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!

Gifts and supplies for the musician
SEARCH
the Forums & Piano World

This custom search works much better than the built in one and allows searching older posts.
Ad (Piano Sing)
How to Make Your Piano Sing
(ad) Pearl River
Pearl River Pianos
(ad 125) Sweetwater - Digital Keyboards & Other Gear
Digital Pianos at Sweetwater
(ad) Pianoteq
(ad) P B Guide
Acoustic & Digital Piano Guide
Who's Online
115 registered (anotherscott, accordeur, ando, Alexander Borro, 36251, 32 invisible), 1614 Guests and 17 Spiders online.
Key: Admin, Global Mod, Mod
Quick Links to Useful Piano & Music Resources
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 & Music Accessories
*Music School Listings
* 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
(ad) Estonia Piano
Estonia Pianos
Page 5 of 7 < 1 2 3 4 5 6 7 >
Topic Options
#1666707 - 04/26/11 07:30 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Folks:

I decided to find something out for myself. Yesterday on a customer’s piano with a friendly pinblock, I tuned Dr. White's sequence (circle of fifths) without any RBI checks or retuning previous intervals. The F-F octave ended up as a pure 4:2. The only note that needed adjusting for proper RBI progression was D#4. It must have been poor pin setting towards the end of the sequence because neither G#3 nor A#3 needed adjusting.

So now what? I guess I have been using the RBI checks as a crutch.

If you think I am lying, that’s OK. I would think the same thing.

Realizing that I can do this bothers me in ways that would be complicated to explain. I slept poorly last night. I think I will take a break from posting for a few days and consider the implications to Pride and Compassion. I am not sure the best way for me to post about tuning now.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
(ad PTG 757) The Value of PTG Membership
The Value of a PTG Membership
#1666712 - 04/26/11 07:42 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
Ron Voy Offline
Full Member

Registered: 02/16/11
Posts: 37
Originally Posted By: UnrightTooner
Folks:

I decided to find something out for myself. Yesterday on a customer’s piano with a friendly pinblock, I tuned Dr. White's sequence (circle of fifths) without any RBI checks or retuning previous intervals. The F-F octave ended up as a pure 4:2. The only note that needed adjusting for proper RBI progression was D#4. It must have been poor pin setting towards the end of the sequence because neither G#3 nor A#3 needed adjusting.

So now what? I guess I have been using the RBI checks as a crutch.

If you think I am lying, that’s OK. I would think the same thing.

Realizing that I can do this bothers me in ways that would be complicated to explain. I slept poorly last night. I think I will take a break from posting for a few days and consider the implications to Pride and Compassion. I am not sure the best way for me to post about tuning now.


The tuner teaching me, does exactly that and does it well, based on 35 years of practical experience, which makes it so difficult to learn from!

Top
#1666733 - 04/26/11 08:35 AM Re: Tuning Circle of Fifths [Re: Gadzar]
Emmery Offline
2000 Post Club Member

Registered: 04/02/08
Posts: 2481
Loc: Niagara Region, On. Canada
Originally Posted By: Gadzar
Unright,

Thank you, but I am not interested in talking with you as you strive to "control" people by making them getting upset.

For all who may be interested in what I am talking about, here is the thread:

How to "control" people on the internet

Or this other one:

How to "get fun" at the expense of others

Bye.



With all due regards Gadzar, his statement was a mere observation of human nature in some people, not a proclimation of his intentions. I've read many of Jeff's postings and don't really think he's trying to control anyone into becoming a Patty Hurst-like desciple of Braide White. Why all the paranoia?


Edited by Emmery (04/26/11 08:36 AM)
_________________________
Piano Technician
George Brown College /85
Niagara Region

Top
#1666855 - 04/26/11 12:06 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Happy Birthday Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Kees,

When I began to tune the CM3, I used to follow the instructions given by Randy Potter in his course of piano technology. But they weren't clear enough to me at how to tune F3. A sort of try and error procedure.

Then I've found the article of Bill Bremmer about tuning the midrange. I read it carefully and I followed his instructions step by step. And I discovered the correct way of setting the CM3s.

First of all, he explains exactly how to tune F3, which was not obvious in other documents I've read before. And secondly, the tuning of C#4 is a key step for the success of the CM3 setting.

You can start puting F3 where you hear a nice tempered M3. And it is the piano who tells you if F3 is sharp or flat. The way you tune C#4 is key in order to know how F3 must be retuned.

Before reading the Bremmer's article, I used to tune F3 as a 7 bps M3, then F4, and then I tuned C#4 by puting it in the middle between A3 and F4, striving to temper equally both M3s A3-C#4 and C#4-F4. That is an error!

