and electronic instructions to tune them, etc.

The ETD I use is based on these principles to calculate each tuning. The user chooses a "style", built in or custom made, which defines the stretch used at each point in the scale.

Piano tuning has not an ideal solution, it is all about compromises.



Edited by Gadzar (05/21/14 07:09 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2279129 - 05/21/14 07:59 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Gadzar:

Always the "Wolf in Sheep's Clothing." You pretend to be peaceably objective, and then attack.

I find that pure 12ths work just fine, except when there are poorly scaled or wound bass strings. Just because you do not doesn't mean a thing. smile
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2279190 - 05/21/14 10:39 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
All pianos have wound strings! Even well scaled pianos have wound strings.

So if, I understand you, are you saying that you find that pure 12ths work fine except on all pianos?
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2279205 - 05/21/14 11:12 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
OK, lobo, let me say "Poorly scaled and/or poorly would bass strings..."

If the scaling is good and the string winding is good there is no problem.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2279220 - 05/21/14 11:38 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Jeff,

You are right I pretend to be objectif. I don't care if I am peaceful or not, that is not my goal.

My goal is to be better at piano tuning.

I find that pure 12ths work fine to tune a certain range of the piano's scale, just above the tenor.

I am not attacking you. I am only saying that pure 3:1 12ths produce narrow octaves in the bass and produce also a flat high treble.

I read, somewhere, that Dr. Albert Sanderson were tuning a piano using an electronic instrument to put the fundamental at the calculated frecuencies of ET, calculated using the model of semitone = 12th root of 2. And to his surprise and after verifying there was no error, the piano sounded out of tune.

He then came with a solution, taking into account iH he designed his F A C tuning curve which gives nice in tune pianos.

When I first read about CHAS, I believed it was a model to solve the puzzle created by iH. But no luck. It is not that. It is a different model for calculating the ET frecuencies without taking into account iH.

That means if you tune a piano to CHASS calculated frecuencies for the fundamentals you'll get an out of tune piano. Just as with the 12th root of 2 model.

You are doing the same when talking about tuning pure 3:1 12ths which do not work fine with bad scaled pianos or wound bass strings. And as in all in this world, if you do the same you get the same results: out of tune pianos.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2279223 - 05/21/14 11:56 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Gadzar:

I would say that no matter how you tune a piano with poor scaling and/or poorly wound bass strings the piano will sound out of tune.

The best that I have come up with is what I mentioned: expand the temperament downward by playing both an octave and a 12th above.

As far as the flat high treble with pure 12ths, well it sounds good (in tune) to me.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2279242 - 05/21/14 12:59 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Anytime one tunes an interval such a 3:1 pure 12th, whether you do it by ear, or by an ETD using the appropriate partials, you are automatically taking into account iH. The issue with pure 12ths temperament is the same as any other temperament, you have to listen to the octaves as well and adjust where necessary. There are times when the amplitude of an octave partial may overwhelm the 12th and require more adjustment to make it sound well.

I just tuned my piano using pure 12ths and it sounds well. The treble is stretched to 34 cents at C8 and I had to widen the twelfths (actually wide 4:2 and 6:3) from G1 down to A0, giving a bass stretch of over 20 cents at A0.

Top
#2279272 - 05/21/14 01:53 PM Re: CHAS for Dummies [Re: prout]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Originally Posted By: prout
Anytime one tunes an interval such a 3:1 pure 12th, whether you do it by ear, or by an ETD using the appropriate partials, you are automatically taking into account iH.


Yes, of course, provided you are tuning a real piano and not talking about what that may sound on an "idealized studio with no iH" as Jeff did.

Originally Posted By: prout
I had to widen the twelfths (actually wide 4:2 and 6:3) from G1 down to A0, giving a bass stretch of over 20 cents at A0.


This is not pure 3:1 12ths!
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2279276 - 05/21/14 02:08 PM Re: CHAS for Dummies [Re: Gadzar]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 802
Originally Posted By: Gadzar
Originally Posted By: prout
Anytime one tunes an interval such a 3:1 pure 12th, whether you do it by ear, or by an ETD using the appropriate partials, you are automatically taking into account iH.


Yes, of course, provided you are tuning a real piano and not talking about what that may sound on an "idealized studio with no iH" as Jeff did.

Originally Posted By: prout
I had to widen the twelfths (actually wide 4:2 and 6:3) from G1 down to A0, giving a bass stretch of over 20 cents at A0.


This is not pure 3:1 12ths!



Correct, but I'm not sure I understand your point.

I think any temperament starts from an idealized base and is then placed as necessary on the instrument. The challenge is to find an idealized temperament that requires the least amount of work to adjust to the particular piano. I found the pure 12ths approach easy to implement and adjust. I may find another approach as I gain more experience that works better for me as well.

Cheers

Top
#2279286 - 05/21/14 02:37 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
When tuning aurally, it is like if there was no iH. Except for the break where sometimes conflicts between different intervals may appear. But for the rest our ears are able to find the sweet spot where all sounds good.

Thee goal here is to find a marhematical model which describes this good sounding tuning.

My point is that if you have to tweak the frecuencies calculated with your model in some regions of the scale, then your model doesn't work.

BTW, Bernhard Stopper's Onlypure tunes pure 12ths, with good results for fine tuners like Kent Swafford.

