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#2194834 - 12/09/13 02:32 AM CHAS for Dummies
pinkfloydhomer Offline
Full Member

Registered: 03/07/08
Posts: 175
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.

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#2194862 - 12/09/13 04:43 AM Re: CHAS for Dummies [Re: pinkfloydhomer]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1922
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)

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

Registered: 11/13/08
Posts: 4908
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?

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

Registered: 08/13/09
Posts: 189
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

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#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: 1922
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)

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

Registered: 03/14/08
Posts: 7223
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.
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Isaac OLEG - http://picasaweb.google.fr/PianoOleg pro

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

Registered: 05/01/10
Posts: 1653
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

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

Registered: 02/09/11
Posts: 1922
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)

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

Registered: 03/07/08
Posts: 175
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.

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

Registered: 05/01/10
Posts: 1653
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

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

Registered: 05/01/10
Posts: 1653
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

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

Registered: 02/09/11
Posts: 1922
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)

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

Registered: 03/26/11
Posts: 405
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)
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#2195008 - 12/09/13 01:12 PM Re: CHAS for Dummies [Re: Withindale]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1653
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

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

Registered: 11/13/08
Posts: 4908
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?

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

Registered: 03/07/08
Posts: 175
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.

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

Registered: 02/09/11
Posts: 1922
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)

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

Registered: 05/01/10
Posts: 1653
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

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

Registered: 03/26/11
Posts: 405
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.

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#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: 556
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

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#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.
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Phil Dickson
The Cycling Piano Tuner

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#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: 1653
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

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

Registered: 03/26/11
Posts: 405
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.

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#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

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

Registered: 03/26/11
Posts: 405
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.

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#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: 1653
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

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

Registered: 04/26/10
Posts: 367
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?

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#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.
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Phil Dickson
The Cycling Piano Tuner

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

Registered: 03/26/11
Posts: 405
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)
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#2195761 - 12/10/13 08:07 PM Re: CHAS for Dummies [Re: pinkfloydhomer]
erichlof Offline
Full Member

Registered: 04/26/10
Posts: 367
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

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