If you do this, things smooth out, and you have a hard time to verify the even progression of M3s, as you already have smoothed the progression between A3-C#4 and C#4-F4.

So it is hard to say if F3 should be corrected and in what direction. F4-A4 is so fast that it helps only a little. And you finish with an acuraty of about 1 to 2 cents.

The point is to tune C#4 hearing the beat rate of A3-C#4 and tuning a 5:4 ratio from F3-A3. Do not hear at C#4-F4 when you are tuning C#4. Only tune a 5:4 ratio between F3-A3 and A3-C#4. Do not cheat, tune the 4:5 ratio!

How?

The speed of F3-A3 is at the limit of what I can reproduce with an alternating movement of my tonge between my teeth. And I can switch from a 4 ticks to the beat to 5 ticks to the beat. So it is easy to find the correct ratio. You can start practicing at a lower speed first, switching from 4 to 5 beats, and then at tempo (at about 7 bps). If your tonge is not fast enough you can play it mentally. Anyway there will always be a way for you to find the correct ratio. Everyone has his own means. Claping hands every 4 beats and every 5 beats, etc...

The trick is to find the correct rythm 4 to 5.

Once you have tuned C#4 in this way you can now check what the beat rate is for C#4-F4. If it is slow you have to raise F3 and if it is fast then you must lower F3.

When you have it right you check the whole set from F3 to A4, and make any needed adjustments, but chances are you have it already right.

The key here is to not put C#4 in the middle of A3 and F4, but try to tune the 5:4 ratio between F3-A3 and A3-C#4.

When I understood this, then my accuraty went to half a cent or even better.

And yes of course, there are pianos where F4-A4 is hard to hear.

My Petrof, for example, has a weakness in F3-A3 which is hard to hear, while F4-A4 is clearly discerned.

Even voicing can affect what you hear from M3s as the relative strength of partials is changed.




Edited by Gadzar (04/26/11 12:26 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#1666872 - 04/26/11 12:44 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Happy Birthday Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
One more point.

In piano tuning there are no magic numbers!

The 5:4 ratio is not a magic number (of 1.25), but an approximation. It will change from piano to piano depending on it's scaling.

Once you have tuned C#4 to have a 4:5 ratio between the beat rates of F3-A3 and A3-C#4 you check C#4-F4, and you retune F3, F4 and C#4 until it is too in the 4:5 ratio.

Now, you finally have to check F4-A4. Why? Because the correct ratio of the CM3s for this piano can be other than 4:5. You can find that F4-A4 is faster or slower than you have expected, and then you have to do some adjustments in the tuning of F3.

The theoretical value of the CM3s ratio is near 1.26 but the iH of the piano changes this ratio all along the scale. However it can be considered constant in the span of the temperament octave, with a little error.

So tuning with a 4:5 ratio will put you very near, and you'll have to do only some little adjustments to have it right.




Edited by Gadzar (04/26/11 12:51 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#1666879 - 04/26/11 12:51 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Thanks Gadzar, indeed I never tried to set the 5:4 beat ratio accurately.
I can do the tongue movement up to 12bps (a left over from the days I was playing baroque concerto's on recorder). I'm going to work on it that way.

Kees

Top
#1666880 - 04/26/11 12:53 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Happy Birthday Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
thumb

Please let me know if your accuraty gets any better.



Edited by Gadzar (04/26/11 01:20 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#1666900 - 04/26/11 01:21 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
Another interesting thing I noticed, when F3-A3 is tuned right and you tune A3-C#4 for the same beatrate as F3-A3, C#4-F4 and F4-A4 beat almost the same, with C#4-F4 beating 0,6 bps slower than F4-A4. The beatrates would be 6,9 6,9 13,25 and 13,85. If you tune F3-A3 less than 6,9 bps and make A3-C#4 the same, C#4-F4 will beat faster than F4-A4. For example if F3-A3 is 6,5, the others are 6,5 14,475 and 13, but if you tune F3-A3 7,5 bps, the others are 7,5 11,625 and 15.

So you can check the accuracy of F3 by tuning the first two contiguous thirds equal beating and if F3 is right the other two should beat roughly the same, with the first of the two beating 0,6 bps slower.


Edited by partistic (04/26/11 01:26 PM)

Top
#1666922 - 04/26/11 01:50 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Happy Birthday Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
That´s very interesting, this is in fact a way of testing F3 for doing a first approximation of near 1 cent!