I am not saying pure 12ths don't work. I say that pure 3:1 12ths don't work. At some point there must be a transition from 3:1 to higher partials

Cheers!



Edited by Gadzar (05/21/14 04:46 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2279400 - 05/21/14 08:36 PM Re: CHAS for Dummies [Re: Gadzar]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Originally Posted By: Gadzar
When tuning aurally, it is like if there was no iH. Except for the break where sometimes conflicts between different intervals may appear. But for the rest our ears are able to find the sweet spot where all sounds good.

Thee goal here is to find a marhematical model which describes this good sounding tuning.




I like that first phrase.

I dont believe it can be described with partial matches, for the second question.

Regards
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2279405 - 05/21/14 08:42 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
IT is easy to get to larger twelves, I stick with tempered ones, and depite that they may sound enlaged if tested at 3:1 in some regions.

The pure twelve is the interval that gives the most large imprecision, but tuning it tempered allow a little more in my opinion.

I also do not appreciate the stretched tone of the enlarged twelves, even if it is discrete sometime.

On small pianos you are obliged to have very compact octaves, they go together with twelves that sound aalmost pure, in my experience.

But anyway a lot of beats appears in octaves and in twelves in the lowest octaves. AInt a problem for me as long as they sound like twelves and octaves
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2279442 - 05/21/14 09:54 PM Re: CHAS for Dummies [Re: Olek]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Olek wrote:

"On small pianos you are obliged to have very compact octaves..."

Why so? Why does it follow that small pianos require compact octaves?

I have heard this said repeatedly, but have never found it to be true.

Specifically, what bad thing happens to the tuning of a small piano if one doesn't tune compact octaves?

Thanks.

Top
#2279983 - 05/23/14 05:55 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
If you tune a 6:3-/4:2+ A3A4 octave in a spinet it won't sound pure, because 4:2 and 2:1 are predominant over 6:3 which is barely audible.

So in this case a 4:2-/2:1+ will sound purer.

Also shorter strings means more iH and there is more distance between partials.

I ve measured a 40" tall console A3A4 octave 6:3 = 4:2+6 cents = 2:1+7.5 cents.

A balanced 6:3/4:2 will give a predominant 4 cents wide 2:1 octave beating at 1 bps. It sounds definitely out of tune.

A balanced 4:2/2:1 will give a 6.5 cents narrow 6:3 octave, almost inaudible. The octave sounds practically pure.


Edited by Gadzar (05/23/14 06:07 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2279994 - 05/23/14 06:53 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Well stated Raphael

That initial octave is obtained by making the partials focusing together. I think I tune some sort of 2:1 octaves on larger pianos too, anyway I refrain to get catch in higher resonances due to partials.

I am not expecting an octave to have no "life" anyway, and the more you stretch the more you "fix" the resonance. may be just because it catch attention more.




Edited by Olek (05/23/14 06:54 AM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2280025 - 05/23/14 08:38 AM Re: CHAS for Dummies [Re: Gadzar]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: Gadzar
If you tune a 6:3-/4:2+ A3A4 octave in a spinet it won't sound pure, because 4:2 and 2:1 are predominant over 6:3 which is barely audible.

So in this case a 4:2-/2:1+ will sound purer.

Also shorter strings means more iH and there is more distance between partials.

I ve measured a 40" tall console A3A4 octave 6:3 = 4:2+6 cents = 2:1+7.5 cents.

A balanced 6:3/4:2 will give a predominant 4 cents wide 2:1 octave beating at 1 bps. It sounds definitely out of tune.

A balanced 4:2/2:1 will give a 6.5 cents narrow 6:3 octave, almost inaudible. The octave sounds practically pure.


I appreciate this reply very much. This explains a few things, at least to me.

I always use an ETD, but with an aural tuning bias.

For better or worse, I tend to judge the width of an octave by the very audible 4:2. And on high inharmonicity pianos, you say the 6:3 can be both way narrow _and_ almost inaudible. Exactly.

So, to me, when I say it isn't necessary to tune "compact" octaves (as defined by the stretched 4:2), and someone else says one must tune "compact" octaves (as defined by the almost inaudible contracted 6:3), we may not have any huge substantial difference in actual tuning practice.

I worry that advocating "compact" octaves in high inharmonicity pianos is misunderstood by some tuners and wrongly taken to mean pure 4:2, which can yield a very unpleasant-sounding tuning to my ears.

Thanks again.

Top
#2280026 - 05/23/14 08:39 AM Re: CHAS for Dummies [Re: Gadzar]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: Gadzar
... A balanced 4:2/2:1 will give a 6.5 cents narrow 6:3 octave, almost inaudible. The octave sounds practically pure.

As far as the octaves go in practice, doesn't that mean a little bit of stretch like CHAS?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2280043 - 05/23/14 09:43 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
All:

Stacked, pure 4:2 octaves will always result in a wide 4:1 double octave. The higher the iH, the wider the resulting 4:1 double octave. And in very high iH pianos the 3:1 12th will also be wide when pure 4:2 octaves are tuned.

