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#1796897 - 11/27/11 08:25 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
The CHAS system is very simple. As Bill has already pretty much established, it is almost identical to ET within his own mindless octaves paradigm. What Alfredo has done has encased it in a bit of esoteric mathematics and a bit of numerology which is valid but a little odd. However, in his analysis he found an important fact about the beat rates of the 4ths and 5ths, and has developed a way to incorporate this into his tuning. I do think the approach is very difficult, and on this forum we've not seen a satisfactory scheme in order to tune it. I've tried before from instructions posted in another thread, to great success. It took me four hours, but the resultant tuning was amazing.

(And had the damn cheek to not have English as his native language, or American as his native culture, and to not know how to use forums properly)

These attempts at character assassination are really petty. It's very difficult to engage with alfredo but that doesn't mean his ideas aren't valid.
_________________________
Phil Dickson
The Cycling Piano Tuner

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#1796902 - 11/27/11 08:45 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Phil D]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1540
Loc: Vancouver, Canada
Originally Posted By: Phil D
The CHAS system is very simple. As Bill has already pretty much established, it is almost identical to ET within his own mindless octaves paradigm. What Alfredo has done has encased it in a bit of esoteric mathematics and a bit of numerology which is valid but a little odd. However, in his analysis he found an important fact about the beat rates of the 4ths and 5ths, and has developed a way to incorporate this into his tuning. I do think the approach is very difficult, and on this forum we've not seen a satisfactory scheme in order to tune it. I've tried before from instructions posted in another thread, to great success. It took me four hours, but the resultant tuning was amazing.

(And had the damn cheek to not have English as his native language, or American as his native culture, and to not know how to use forums properly)

These attempts at character assassination are really petty. It's very difficult to engage with alfredo but that doesn't mean his ideas aren't valid.

To be clear: I am not going for character assassination, I just believe there is nothing to this Chas "theory".

I am not surprised if you spend 4 hours on a tuning the result will be good.

Kees

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#1797027 - 11/28/11 05:54 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Phil D]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi.

Ian, here you find the review "QUADERNI DI RICERCA IN DIDATTICA" of G.R.I.M. N.19- PALERMO 2009

Chas research report is n. 5:

http://math.unipa.it/~grim/quaderno19.htm

There you read: "Every article published on the review is submitted referee from at least two members of editorial board." You'll also find the Editorial Board list of members.

Phil,

thank you for your words. Perhaps I don't know how to use forums properly* and for sure English is not my native language. Nevertheless the picture I'm getting is quite well defined and it is not difficult for me to recognize serious contributors.

I was asked for a tuning sequence and that was provided. Also Chas publication was called into question and I provided some links. Someone found that Chas maths had symbols that they could not understand, so I provided a simplified version. The same happened with Chas tuning recordings.

I agree, now it is petty and I cannot afford to go in circles, I cannot discuss absurdities and nonsense over and over again. Now I should prove that I exist... In any case, the validity of Chas materials and Chas threads contents is submitted to PW readers and colleagues.

(*):

#1792121 - November 19, 2011 07:33 PM
Re: CHAS PREPARATORY TUNING [Re: alfredo capurso]

DoelKees:

..."What I find disturbing is the refusal by Alfredo to provide a clear tuning sequence, despite being told by several of the most distinguished piano technicians in the USA and Europe, why the sequence he posted is too vague.

From this I conclude (no personal insult intended) that the whole Chas tuning is an illusion. There is no such thing. Alfredo just tunes ET like the best but that's all it is.

Added to this deception is the "mathematical" paper, which in my expert opinion as mathematician and tuning theory expert is what Wolfgang Pauli coined as "not even wrong". I call it crackpottery. You can find a forum on "not even wrong".

Reason I'm restating this and undoubtedly upsetting Alfredo again is that novice and aspiring tuners seem somehow drawn to this Chas stuff, and naively believe it must be better than the "conventional ET" that is usually taught (wow, so many equations!) and are thus led astray.

Hence I'd like clearly stated why Chas is not taken seriously by many (if not all) experts in the area.

Alfredo, you will get an apology from me if you can prove me wrong."...

Regards, a.c.