For F3 tuned at -0.5 cents we have:

F3-A3: 7.2 bps
A3-C#4: 7.2 bps
C#4-F4: 12.9 bps
F4-A4: 13.9 bps

For F3 tuned at + 0.5cents we have:

F3-A3: 6.7 bps
A3-C#4: 6.7 bps
C#4-F4: 13.6 bps
F4-A4: 13.9 bps

But for F3 tuned at + 1 cent we have inverted CM3s:

F3-A3: 7.4 bps
A3-C#4: 7.4 bps
C#4-F4: 13.88 bps
F4-A4: 13.86 bps

In order to have inverted CM3s the error in F3 must be greater than +1 cent.



Edited by Gadzar (04/26/11 01:52 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#1667363 - 04/27/11 09:34 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
I think you made an error somewhere, or took into account inharmonicity or some other variables, because the F4-A4 should beat twice as fast as F3-A3 if we forget inharmonicity.

Here are the numbers I get by inserting the beatrates for the first two thirds:

F3-A3: 7,2 bps
A3-C#4: 7,2 bps
C#4-F4: 12,5 bps
F4-A4: 14,4 bps

And

F3-A3: 6,7 bps
A3-C#4: 6,7 bps
C#4-F4: 13,9 bps
F4-A4: 13,4 bps

Beatrates when F3 is correct:

F3-A3: 6,9 bps
A3-C#4: 6,9 bps
C#4-F4: 13,3 bps
F4-A4: 13,9 bps

I haven't tried this in practice and cannot say how hard it is to determine whether one third is beating 0,5 bps faster or if they would sound the same at almost 14 bps, but it seems if the inversion of the CM3s beating that fast can be heard you could set the F3 with 0,5 cent accuracy using this without having to guess anything.

Top
#1667407 - 04/27/11 11:12 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
Happy Birthday Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
You are right, I made an error.

In fact it is as you say: For F3 tuned at + 0.5 cents CM3s have already inverted with C#4-F4 = 14.0 bps and F4-A4 = 13.4 bps.

So we can detect a deviation of less than + 0.5 cents in the tuning of F3.

I've not tried this technique neither but I can anticipate it's easy to discern if one of the CM3s is faster and if they are inverted or equal beating.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#1667485 - 04/27/11 01:51 PM Re: Tuning Circle of Fifths [Re: Gadzar]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Originally Posted By: Gadzar
You are right, I made an error.

In fact it is as you say: For F3 tuned at + 0.5 cents CM3s have already inverted with C#4-F4 = 14.0 bps and F4-A4 = 13.4 bps.

So we can detect a deviation of less than + 0.5 cents in the tuning of F3.

I've not tried this technique neither but I can anticipate it's easy to discern if one of the CM3s is faster and if they are inverted or equal beating.



Thank you Rafael,

This had always been my sense of it although I was unable to prove it mathematically. If properly executed with all five notes from F3-A4, the greatest possible error would be within 1/2 cent.

Incidentally, the first piano I tuned on Monday was a Steinway model A. I tried my latest suggestion. I fist tune A4, then F4 to it. There is a very small margin between a beat that is easily heard (too slow) and one that is too fast to discern. I placed F4 at the spot where it can just barely be heard clearly.

I then tune F3 to F4 and filled in C#4. I don't really think so much in terms of 4:5 but merely what I call a "small difference" (not the smallest difference that can be discerned but a small difference). The sequence revealed a perfectly even progression on the very first attempt.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

Top
#1667504 - 04/27/11 02:27 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Happy Birthday Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Chapeau!

I guess you already have the ear of how a M3 should sound on a S&S. I seldom have the opportunity to tune such a nice piano.

When I set the CM3s, usually it takes me from 2 to 3 tunings of F3: my initial estimation and then a second tuning after hearing the progression, sometimes I have to retouch F3 if F4-A4 doesn't fit the rest.

I've never tuned F4 to A4. I'll give it a try.






Edited by Gadzar (04/27/11 02:28 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

Top
#1667523 - 04/27/11 03:08 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Gadzar,

I while back, Patrick brought up an interesting point. While the beat rate of all Major thirds in ET is different, they are all of the same size and therefore the same quality sound. Perhaps the idea of tuning the F4-A4 M3 first would not work well for all people but it is worth giving it a try.

Some have said that they cannot hear the beats in that interval at all. Indeed, at some point, the coincident partials are too high and faint to be heard. In my writings, I have always said that the F4-A4 M3 is at or near the limit of discernibility. Normally, we would not listen to chromatic M3's this high in the scale.

However, for the A4 to be truly and exactly at pitch, we must work from that note. Therefore, the F4-A4 M3 must be correct. If one likes 4ths & 5ths, one can also tune D4 and E4 between A3 and A4 and make the resultant 4ths and 5ths be correctly proportionate.