I find it is best to tune the octaves just above the break on spinets and short consoles narrow of 4:2. But then that is the natural result from tuning pure 12ths and prioritizing the 5ths across the break(s).
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2280572 - 05/24/14 04:37 PM Re: CHAS for Dummies [Re: UnrightTooner]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: UnrightTooner
All:

Stacked, pure 4:2 octaves will always result in a wide 4:1 double octave. The higher the iH, the wider the resulting 4:1 double octave. And in very high iH pianos the 3:1 12th will also be wide when pure 4:2 octaves are tuned.

I find it is best to tune the octaves just above the break on spinets and short consoles narrow of 4:2. But then that is the natural result from tuning pure 12ths and prioritizing the 5ths across the break(s).


This is a very interesting set of statements that took a good bit of time to think through.

Actually, stacked pure 4:2 octaves will not necessarily result in a wide 4:1 double octave. One only need find one exception to your rule to prove it false, but I have several.

1. In a zero-inharmonicity situation, stacked pure 4:2 octaves will form a pure 4:1 octave.

Both Al Sanderson and Daniel Levitan teach about piano scales with "ideal" inharmonicity.

"In fact, whenever the inharmonicity of the lower note of an octave is 1/4 that of the upper note, the inharmonicity of the virtual 1/2-strings of the lower note exactly match the inharmonicity of the whole string of the upper note, and there is no inharmonicity in the octave. The experience of tuning such an octave is indistinguishable from the experience of tuning an octave beween two strings with no inharmonicity at all."

-- Daniel Levitan

2. With ideal inharmonicity as described above, then, stacked pure 4:2 octaves will also form a pure 4:1 double octave, just as if there were zero inharmonicity.

3. All that is required for 2 stacked pure 4:2 octaves to form a _narrow_ 4:1 double octave, is for the measurement in cents between the 2nd and 4th partials of the middle note of the stack to be less than the measurement between the 1st and second partials of the uppermost note of the 3. Such cannot be particularly unusual; it only means that the inharmonicity is increasing as you go up the scale more than the inharmonicity is increasing as you go up the partial series. Or you could say that the inharmonicity is increasing more than the ideal amount as you go up the scale.

Top
#2280658 - 05/24/14 09:16 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1759
Loc: Mexico City
Wow!

Very clever!

And surprising! (for me, at least). I'd never seen it this way.

In fact I have allways seen iH as it is in the tenor and bass, i.e. lower notes have more iH. And thinking in stretching intervals to compesate the effects of iH.

But, indeed, at the treble it reverses and higher notes have higher iH. Does that means that to compensate for iH in the treble, in some instances, one has to shrink intervals instead of stretching them?
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#2280752 - 05/25/14 07:38 AM Re: CHAS for Dummies [Re: Gadzar]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: Gadzar
Wow!

Very clever!

And surprising! (for me, at least). I'd never seen it this way.

In fact I have allways seen iH as it is in the tenor and bass, i.e. lower notes have more iH. And thinking in stretching intervals to compesate the effects of iH.

But, indeed, at the treble it reverses and higher notes have higher iH. Does that means that to compensate for iH in the treble, in some instances, one has to shrink intervals instead of stretching them?


The answer to your question is "Yes, but beware!"

Two decades ago I had been tuning with the SAT for a decade, and became dissatisfied with SAT FAC tunings for 2 overwhelming reasons. 1) B2 was tuned from partial 6 which was wildly inappropriate on some small pianos with a plain-wire string on B2. 2) And a standard feature of FAC tunings was tuning up into the treble with narrowed 4:2 octaves. (This was before the DOB adjustment was available on the SAT.)

Apparently, Dr. Al thought it was very common for inharmonicity to increase too slowly going up the scale.

We tuners have an unbelievably complex set of rules of thumb for dealing with inharmonicity, of which the treble narrowed 4:2 is an example.

However, all such rules of thumb are wrong for some individual pianos, and will sometimes lead us astray in tuning the one piano that is actually in front of us.

I have come to believe that for the best tunings we must forget the rules of thumb and tailor our tunings for the specific challenges of each individual piano.

Levitan says we should try to emulate the beat rates of the model(s) of ET; I believe he is correct.





Edited by Kent Swafford (05/25/14 02:48 PM)

Top
#2280769 - 05/25/14 08:56 AM Re: CHAS for Dummies [Re: Kent Swafford]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
Originally Posted By: Kent Swafford
Levitan says we should try to emulate the beat rates of the model(s) of ET; I believe he is correct.

Kent, do you mean to cover any model of an ET from pure octaves to CHAS to pure 12ths, even pure 5ths (Cordier)?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2280995 - 05/25/14 06:53 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
The human ear like to have that raised treble. If the ear ask for 1/4 tone on a 3 span octave, that mean a 25 cts C88 would be perfect for a 0cts at c5.

It is globally accepted that a medium iH is in the 0.6 0.7 range for A49, then the way it is suppose to raise is mostly for a more crisp and more acceptable treble.

I hae tuned many pianos Pleyel that have a reversing of iH progression in the last treble octaves may be about C6 an abovve.