Chas tuning mp3 - live recording on Fazioli
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

C.HA.S. The Harmonic Temperament, Chopin - Rondo in E-flat major, Op.16
http://www.youtube.com/watch?v=fWlTHnnN4cc

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Professor Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte


Edited by alfredo capurso (11/28/11 12:40 PM)
_________________________
alfredo

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#1797068 - 11/28/11 08:45 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1795
Loc: Suffolk, England
Originally Posted By: alfredo capurso
Ian, here you find the review "QUADERNI DI RICERCA IN DIDATTICA" of G.R.I.M. N.19- PALERMO 2009

Chas research report is n. 5:

http://math.unipa.it/~grim/quaderno19.htm

There you read: "Every article published on the review is submitted referee from at least two members of editorial board." You'll also find the Editorial Board list of members.


Alfredo

It was Kees who questioned whether or how your paper had been reviewed.

What concerns me about the mathematics is the definition and meaning of delta in your algorithm. As I said in a previous post, I am inclined to think the scale factor should be allowed to emanate from inharmonicity rather than equal deviations in frequency from just intonation.

My suggestion is to rewrite your algorithm like this:

(3 − Δ3)^(1/19) = (4 + Δ4)^(1/ 24)

and substitute (3 − Δ3) for (3 - Δ) and (4 + Δ4) for (4 + Δ) in sections 3.4 and 3.5.

Δ3 = Δ4 would be the special case you describe (S=1) but there would be no need for any S variable. Another special case could be 4*Δ3 = 3*Δ4.


Edited by Withindale (11/28/11 07:29 PM)
Edit Reason: Alternative statement of algorithm
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#1798180 - 11/30/11 05:24 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Withindale]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi Ian.

#1796814 - 11/27/11 04:46 PM
Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: DoelKees]

Withindale:

"Come on Kees.

Theory and practice have become badly entangled in this thread."...

Really? Well, one of the original attempts here is to keep theory and practice separate.

..."You and I both know the model will not stand up to rigorous mathematical scrutiny."...

It will be relevant to exactly understand what you meant.

..."That should not detract from Alfredo's tuning methodology or indeed from striving to translate his experience into a model."...

We would not be here if the "striving" you mention hadn't already come to an end.

..."From what I read in some of his posts, Isaac Oleg (Kamin) took Alfredo's approach seriously. When it came to comparing, so to speak, one fine wine with another, Isaac preferred French to Sicilian. Those posts may have preceded Alfredo's visit that Dan mentioned."...

Perhaps you could read about Isaac's comments and preferences also at the Canadian Association of Piano Technicians Community Forum and here:

Accord tempéré en équation - CHAS
http://www.pianomajeur.net/forum/viewtopic.php?f=7&t=6210

..."I also wonder whether some temperaments, such as those Alfredo is aiming for, can have too much consonance, if that is the right way to describe how they sound, or whatever it was that led Isaac Oleg to say something was lacking."...

Perhaps you can explain "too much consonance" and also report what Isaac said that was lacking.

More recently you wrote:

..."What concerns me about the mathematics is the definition and meaning of delta in your algorithm. As I said in a previous post, I am inclined to think the scale factor should be allowed to emanate from inharmonicity rather than equal deviations in frequency from just intonation."...

Your premise needs to be corrected: Chas scale factor does not emanate from equal deviations in frequency; the scale factor emanates from the "s" variable.

You wrote:..."Δ3 = Δ4 would be the special case you describe (S=1) but there would be no need for any S variable. Another special case could be 4*Δ3 = 3*Δ4."...

As you say, (s = 1) is a special case. How would you cope with infinite special cases?

In section (3.3) you can read: "Equal temperament’s geometric progression, when clear of unjustified premises, suggested infinite exponential curves related to oscillations of partial values, and identifiable through a second variable, expressing an “elastic” potential and enabling the system to evolve."

As I've mentioned, when we get to practice, "equal deviations in frequency from just intonation" as a rigid solution would not work, in that "tuning" is like drawing on a sheet of paper that is constantly shifting. For this reason we must be able an ready to tune different curves. This is what "s" represents.

Regards, a.c.