To tune F4 as the first note after A4, sharpen or flatten F4 until you can hear a gentle beat, then flatten F4 until the sound becomes too fast, "sour" and indiscernible. Sharpen F4 again until you hear that moderate sound, not easily heard and barely discernible. Now, this may be no more accurate than guessing at the approximately 7 beats per second that the F3-A3 M3 should have but if the initial estimate is inaccurate, the rest of the sequence will show that.

Certainly, if one has F3-A3-C#4-F4-A4 with a reasonably even progression, no two exactly alike, no large differences, the two pairs of octaves, F3-A4 and A3-A4 are proven similar in width and D4 & E4 are tuned as proportionate 4ths & 5ths, one has fully half of the notes of the F3-F4 temperament octave already tuned plus one more outside note. How could anyone go very far astray with a framework like that?
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

Top
#1667896 - 04/28/11 08:14 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
Theoretically there can be an up to 3 cent error without reversing the beatrate progression of the contiguous thirds. But with a little practice I don't think I'd make an error of over 1 cent without noticing. With more practice it could become even more accurate.

The 0,5 cent error was for the other method of setting F3 by making F3-A3 and A3-C#4 beat the same and then the other two thirds should be almost the same, with C#4-F4 being 0,6 bps slower than F4-A4.

Top
#1667905 - 04/28/11 08:49 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: Ron Voy


The tuner teaching me, does exactly that and does it well, based on 35 years of practical experience, which makes it so difficult to learn from!


Ron:

I just skimmed through this entire Topic. It is obvious that you are not interested in CM3 sequences. Sorry that this Topic got hijacked and I apologize for my part in it.

I realize I have been “on the fence” about what 4th and 5th tuning is really all about. I had fallen for the trap of trying to beat someone at their own game. 4th and 5th tuning is not about making the RBIs progressive. It is about tuning properly tempered SBIs. RBIs can only go so far into helping this happen.

It would be like trying to be a good person by obeying all the rules rather than by developing good character. Obeying some rules shows poor character. And trying to explain what good character is, by putting forth a bunch of rules, is self-defeating. Likewise, if SBIs are properly tempered, the progression of RBIs is not an issue. It happens naturally. Just like a person with good character does not steal, unless it is to take something away that is meant to harm and probably many other reasons. (See what I mean about rules?) And RBIs should not be progressive when crossing a jump in scaling if the goal is to have SBIs properly tempered.

So putting aside RBIs, for now, how do you properly temper SBIs? It is pretty simple, really. In the temperament octave the 4ths should beat about 1 bps and the 5ths about 1/2bps. And by saying ”about” I do not mean that on some pianos it will be 1.2 bps for the 4ths and on others 2/5bps for the 5ths. I mean any 4th or 5th on any piano will be about these speeds in the temperament. Why? A number of reasons:

First, Inharmonicity is largely self-correcting when considering beatspeeds in the temperament, unless there is a jump in scaling. And a couple of tenths of bps on a SBI is very little change in pitch. It may not even be tunable depending on the pinblock, and won’t make a bit of difference in RBIs that are already properly progressive. RBIs are tempered 7 times as much as SBIs.

So what about RBIs and their checks? Let me quote Dr White again:

From page 85:

http://www.archive.org/stream/modernpianotunin00whit#page/84/mode/2up

Experience shows that it is easiest to tune by Octaves, Fifths and Fourths; by Fifths and Fourths for the octave of tones, usually F2-F3 chosen for the “bearings” or foundation work and by Octaves up and down thereafter. The other intervals involved are best used for testing the correctness of the work as it proceeds. (Bold added for emphasis.)

Of course we would now say F3-F4, the notation has changed. ”The other intervals involved are best used for testing the correctness of the work as it proceeds.” I now understand what this statement really means. Without getting into detail of the tests themselves, which Dr. White does later, let me explain the right and wrong way to use the RBIs as checks.

As the circle of fifths is constructed more and more RBIs become available. Each one gives an indication of how equal the temperament is. The first one only gives beatrate information, which is actually reliable despite iH. And if there is a question, simply go back and listen to the SBIs. If the 4ths are about 1bps and the 5ths are about ½ bps, continue on! That is the right way. The wrong way would be to adjust the 4ths and 5ths to obtain a theoretical beat speed for an RBI. If we do that, then we are letting the tail wag the dog.

The next RBI will give us two different beatrates to compare. Then later some beatrates will be the same. Then some beatrates will fall between two others. As the circle is formed it may be noticed, for example, that two beatrates that should be the same are not quite the same. It is then an easy thing to check the SBIs that formed those RBIs. If any seem a bit slower or faster than others, and bringing them in line with the others will make the RBIs beat closer together, then do so. If not, it is probably a due to a jump in scaling. If it is not a jump in scaling then perhaps you do not have a good feel for what a properly tempered SBI sounds like. This takes practice. But it is easy to recognize jumps in scaling.