While singing clear and long they are difficult to match ((an ETD are lost in computing there)

Pianos with low iH in treble can sound very well and still lack some "presence", the tone is not "irritating" enough. Too pure, the ear is not cheated enough may be.

the 1930 US upright pianos seem to have low iH in treble. Very agreable color, but somewhat limited for the available "palette"
As if a goo iH is producing different tone color depending of the style of stroke (and the global harmony/consonance)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2281140 - 05/26/14 06:38 AM Re: CHAS for Dummies [Re: Withindale]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: Withindale
Originally Posted By: Kent Swafford
Levitan says we should try to emulate the beat rates of the model(s) of ET; I believe he is correct.

Kent, do you mean to cover any model of an ET from pure octaves to CHAS to pure 12ths, even pure 5ths (Cordier)?


Sorry, I don't understand what you are asking...

Top
#2281149 - 05/26/14 07:45 AM Re: CHAS for Dummies [Re: Kent Swafford]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1940
Loc: Suffolk, England
I was asking about equal division of the octave. Was Levitan perhaps referring to tuning model(s) of ET with pure octaves?

Either way, I had understood you to be saying forget about iH and tune each piano with a target set of beat rates in mind.


Edited by Withindale (05/26/14 07:58 AM)
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2281186 - 05/26/14 09:53 AM Re: CHAS for Dummies [Re: Withindale]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
it is may be possibe when referring to pure ratios or pure balance of ratios.

Not proved, but as some intervals, as the 12th or the mix 12 th 15th, are "absorbing much iH" (gives a larger leeway than octave tuning, I have wondered about that.

COrdier pure 5th was told by fixed beat rates, if memory serves.

Now I also believe that this type of foundation, is slightly compromised by extremes iH or unevenness in iH progression (or for musicality, simply)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2281303 - 05/26/14 03:26 PM Re: CHAS for Dummies [Re: Withindale]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: Withindale
I was asking about equal division of the octave. Was Levitan perhaps referring to tuning model(s) of ET with pure octaves?

Either way, I had understood you to be saying forget about iH and tune each piano with a target set of beat rates in mind.


Yes, I assume that Levitan was talking about ET with pure octaves.

But when we actually tune, to the extent that we stretch, we are not really tuning ET with pure octaves and so I believe we should adjust our target beat rates to that of the ET we are actually trying to execute, be it CHAS (pure 26th?), pure 12th, pure 5th, maybe even pure 19th, or "ET with 2-cents-expanded-octaves", etc.

I don't believe the beat rates of the various ETs have been studied sufficiently.

Top
#2281746 - 05/27/14 10:45 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Kent Swafford
Originally Posted By: UnrightTooner
All:

Stacked, pure 4:2 octaves will always result in a wide 4:1 double octave. The higher the iH, the wider the resulting 4:1 double octave. And in very high iH pianos the 3:1 12th will also be wide when pure 4:2 octaves are tuned.

I find it is best to tune the octaves just above the break on spinets and short consoles narrow of 4:2. But then that is the natural result from tuning pure 12ths and prioritizing the 5ths across the break(s).


This is a very interesting set of statements that took a good bit of time to think through.

Actually, stacked pure 4:2 octaves will not necessarily result in a wide 4:1 double octave. One only need find one exception to your rule to prove it false, but I have several.

1. In a zero-inharmonicity situation, stacked pure 4:2 octaves will form a pure 4:1 octave.

Both Al Sanderson and Daniel Levitan teach about piano scales with "ideal" inharmonicity.

"In fact, whenever the inharmonicity of the lower note of an octave is 1/4 that of the upper note, the inharmonicity of the virtual 1/2-strings of the lower note exactly match the inharmonicity of the whole string of the upper note, and there is no inharmonicity in the octave. The experience of tuning such an octave is indistinguishable from the experience of tuning an octave beween two strings with no inharmonicity at all."

-- Daniel Levitan

2. With ideal inharmonicity as described above, then, stacked pure 4:2 octaves will also form a pure 4:1 double octave, just as if there were zero inharmonicity.

3. All that is required for 2 stacked pure 4:2 octaves to form a _narrow_ 4:1 double octave, is for the measurement in cents between the 2nd and 4th partials of the middle note of the stack to be less than the measurement between the 1st and second partials of the uppermost note of the 3. Such cannot be particularly unusual; it only means that the inharmonicity is increasing as you go up the scale more than the inharmonicity is increasing as you go up the partial series. Or you could say that the inharmonicity is increasing more than the ideal amount as you go up the scale.



Mr. Swafford:

Thanks for the reply.

I guess I should have said that I am talking about a piano with iH.

OK, I took a look at the iH being one quarter the value of the note an octave above, which is another way of saying the iH doubles every 6 semitones. I used A4 having an iH of 0.74 (about like a Baldwin R), A3 having an iH of 0.185, and A5 having an iH 2.96. With stacked, pure 4:2 octaves I get a 4:1 double octave that is narrow at -1.0 bps. A3 was -0.05 cents, A5 was at +0.05 cents.

The iH (logarithmic) slope on a concert grand will be much flatter, doubling only about every 8 semitones. (This is mentioned in Young's paper on iH of piano strings.) The example of iH doubling every 6 semitones represents a piano with an iH (logarithimc) slope that is steeper than even a concert grand.

I played around a little and found that if the iH is tripled, starting with A4 being 0.74, then stacked, pure 4:2s will result in a pure 4:1. But when continuing this to A6 the 4:1 becomes wide. So it seems that it is not so simple, but then I am using Tunelab's empirical, tabulated values rather than Young's theroetic values. But it is a moot point. This would still be a steeper iH curve than even a concert grand. (The steeper the slope, the less the difference in octaves, the less aurally perceivable effect that iH has.)