Edited by alfredo capurso (11/30/11 07:07 AM)
_________________________
alfredo

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#1798241 - 11/30/11 09:26 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1795
Loc: Suffolk, England
Hi Alfredo

Originally Posted By: alfredo capurso
As I've mentioned, when we get to practice, "equal deviations in frequency from just intonation" as a rigid solution would not work, in that "tuning" is like drawing on a sheet of paper that is constantly shifting. For this reason we must be able an ready to tune different curves.


This explains the difference between theory and practice very clearly. Practice does not depend on the way theory is written down on paper or whether it is written down at all.

I wrote from memory and I have not been able to find the post I had in mind. Perhaps it was not from Kamin as I thought. I am happy to add him to list of experienced tuners, like Phil, who really like the Chas tuning method.

Thank you for the links; unfortunately some of the sound samples they contain are no longer available.

When you tune an equal temperament as perfectly as you can, you are eliminating as many imperfections as possible. I used the word consonance to describe the results. Maybe it was not a good word to use. The more successful you are, the more you will emphasize any differences from the colour and character of other temperaments people hear and like. There is nothing you can do about this; it's their preference.

The equation I suggested is always true when the scale or stretch factor is constant across the octaves of interest. It could also be called s.

(3 − Δ3)^(1/19) = (4 + Δ4)^(1/ 24) = s * 2^(1/12)

This s is not the same as your s, but it covers the same infinite set of possibilities. [Note: other possibilities arise when s changes from note to note; Δ3, Δ4 will then have to change too or a pair of difference variables will have to come into the equations]

What would be really helpful to me, and maybe others, is a numerical example to illustrate sections 3.4 and 3.5.

PS This is what Kamin wrote and your reply:

..."BTW I managed to tune with a more closed tone than yours, giving all the energy to the attack and leaving the piano find its tone by itself for the rest, and I like it, it provide more tactile sensations to the pianist hence a larger dynamic palette. On a piano with not so rich tone due to old strings (I've done it yesterday with some at last 50 years old wire) that gives very pleasing results."...

I'm looking forward to hearing the tone you like the best, no doubt about superb results...Is it warmer now in Paris?


Edited by Withindale (11/30/11 02:09 PM)
Edit Reason: PS Kamin's post
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#1798487 - 11/30/11 05:48 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Withindale]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi Ian,

You wrote:..."This explains the difference between theory and practice very clearly. Practice does not depend on the way theory is written down on paper or whether it is written down at all."...

I'm not sure I understand what you mean, but whichever way I read your statement I get puzzled. Are you saying that theories, when it comes to practice, have no meaning? I try not to confuse, but "fuse" theory and practice. In my view, practice too can inspire theory and, if correct, the latter will improve the first.

..."Thank you for the links; unfortunately some of the sound samples they contain are no longer available."...

Thanks for reporting. I'm going to see what happened.

..."When you tune an equal temperament as perfectly as you can, you are eliminating as many imperfections as possible."...

Nop, it's not a question of imperfections alone, actually I like imperfections when I get their meaning.

..."I used the word consonance to describe the results. Maybe it was not a good word to use."...

The word is ok, do you hear too much consonance? If yes, what do you mean?

..."The more successful you are, the more you will emphasize any differences from the colour and character of other temperaments people hear and like. There is nothing you can do about this; it's their preference."...

We were not discussing people's preferences, nor color again.

..."The equation I suggested is always true when the scale or stretch factor is constant across the octaves of interest. It could also be called s.

(3 − Δ3)^(1/19) = (4 + Δ4)^(1/ 24) = s * 2^(1/12)

This s is not the same as your s, but it covers the same infinite set of possibilities."...

Have you checked (your) s ≤ 0 ?

..."[Note: other possibilities arise when s changes from note to note; Δ3, Δ4 will then have to change too or a pair of difference variables will have to come into the equations]"...

Hmmm…, do you prefer that way? If yes, why?

..."What would be really helpful to me, and maybe others, is a numerical example to illustrate sections 3.4 and 3.5."...

Numerical of which kind? Thanks for this feedback.

I see:..."PS This is what Kamin wrote...:

..."...more closed tone than yours, giving all the energy to the attack..."...