A jump in scaling can be expected from one bridge to another, when going from wound to unwound strings on the same bridge, and when the number of strings per unison changes on the same bridge. Usually, major thirds will beat faster than expected when straddling a break and slower than expected above a break. Also if a break is much lower than it should be for the size of the piano, the lowest M3s above the break will beat slower than expected.

But there are exceptions. On the Kimball console, the M3s that straddle the wound/unwound break beat slower, not faster than expected when the SBIs are properly tempered. Kohler Campbell consoles have some surprises, too.

So then how to determine the correct beatspeeds for intervals that straddle or are near a jump in scaling? By tuning properly tempered SBIs to construct them. Don’t let the tail wag the dog!

OK, more about actually tuning properly tempered SBIs. It is challenging to play an SBI and say if it is properly tempered, although it is easy to play a series of them and tell which ones are different. Here is my suggestion for actually tuning SBIs. Start a bit below pitch so that the beat is easily heard. If both faster and slower beats are heard, lock onto the slower one. The faster one is from a set of higher partials and will lead you astray. Bring the pitch up with a smooth pull until it beats the proper speed and get this sound in your head! It is not just a beat speed it is also a tonal color. We are tempering intervals not just setting beatrates. It is this color difference that makes incorrectly tempered SBIs stick out more than the beatspeed. Now you are going to have to do whatever is necessary to actually leave this interval where it belongs. Usually some overshoot and then easing the pitch back down. But let’s not get into hammer technique. That’s a whole other subject.

Don’t know if this will help you, Ron. I hope it does. It helped me. I am now off the fence. I won’t fall for trying to beat someone at their own game in regards to 4th and 5th tuning. I am off the fence now. (Still have a couple splinters in interesting places, though wink )
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1668253 - 04/28/11 09:40 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Jeff: I tried a bit of 4th and 5th tuning.

A3 from fork (ETD actually). Then D4, G3 C4 F3. Now I check F3A3. It was too slow. So I adjust F3 so F3A3 beats at 7bps and go back and fix G3 C4 and D4 to all beat proportional.

Now why not set F3 right away at 7bps from A3 and then tweak G3 C4 and D4 to fit?

Kees

Top
#1668273 - 04/28/11 10:21 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner

So putting aside RBIs, for now, how do you properly temper SBIs? It is pretty simple, really. In the temperament octave the 4ths should beat about 1 bps and the 5ths about 1/2bps

I computed the error from blindly tuning 5ths 1/2 bps and 4ths 1 bps, using White's sequence. "Error" as compared to taking the F3F4 octave that would result from such a scheme and then dividing that (stretched) octave in 12 equal parts. All with zero inharmonicity. I get the following errors:

C 0.0
C# 0.9
D -0.2
D# 0.9
E -0.0
F 1.2
F# 2.0
G 0.8
G# 1.8
A 0.9
A# 2.1
B 1.3

Doing the same with a typical IH model doesn't change this much.

Not sure what to conclude. I guess what I'm after is some instruction on what to do if the RBI tests (e.g. steps 5 and 8 in his sequence) fail the test. Not that I mind figuring out what to do myself, but the RBI tests should come with some instruction on what to do if the test fails.

Kees

Top
#1668369 - 04/29/11 04:01 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
UnrightTooner, I wonder how big is the jump in scaling, does the IH double?. How much does the expected beatrate change and if you make the M3s beat correct, is there an obvious flaw in the fifths?

Top
#1668405 - 04/29/11 07:12 AM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Because then you are not
Originally Posted By: DoelKees
Jeff: I tried a bit of 4th and 5th tuning.

A3 from fork (ETD actually). Then D4, G3 C4 F3. Now I check F3A3. It was too slow. So I adjust F3 so F3A3 beats at 7bps and go back and fix G3 C4 and D4 to all beat proportional.

Now why not set F3 right away at 7bps from A3 and then tweak G3 C4 and D4 to fit?

Kees


Because then you are not creating a M3 by tuning 4ths and 5ths, you are fitting 4ths and 5ths into a M3. (The tail is wagging the dog.) But how do you know that the M3 was beating too slow? If it was way, way slow then your SBIs were way off. If it was only a little slow, that may be the correct speed for that M3.