Glad you questioned me on this. I stand by what I said, with a small clarification:

"Stacked, pure 4:2 octaves will always result in a wide 4:1 double octave on an actual acoustic piano."
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2281779 - 05/27/14 12:05 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
I do not believe the slope differs so much from one piano to the next in the octaves 5-6-7.

Concert pianos can be a little apart but with 48>52 mm for C88, the slope going to 0.6-0.7 at A49 is generally very similar on small and large pianos.

the progression of lengths from A88 to A49 is following different sequences depending of the model/school used.
However the differences are not large with A 49 +- 400 mm and C88 as said above ranging from 48 to 52 (often the last octave is lengthened to obtain 52 mm, higher tension hence better solicitation in high treble (just under the danger zone).

Let me know if you wish some readings on the matter.
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2281781 - 05/27/14 12:07 PM Re: CHAS for Dummies [Re: UnrightTooner]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
UnrightTooner posted:

"Glad you questioned me on this. I stand by what I said..."

As do I, but with no clarification needed, as far as I know. 8^)

Top
#2281794 - 05/27/14 12:46 PM Re: CHAS for Dummies [Re: Kent Swafford]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Kent Swafford
UnrightTooner posted:

"Glad you questioned me on this. I stand by what I said..."

As do I, but with no clarification needed, as far as I know. 8^)


Fair enough.

Now to what I consider is the real application. When there is a larger difference between octave types (due to iH, of course) the 4:1s will be wider when stacked 4:2s are tuned. The 3:1s can also become wide. So if you do not want wide 3:1s and/or 4:1s that are too wide, the answer is to tune at least some octaves narrow of 4:2 on pianos when there is a large difference between octave types. This, of course, is the case in smaller pianos especially just above the break.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2281814 - 05/27/14 01:52 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7573
Loc: France
Definition of the plain strings lengths

Since all parameters listed influence each other the impact of each modification to the previously specified data must be checked.
Therefore it is important to organize all the influences and proceed in a sensible order.

You can begin to set the aspect ratio of the octave for the whole plain wire section.

Siegfried Hansing has proposed a method that is still used today in many ways :

Instead of doubling the length of strings per octave (2:1 scale), the string is truncated to the lower octave by 1/16 from twice the length, so that a Octave ratio of 1,875:1 results

The lnharmonicity ratio between the two tones in the octave is then with the same tensile force approx. 1:2.7. (For a 2:1 - Scale the ratio would be 1:4.)

Whether arising from Hansings process, scale values actually correspond to the general taste, is by no means proven.

Hansings theoretical derivation of his method has proved to be unfounded, but this also does not speak absolutely against it.

(1:12 root 2) Ulrich Laible has proposed lnharmonicity from octave to octave of 1/12root 2 , which requires a slightly different “aspect” (length) ratio.

Ultimately, it is of course only necessary to obtain a desired sonic result. On account of a lot of experiences, a possibly unusual appearing ratio of the octaves of 1:1,91 is suggested.

With c ' ( c88) with a length of 49 mm arises for a ' (A49 -) in length of 401 mm.

Such short c ' appears as well unusual as the "long" octave relation. However, there is no plausible explanation (statement), why the so-called "standard length" of 52 mms should be for c5 the only correct one.

The relatively short length standard in the treble in conjunction with a small reduction has the advantage of giving in the high registers a fairly large lnharmonicity, that lower much more than usually when going down the mediums to the break.

The former provides the desired spreading of the harmonic series in the treble and therefore comes to meet a need of the hearing, while the latter provides a good tunable and sonically unobtrusive transition to the bass, where because of the great significance of the difference of tones between the individual tones for a clear pitch perception such spread is not desired.

Another advantage of the relatively short scale in the treble is that they transfer of string vibration to the bridge ensures a better energy, what is still to come back later.

If you can run string lengths through the plain wire string region with geometric series with a constant ratio,it is regarded as good manners, then it results in the proposed octave
ratio of 1: 1.91 for the aspect ratio of a semitone :
1:1,0554057 or 1 12th root of 1.91.

But giving up somewhere in the scale lengths with the geometric series from to the scale,

then automatically also there is an error in lnharmonicity progression or in the uniformity of tensile result, possibly because of a rotten compromise, or two.

Not infrequently, a flatter course curve is selected in the treble, which can end with the familiar c5 (88) with 52 mm then, or if not a "length belly" is taken in the octave 5 to increase the string stretch in favor of better tuning stability at this point .

Whether this desired effect ever comes to realization, is by no means certain, however, the neglect of lnharmonicity course mean that no beatless double octaves can be achieved then.

One can only speculate how scales with such inconsistencies in individual cases may arrive. Is it the will of the designer's sound design, the deliberate nature of a manufactured product or of blind chance? A tonally or otherwise motivated decision for an unusually short or unusually long scale is basically hardly objectionable. As long as it revolves around questions of taste, a specialized theory-based criticism is ineffective.