Yes, we were talking about attack Vs sustain. Isaac likes "all the energy to the attack", I prefer a beam.

Regards, a.c.

P.S.: ..."You and I both know the model will not stand up to rigorous mathematical scrutiny."...

It will be relevant to exactly understand what you meant.


Edited by alfredo capurso (11/30/11 05:57 PM)
_________________________
alfredo

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#1798566 - 11/30/11 07:46 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1795
Loc: Suffolk, England
Hi Alfredo

Theory and practice

You have explained how your experimentation led to your theory and, without question, your theory will have improved your practice. But you also imply you apply a more complex version of your theory than you have written down:

"As I've mentioned, when we get to practice, "equal deviations in frequency from just intonation" as a rigid solution would not work, in that "tuning" is like drawing on a sheet of paper that is constantly shifting. For this reason we must be able and ready to tune different curves."

In the paper the Chas Algorithm is stated in its simplest form in 3.1, and in 3.2 you say "the delta variable obtains two differences, in a 1:1 ratio, equal in value and opposite in
sign, one negative and one positive (0-19 negative and 0-24 positive)"
. We see that in 4.0, Table 1; deviations of -/+ 0.93517 at XII (3-Δ) and XV (4+Δ).

It appears that you are talking about this specific scale of frequencies, but it is not explained where the differences in Table 2 come from or, because the rows are not identified, what they relate to. Nor is it explained how the beats and ratios in sections 3.4 and 3.5 relate to the numbers in in sections 4.0 and 4.1, or vice versa. This is makes it difficult for us to understand how to put the theory in practice. You know what it all means so you do not have the same problem.

So far I have been talking about s=1, but going back to section 3.3, you introduce integer and fractional values for s. Again it is very difficult to understand how these would be applied in practice. The significance of equations (5) and (6) and the two different values of delta is not clear. Without an explanation equations (5) and (6) seem to be in contradiction of each other.

All this is just an indication of why the paper, as it is, would not begin to stand up to the sort of scrutiny mathematicians such as Kees would undertake.

If we can see examples of specific values of delta and s resulting in specific beats and frequencies, we may begin to fully understand the theory.

I hope this answers your main questions, but it is getting rather late.


Edited by Withindale (12/01/11 04:29 AM)
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#1798756 - 12/01/11 05:52 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Withindale]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi Ian,

Thank you for your reply:

"Theory and practice

You have explained how your experimentation led to your theory and without question your theory will have improved your practice. But you also imply you apply a more complex version of your theory than you have written down.

"As I've mentioned, when we get to practice, "equal deviations in frequency from just intonation" as a rigid solution would not work, in that "tuning" is like drawing on a sheet of paper that is constantly shifting. For this reason we must be able and ready to tune different curves."

I see, actually I meant to say the opposite; in fact, at the end of that sentence I wrote "This is what "s" represents.", meaning that what I/we apply is not more complex than what is written down. We must be able and ready to tune different curves (in practice); and (in theory) This is what "s" represents.

..."In the paper the Chas Algorithm is stated in its simplest form in 3.1 and in 3.2 you say "the delta variable obtains two differences, in a 1:1 ratio, equal in value and opposite in sign, one negative and one positive (0-19 negative and 0-24 positive)" . We see that in 4.0, Table 1 deviations of -/+ 0.93517 at XII (3-Δ) and XV (4+Δ).

It appears that you are talking about this specific scale of frequencies, but it is not explained where the differences in Table 2 come from, or what they relate to (because the rows are not identified)."...

I hope this helps: the first line of differences in Table 2 (below) come from Table 1. If you notice, they are on the left in bold. All the other difference values come from chromatic octaves, 12ths and 15ths, i.e. differences related to partials 2, 3 and 4.

section 4.1 - Table 2
Partial 2 differences......Partial 3 differences.......Partial 4 differences
...0.0005312769............-0.002125389965.........0.002125389965

..."Nor is it explained how the beats and ratios in sections 3.4 and 3.5 relate to the numbers in in sections 4.0 and 4.1, or vice versa."...