The first M3 is no place to work backward. If the first couple of RBIs show a problem it is best to start over. Including the complimentary SBIs and listening to the resulting octave will help things get started right.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1668420 - 04/29/11 08:30 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner

So putting aside RBIs, for now, how do you properly temper SBIs? It is pretty simple, really. In the temperament octave the 4ths should beat about 1 bps and the 5ths about 1/2bps

I computed the error from blindly tuning 5ths 1/2 bps and 4ths 1 bps, using White's sequence. "Error" as compared to taking the F3F4 octave that would result from such a scheme and then dividing that (stretched) octave in 12 equal parts. All with zero inharmonicity. I get the following errors:

C 0.0
C# 0.9
D -0.2
D# 0.9
E -0.0
F 1.2
F# 2.0
G 0.8
G# 1.8
A 0.9
A# 2.1
B 1.3

Doing the same with a typical IH model doesn't change this much.

Not sure what to conclude. I guess what I'm after is some instruction on what to do if the RBI tests (e.g. steps 5 and 8 in his sequence) fail the test. Not that I mind figuring out what to do myself, but the RBI tests should come with some instruction on what to do if the test fails.

Kees


I was not very satisfied with how I wrote about this. Sorry that my thoughts did not come across very well. Let me try again.

But first, there seems to be a problem with your error list. I checked the error for F and G and get only -0.3 cents. Not that it matters. If you take a look at the theoretic or even the actual SBI beatrates, they will all be about 1 bps for 4ths and ½ bps for 5ths. And any SBI that is tuned to these beatrates will be acceptable. But I am not saying that all of them can be tuned to this beatrate. For that matter I don’t think it would be possible to do so. It is beyond human capability to tune consistently within 0.1 bps. That is about 0.2 cents for these intervals.

You can form any RBI with 3 or 4 SBIs. If the SBIs are about at these beatrates, the RBI will also be at about its correct beatrate. Temper the SBIs correctly and the RBIs will also be tempered correctly. When I did my parlor trick experiment the other day, I was surprised at the resulting beatrates. F3 was wound and as expected F3-A3 beat faster than F#3-A#3. This is what I meant by a proper progression. But it was much more than I would have tuned it if I was using RBI checks all along the way. I had been letting the tail wag the dog and didn’t realize it. It was disturbing…

OK, let’s look specifically at the tests for tuning D4 and A3. If F3-D4 is way off then an SBI may have been tempered to the wrong side of just intonation. If it seems a little fast or slow, then the 4ths and 5ths should be checked. If they are tempered correctly, then that is the beatrate for the F3-D4. Otherwise the tail is wagging the dog.

Ron mentioned a little while ago that to avoid problems with scaling, the temperament (with an ETD!) should be set at least half an octave away from the break. I guess he should know, though I doubted it at the time. So unless the piano is a full sized upright or a parlor grand any beatrates involving F3 can be off a bit. That is one reason why I have been using a sequence where the first RBI is A#3-G4. I may change what I am doing now, though…

Anyway, the test for A4 is an interesting one. Since the only RBIs are F3-D4 and F3-A3, and F3-D4 has been determined to be correct (or you shouldn’t tune A4 yet) then the test is comparing the beatrate of these two RBIs. The difference should be about 1 bps regardless of scaling and regardless of the actual beatrates. This is the M3-M6 test for a 4:3 P4. You are directly testing the tempering of the SBI that was tuned last: A3-D4.

I have also wondered why Dr. White did not give more detailed instructions in what to do with the tests and what they actually mean. And also about including F3 at the beginning but not having a better check for C#4, like with F4. That is why I include A#3 at the beginning, so there is a good check with F#3. Now I think that Dr. White meant all these tests to merely assist in learning to tune properly tempered SBIs. When this is done, then there are just minor adjustments to be made as you proceed, like adjusting a bunched up curtain on a rod. And, as he mentions, F3 is tossed in to get the ball rolling at the beginning. F4 is when the circle is completed, not A#3. Then it makes sense that the ninth note in the circle (starting with C4, not F3) is G#3 giving a M3 that is tuned between two others and includes the starting tone (C4).

I hope you have more questions!
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1668421 - 04/29/11 08:40 AM Re: Tuning Circle of Fifths [Re: partistic]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: partistic
UnrightTooner, I wonder how big is the jump in scaling, does the IH double?. How much does the expected beatrate change and if you make the M3s beat correct, is there an obvious flaw in the fifths?


Here is a link to some graphs that include iH curves: http://www.goptools.com/gallery.htm

Notice that the scale for iH is logarithmic. It doubles about every 8 semitones. It is not like a piano has an iH number for all its strings. Problems occur when the curve bends or jumps. Then the combined effects of iH are no longer self-correcting in regards to beatrates.