Why should be of one’s dream be the other nightmare ? But if, as is all too rarely seen even in the so-called top-class encounter some bugs and inconsistencies within a scale, then one can no longer be dismissed as a matter of taste.. Regardless of the tonal desires that stand behind a scale, in any case is a uniform scale with regard to the progression of lnharmonicity values is indispensable.
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


Top
#2281832 - 05/27/14 02:34 PM Re: CHAS for Dummies [Re: UnrightTooner]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: UnrightTooner
Originally Posted By: Kent Swafford
UnrightTooner posted:

"Glad you questioned me on this. I stand by what I said..."

As do I, but with no clarification needed, as far as I know. 8^)


Fair enough.

Now to what I consider is the real application. When there is a larger difference between octave types (due to iH, of course) the 4:1s will be wider when stacked 4:2s are tuned. The 3:1s can also become wide. So if you do not want wide 3:1s and/or 4:1s that are too wide, the answer is to tune at least some octaves narrow of 4:2 on pianos when there is a large difference between octave types. This, of course, is the case in smaller pianos especially just above the break.


Most of this last response of yours is in some instances correct, maybe even mostly correct; however, it is still an example of a "rule of thumb" that is sometimes wrong. I wouldn't have claimed that a stack of pure 4:2 octaves could result in a narrow 4:1 if I hadn't actually gone to a real piano and measured just such an example. It wasn't at all hard to find! Funny you should mention the tenor just above the break. Think about the large rise in inharmonicity between wound strings in the tenor/upper bass and a plain-wire string an octave above...

Top
#2281871 - 05/27/14 04:06 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford
Originally Posted By: UnrightTooner
Originally Posted By: Kent Swafford
UnrightTooner posted:

"Glad you questioned me on this. I stand by what I said..."

As do I, but with no clarification needed, as far as I know. 8^)


Fair enough.

Now to what I consider is the real application. When there is a larger difference between octave types (due to iH, of course) the 4:1s will be wider when stacked 4:2s are tuned. The 3:1s can also become wide. So if you do not want wide 3:1s and/or 4:1s that are too wide, the answer is to tune at least some octaves narrow of 4:2 on pianos when there is a large difference between octave types. This, of course, is the case in smaller pianos especially just above the break.


Most of this last response of yours is in some instances correct, maybe even mostly correct; however, it is still an example of a "rule of thumb" that is sometimes wrong. I wouldn't have claimed that a stack of pure 4:2 octaves could result in a narrow 4:1 if I hadn't actually gone to a real piano and measured just such an example. It wasn't at all hard to find! Funny you should mention the tenor just above the break. Think about the large rise in inharmonicity between wound strings in the tenor/upper bass and a plain-wire string an octave above...

This can easily be checked in tunelab. Select 4:2 and generate a tuning curve for that, then display 4:1.

I tried on about 10 piano's in my database with one getting a narrow 4:1, the rest were wide.

Correction: all of them have 4:1 wide.


Kees


Edited by DoelKees (05/27/14 04:47 PM)

Top
#2281919 - 05/27/14 05:43 PM Re: CHAS for Dummies [Re: DoelKees]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: DoelKees


This can easily be checked in tunelab. Select 4:2 and generate a tuning curve for that, then display 4:1.

I tried on about 10 piano's in my database with one getting a narrow 4:1, the rest were wide.

Correction: all of them have 4:1 wide.


Kees


What you are seeing there in TuneLab is a calculated tuning curve. It is in no way an exact representation of the results of measuring each interval individually. I would say this is an example of a rule of thumb being built into a tuning calculator. I'm sure it works great -- except for when it doesn't.

I have suggested a place where it might be likely to be able to tune stacked pure 4:2 octaves and still yield a contracted 4:1. The place I suggested is an octave above and below the wound strings in the tenor on the long bridge.

Try it!

Top
#2281945 - 05/27/14 06:52 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
gynnis Offline
Full Member

Registered: 02/16/14
Posts: 122
Loc: Florida, Connecticut
I think a lot of issues arrive when one transitions from one part of the piano to another, i.e. single wound strings to double wound strings, double wound strings to wire strings across the break, and wire strings under the capo. Whatever the theoretical iH, these physical differences in the piano make radical changes to the sound of the strings. Sometimes designers want to exploit this difference to color the sound in different parts of the piano.
_________________________
Seiler 206, Chickering 145, Estey 2 manual reed organ, Fudge clavichord, Zuckerman single harpsichord, Technics P-30, Roland RD-100.

Top
#2281961 - 05/27/14 07:26 PM Re: CHAS for Dummies [Re: Kent Swafford]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Kent Swafford
.....

I have suggested a place where it might be likely to be able to tune stacked pure 4:2 octaves and still yield a contracted 4:1. The place I suggested is an octave above and below the wound strings in the tenor on the long bridge.

Try it!


Ah, well, if the middle note is the highest wound string I could see the iH slope of the upper octave being steep enough and the iH value of the lower octave being low enough for this to happen. The other possibility is a wild partial or two from the wound strings. I think you would need to have a few instances of this happening within a few semitones to rule out a fluke instead of the scaling of an actual piano.