Typically when F3 is wound and A3 is not, it will beat 1 or 2 bps faster than theoterical. And yes, if you make the M3s beat at their theoretical speed the SBIs sound horrible, at least to me.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1668439 - 04/29/11 09:25 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
UnrightTooner, are the 5ths and 4ths progressive in the temperament region? Because if you also have to worry about making them progressive, it is much easier to make mistakes. Maybe the F3 should have been made 1 or 2 bps faster and the difference should have been divided between the fifths? How certain can you be the fifths were correct, especially if they should be made progressive? F is four fifths away from A.

Top
#1668450 - 04/29/11 09:55 AM Re: Tuning Circle of Fifths [Re: partistic]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: partistic
UnrightTooner, are the 5ths and 4ths progressive in the temperament region? Because if you also have to worry about making them progressive, it is much easier to make mistakes. Maybe the F3 should have been made 1 or 2 bps faster and the difference should have been divided between the fifths? How certain can you be the fifths were correct, especially if they should be made progressive? F is four fifths away from A.


I used to worry about this. It is too small an amount to be able to tune. Here is how it works. If SBIs double every octave, then the 12th root of two can be used to determine what the tempering error is if they are not progressive. Like if a particular SBI beats 1 bps and is tempered 2 cents from just intonation, and then if it is tuned 4 cents from just intonation it will beat 2 bps, the same as the SBI an octave higher. So how much would an SBI be in error if it beat the same speed as the one a semitone away? Only about 1/8 of a cent! And using the same method on an M3, it takes seven times as much error to make an M3 unprogressive: about 7/8 cent. The SBIs do not need to be progressive for the RBIs to be progressive. But when we are talking about SBIs that are contiguous, like F#3-B3 and B3-E4 then yes they are tuneably progressive. I have pointed out the method, you can do the math. smile

But SBIs less than double each octave, so the error is a little less. And 5ths are tempered less than 2 cents, because of iH, which reduces their error even more. But none of this is very noticeable.

And actually F is two 4ths and two 5ths away from A. I mention this now anticipating later questions about the inside/outside test.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1668494 - 04/29/11 11:14 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
If they should be progressive, but too little to be tunable, doesn't that allow too much room for error when you are doing one after another? There is the human error, maybe 0,1 bps or less, also the fact that they should be progressive by a little amount which in not tunable and when you do four of those in a row using the last one for the next one, aren't mistakes too easy to make?

I calculated the error for F3 by going from A4 to D4, to G3, to C4, to F3 and by making every 5th beat 0,5 bps and 4th 1 bps. The F3 would be 1,499 cents flat, making the F3-A3 M3 beat faster. I guess it would pass, because it isn't way off and there is nothing to compare it to. If you add in the human error and consider that these are only the first 5 notes, the error could get bigger at some point, but would probably correct itself so the last P4 or P5 wouldn't sound wrong, because if you take the average beatrate the last one should be roughly right, because at some point you tune the interval flat, at others sharp.

In the end I think it comes down to if it is easier and more accurate to set three notes with an absolute error of 1 cent and work from there or do a fifths and fourths from the beginning, very possibly going flat more than 1 cent somewhere and making up for it somewhere else.

What is the inside/outside test?

Top
#1668516 - 04/29/11 11:50 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Could you check your math? I get 1/2 cents wide, or about 1/4 bps error on the F3-A4 M3. But I am not just talking about math. I am talking about aural tuning, too.

I think 1 cent error is too much for a polished temperament. Something won't sound right somewhere. But how would YOU set three notes with an absolute error of 1 cent across a jump in iH, and know that the 4ths and 5ths will be properly tempered?

The inside outside test is when you compare the beating of F3-D4 with G3-B3. They should beat the same. Well aurally, not necessarily theoretical.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1668520 - 04/29/11 12:03 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
But first, there seems to be a problem with your error list. I checked the error for F and G and get only -0.3 cents

That sounds more right, but the other guy got the same numbers as I. You realize you are comparing against a stretched octave? (Academic, I agree it matters not.)
Quote:

You can form any RBI with 3 or 4 SBIs. If the SBIs are about at these beatrates, the RBI will also be at about its correct beatrate. Temper the SBIs correctly and the RBIs will also be tempered correctly. When I did my parlor trick experiment the other day, I was surprised at the resulting beatrates. F3 was wound and as expected F3-A3 beat faster than F#3-A#3. This is what I meant by a proper progression. But it was much more than I would have tuned it if I was using RBI checks all along the way. I had been letting the tail wag the dog and didn’t realize it. It was disturbing…

I think the tail is still wagging the dog. The goal is really to have all semitones to be locally equal. Tuning with 4ths and 5ths is a technical trick to achieve this, there is nothing particularly musically important about those intervals. I could argue in your example it's worse to let F major be harsher than F# major and it would be better to accept some irregularity in the 4th/5ths.