But... this is still getting away from what I am saying about what happens when octaves in a flatter part of an iH curve are tuned 4:2. The 3:1 can be wide and/or the 4:1 can be too wide. When the effects of iH are strong, octaves narrower than 4:2 are called for.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2282009 - 05/27/14 09:22 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Originally Posted By: Kent Swafford
Originally Posted By: DoelKees


This can easily be checked in tunelab. Select 4:2 and generate a tuning curve for that, then display 4:1.

I tried on about 10 piano's in my database with one getting a narrow 4:1, the rest were wide.

Correction: all of them have 4:1 wide.


Kees


What you are seeing there in TuneLab is a calculated tuning curve. It is in no way an exact representation of the results of measuring each interval individually. I would say this is an example of a rule of thumb being built into a tuning calculator. I'm sure it works great -- except for when it doesn't.

I have suggested a place where it might be likely to be able to tune stacked pure 4:2 octaves and still yield a contracted 4:1. The place I suggested is an octave above and below the wound strings in the tenor on the long bridge.

Try it!

Well I didn't look that low. Doesn't one usually tune more like 6:3 octaves in that range anyways? I guess I'm not getting why it is interesting to figure out the effect of 4:2 octaves on the 4:1 in that range.

If you don't trust ETD's maybe you can post an audio of a narrow 4:1 with stacked 4:2's?

Kees

Top
#2282164 - 05/28/14 07:55 AM Re: CHAS for Dummies [Re: DoelKees]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
"transition issues"

"strong effects of iH"

"6:3 octaves in that range"

My interest is going beyond what I am calling the rules of thumb and learning the issues that underly the rules.

I don't wish to be taught to tune narrow 4:2 octaves in the treble; I want to be taught that narrow 4:2 octaves might be appropriate to avoid tuning the 4:1 too wide, for example.

I do not wish to be taught to tune 6:3 octaves in the bass; I wish to know that tuning 6:3 octaves in the bass might avoid 4:1 octaves that are too _narrow_, among other reasons.

And so on. Unless one knows the underlying reasons for all the "rules", I don't see how one can deal with the scale transition areas, or pianos with unusual scales, etc.

I don't like "tuning rules"; they don't alway work out, and when I "correct" them in certain situations, other tuners jump to the conclusion that I just don't know the rules. Here is an example. There is a tuning rule that says the larger the piano, the higher the partial to be used in tuning the low bass. Not necessarily. The Bosendorfer Imperial is an exception. In tuning the B'dorf' bass with RCT, the rule says use partial 12. What isn't known is that when tuning with the higher partials in the low bass with RCT, the tuning curve assumes a pure 12:6. But the inharmonicity of the B'dorf' is so low that the small amount of artificial stretch introduced when tuning with the 6th partial may actually tune the low bass flatter with the 6th partial than with the 12th. _And_ using the 6th partial in the low bass makes tuning the "zero" octave dead simple. You tune A0 from the 6th partial, then hit the octave up button, and tune G#0 at its 12th partial by using the RCT reading for G#1 at the sixth partial.

The "rule" take only a few words to explain, the exception takes many words to explain, but results in a better tuning. Take your pick; I've taken mine. 8^)

Top
#2282380 - 05/28/14 04:35 PM Re: CHAS for Dummies [Re: Kent Swafford]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1724
Loc: Vancouver, Canada
Kent:

Thanks for that clarification, now I understand where you're coming from, or rather where you're going. smile

I thought the reason for not tuning 4:2 was a) those partials too high to be relevant b) if you'd tune 4:2 you get too much stretch which results in particular in wide 4:1. I tried 4:2 all the way up once on my piano. Apart from breaking a string it didn't sound right.

I though the reason to focus more on 6:3 from say C3 on and down was that those partials are more audible than the 4:2 partials in that range.

Kees

Top
#2282405 - 05/28/14 05:29 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 626
Loc: Canberra, ACT, Australia
When I tune a piano I dont think anything whatsoever about particular X:Y octaves.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

Top
#2282614 - 05/29/14 07:42 AM Re: CHAS for Dummies [Re: Kent Swafford]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: Chris Leslie
When I tune a piano I dont think anything whatsoever about particular X:Y octaves.


OK, then what do you think about?

All:

This sort of thing often happens with tuning discussions. One tuner will say something like "Oh, I tune "x" way because it makes such and such happen." A response will be something like "But that is not what actually happens when you tune "x" way. My _________ (ears, calculation, ETD, instructor, manual, familiar spirit...) says otherwise." And somehow the source of this information is irrefutable. Then someone will chime in with "Who cares? The question is what does it sound like?" which takes the discussion in such a totally subjective direction that it becomes useless.

The problem is that we are human, social by nature, and naturally focus on who is right rather on what is true.

For example:

Originally Posted By: Kent Swafford
.....

I don't like "tuning rules"; they don't alway work out, and when I "correct" them in certain situations, other tuners jump to the conclusion that I just don't know the rules. Here is an example. There is a tuning rule that says the larger the piano, the higher the partial to be used in tuning the low bass. Not necessarily. The Bosendorfer Imperial is an exception. In tuning the B'dorf' bass with RCT, the rule says use partial 12. What isn't known is that when tuning with the higher partials in the low bass with RCT, the tuning curve assumes a pure 12:6. But the inharmonicity of the B'dorf' is so low that the small amount of artificial stretch introduced when tuning with the 6th partial may actually tune the low bass flatter with the 6th partial than with the 12th. _And_ using the 6th partial in the low bass makes tuning the "zero" octave dead simple. You tune A0 from the 6th partial, then hit the octave up button, and tune G#0 at its 12th partial by using the RCT reading for G#1 at the sixth partial.