Quote:
I have also wondered why Dr. White did not give more detailed instructions in what to do with the tests and what they actually mean.

I suspect he didn't know what to do. It's probably like the famous prime number factorization problem; there is no method to compute the prime factors of a very large number, but once you have the factors it's easy to check they are right (by just multiplying them).

Kees

Top
#1668521 - 04/29/11 12:07 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
Here's how I calculated it:

A4=440hz
D4=(2*440+0,5)/3=293,5
D4-A4 beatrate=3*293,5-2*440=0,5
G3=(2*293,5+0,5)/3=195,833..
G3-D4 beatrate=3*195,833..-2*293,5=0,5
C4=(4*195,833..+1)/3=261,44..
G3-C4 beatrate=3*261,44..-4*195,833..=1
F3=(2*261,44..+0,5)/3=174,462963
F3-C4 beatrate=3*174,462963-2*261,44..=0,5

F3 should be 440*2^(-16/12)

Difference in cents = log(174,462963/(440*2^(-16/12)))to base 2 * 1200=-1,499 cents

Top
#1668537 - 04/29/11 12:28 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
Thomas Dowell Offline
Full Member

Registered: 11/18/09
Posts: 122
Loc: Twin Lakes, WI
Originally Posted By: UnrightTooner
But how would YOU set three notes with an absolute error of 1 cent across a jump in iH, and know that the 4ths and 5ths will be properly tempered?


Remember, there are different perspectives on which intervals to compromise, the RBI's or SBI's. It seems that you feel that the SBI's are what make a piano sound "in-tune", while others will say that it is the RBI's. I remember an article that Owen Jorgensen published shortly before he died, in which he recommended tuning progressive minor thirds below the break, and leaving the atrocious sounding octave, as he felt musicians were more sensitive to changes in the RBI of the m3 than the quality of the octaves, fourths and fifths.

The idea behind CM3's is the have evenly tempered RBI's, not SBI's.
_________________________
Thomas Dowell, R.P.T.
Dowell Piano
www.dowellpiano.com

Top
#1668564 - 04/29/11 01:26 PM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Kees:

I really enjoy your hard nosed analyses! smile

Yes, I realize now that the difference is stretched octaves. Not sure if you stretched them in the order it was tuned, though. And I agree, it matters not.

But if there is nothing musically important about 4ths and 5ths then there certainly could not be anything musically important about locally equal semitones. Who could notice?

Yes, you could argue that it is worse to let F major be harsher than F# major. And I would counter with it is better to have harmonious SBIs, which I believe is the goal, not locally equal semitones (…uh, at which partial? wink )

Edit: Hoooo! But wait! If the goal is locally equally semitones, the closer the partials are to the fundamental (lower partials) the better. That means SBIs would give more locally equal semitones than RBIs. laugh laugh laugh


Edited by UnrightTooner (04/29/11 01:47 PM)
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
Page 5 of 7 < 1 2 3 4 5 6 7 >

Moderator:  Piano World 
What's Hot!!
Christmas Header
- > Gift Ideas for Music Lovers < -
From PianoSupplies.com a division of Piano World.
-------------------
The December Free Piano Newsletter
-------------------
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) Yamaha CP Music Rest Promo
Yamaha CP Music Rest Promo
(ad) HAILUN Pianos
Hailun Pianos - Click for More
Ad (Seiler/Knabe)
Knabe Pianos
(125ad) Dampp Chaser
Dampp Chaser Piano Life Saver
(ad) Lindeblad Piano
Lindeblad Piano Restoration
(ad) Piano Music Sale - Dover Publications
Piano Music Sale
Sheet Music Plus (125)
Sheet Music Plus Featured Sale
New Topics - Multiple Forums
mp11
by mike2014
12/20/14 11:42 AM
Merry Christmas from TromboneAl
by TromboneAl
12/20/14 10:26 AM
Odd sound effect on old upright
by 661-Pete
12/20/14 06:38 AM
Define "atmospheric" in piano music
by Pianolism
12/20/14 06:18 AM
1 Hour 2-5-1 Jazz Workout Backing Track - Slow to Fast Swing
by Nahum
12/20/14 05:36 AM
Forum Stats
77369 Members
42 Forums
160010 Topics
2349802 Posts

Max Online: 15252 @ 03/21/10 11:39 PM
Gift Ideas for Music Lovers!
Find the Perfect Gift for the Music Lovers on your List!
Visit our online store today.

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