The "rule" take only a few words to explain, the exception takes many words to explain, but results in a better tuning. Take your pick; I've taken mine. 8^)


Mr Swafford says he doesn't like tuning rules, and then goes into detail of how to use a particular procedure on a particular piano (that very few will actually tune) with a particular device by changing the way the device is intended to be used. It sounds like just changing one rule with an exceptional rule.

I really don't mean to pick on you, Mr. Swafford. I just don't know what to do with this type of post, yours just being the latest example.

Are we making the ETD happy, the piano sound a certain way, defeating one rule with an exceptional rule thereby inviting a super-exceptional rule, or what. ?!?!?!

... I'm just a little frustrated, mad at myself for having an unreasonable expectation that this discussion would be worthwhile ...
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2282615 - 05/29/14 07:52 AM Re: CHAS for Dummies [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4940
Loc: Bradford County, PA
Originally Posted By: DoelKees
...

I though the reason to focus more on 6:3 from say C3 on and down was that those partials are more audible than the 4:2 partials in that range.

Kees



Oh, not at all. "The reason to focus more on 6:3 from say C3 on and down" is to keep the 12ths pure! wink
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#2282648 - 05/29/14 09:09 AM Re: CHAS for Dummies [Re: UnrightTooner]
Kent Swafford Offline
Full Member

Registered: 06/06/07
Posts: 80
Loc: Kansas City
Originally Posted By: UnrightTooner


Are we making the ETD happy, the piano sound a certain way, defeating one rule with an exceptional rule thereby inviting a super-exceptional rule, or what. ?!?!?!

... I'm just a little frustrated, mad at myself for having an unreasonable expectation that this discussion would be worthwhile ...


All of the above? 8^)

Sorry for your frustration. I am thrilled to be able to take part in this discussion. I am very pleased by what I have been able to learn here.

I don't much understand how the conversation should go other than; I and/or someone else states what they think they know and others respond. Learning ensues. But learning, especially about a subject as complex as piano tuning, is inherently messy, don't you think? I do happen to believe that we tend to try to over-simplify.

I originally came here to try out an alternative way of describing CHAS, because I thought it was a truth others might find valuable. It was an attempt to establish "what is true" about CHAS, a subject that I have found fascinating for years, but had been frustrated in my attempts to learn about and discuss.

I love your suggestion that tuning the 6:3 in the bass is about keeping the 12ths pure. I'll resist the temptation to comment about the limitations to that. LOL

I mean, even though no one has a lock on knowing what is true, _someone_ must first voice the truth. Why suggest that doing so is about _who_ is right?

I am right. And I am wrong. Both are true of you, too!

Top
Page 1 of 10 1 2 3 ... 9 10 >

Moderator:  Piano World 
What's Hot!!
HOW TO POST PICTURES on the Piano Forums
-------------------
Sharing is Caring!
About the Buttons
-------------------
Forums Rules & Help
-------------------
ADVERTISE
on Piano World

The world's most popular piano web site.
-------------------
PIANO BOOKS
Interesting books about the piano, pianists, piano history, biographies, memoirs and more!
(ad) HAILUN Pianos
Hailun Pianos - Click for More
ad (Casio)
Celviano by Casio Rebate
Ad (Seiler/Knabe)
Seiler Pianos
Sheet Music
(PW is an affiliate)
Sheet Music Plus Featured Sale
(125ad) Dampp Chaser
Dampp Chaser Piano Life Saver
(ad) Lindeblad Piano
Lindeblad Piano Restoration
New Topics - Multiple Forums
Mason & Hamlin- The Skinny?
by Miguel Rey
09/23/14 09:55 PM
crazy fingers, or mind of their own
by Barry1963
09/23/14 09:52 PM
Request opinion YC G-175
by ivoryguy36
09/23/14 08:31 PM
"Break Free" by Ariana Grande on Piano
by Zach Evans
09/23/14 06:37 PM
V-Grand delivery on Friday!
by TonyB
09/23/14 06:36 PM
Who's Online
122 registered (accordeur, ando, AEMontoya, 31 invisible), 1401 Guests and 13 Spiders online.
Key: Admin, Global Mod, Mod
Forum Stats
76297 Members
42 Forums
157717 Topics
2316684 Posts

Max Online: 15252 @ 03/21/10 11:39 PM
(ads by Google)

Visit our online store for gifts for music lovers

 
Help keep the forums up and running with a donation, any amount is appreciated!
Or by becoming a Subscribing member! Thank-you.
Donate   Subscribe
 
Our Piano Related Classified Ads
|
Dealers | Tuners | Lessons | Movers | Restorations | Pianos For Sale | Sell Your Piano |

Advertise on Piano World
| Subscribe | Piano World | PianoSupplies.com | Advertise on Piano World | Donate | Link to Us | Classifieds |
| |Contact | Privacy | Legal | About Us | Site Map | Free Newsletter | Press Room |


copyright 1997 - 2014 Piano World ® all rights reserved
No part of this site may be reproduced without prior written permission