In section 3.4 and 3.5 beats symmetries deriving from delta are visualized. (3–∆) and (4+∆) are also in section 4.0 - Table 1, on the left (red and green).

..."This makes it difficult for us to understand how to put the theory in practice. You know what it all means so you do not have the same problem."...

Yes, I understand that it is not straightforward, that's why I'm happy to help.

..."So far I have been talking about s=1, but going back to section 3.3, you introduce integer and fractional values for s. Again it is very difficult to understand how these would be applied in practice."...

As I've mentioned, integer and fractional values for s and s1 represent no more no less what we apply in practice.

..."The significance of equations (5) and (6) and the two different values of delta is not clear. Without an explanation equations (5) and (6) seem to be in contradiction of each other."...

Equations (5) and (6) were first pointed out by Roy123. So, I provided a case (s = -9/8) as a demonstration; you can find it here:

#1208057 - 05/29/09 01:19 PM
Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: UnrightTooner]
alfredo capurso

and I thought it was reasonable to improve the explanation in the paper along Roy123's advice:

#1208202 - 05/29/09 04:47 PM
Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]

Roy123:

..."In order to make your paper read correctly, I suggest that you add some words to make your intent clear. You could say, for example. "In equation five, we will select values for S and S1, and calculate a new value for delta that makes the equality true. In Equation 6, we keep the same values of S and S1 and compute yet another value of delta that makes the equality true."

With such an explanation, I think your readers would have correctly interpreted your math--I certainly would have."


..."All this is just an indication of why the paper, as it is, would not begin to stand up to the sort of scrutiny mathematicians such as Kees would undertake."...

Well, Ian, we are both making a little, in my view positive effort and I hope we are making some progress. Even now, having acknowledged your points, I cannot imagine what sort of mathematicians Kees comments may belong to.

..."If we can see examples of specific values of delta and s resulting in specific beats and frequencies, we may begin to fully understand the theory."...

You can use the scale ratio and calculate specific frequencies; you can find specific beats in Chas sequence and flowchart.

Thank you very much for your valuable feedbacks. Let me know about any other question.

Regards, a.c.
.
_________________________
alfredo

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#1798773 - 12/01/11 07:31 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1795
Loc: Suffolk, England
Hi Alfredo

I'll have a look at the posts you mention, no point in repeating what has already be said.

Although I can't speak for Kees, my idea of a mathematical model is to represent what happens in practice with some accuracy.

What I'd be interested to know is how closely one of you tunings conforms to Table 1, or its equivalent for a particular piano. For instance, if your (4+Δ) was tuned to 1760.9 what might the actual values for the other notes be? Do you have some measurements of these frequencies (or cents) for any value of (4+Δ)?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#1799011 - 12/01/11 05:03 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Withindale]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi Ian,

You wrote:..."...my idea of a mathematical model is to represent what happens in practice with some accuracy."...

I hope I've managed to explain how the Chas model can represent what happens in practice with "some" accuracy, to the seventh decimal point.

..."What I'd be interested to know is how closely one of you tunings conforms to Table 1, or its equivalent for a particular piano."...

Beat-wise? Very much. As for frequency values, you have certainly understood that Table 1 refers to one case: s = 1; that is the equivalent for a particular piano. For many other pianos we manage "s".

..."For instance, if your (4+Δ) was tuned to 1760.9 what might the actual values for the other notes be?"...

The actual values for the other notes may well be those which derive from Chas scale ratio. I have made a digital comparison with 12th root of two ET and shared it here in PW.

"s" frequency values for all particular pianos, i.e. the equivalent of Table 1, may depend on the piano's particular scaling.

Regards, a.c.

Chas tuning mp3 - live recording on Fazioli
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

C.HA.S. The Harmonic Temperament, Chopin - Rondo in E-flat major, Op.16
http://www.youtube.com/watch?v=fWlTHnnN4cc

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Professor Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte


Edited by alfredo capurso (12/01/11 05:36 PM)

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#1799078 - 12/01/11 07:22 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Withindale]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1795
Loc: Suffolk, England
Hi Alfredo

Thank you for all your replies; I have looked at Roy's postings and some others.

On reflection, maybe we should not tune pianos by mathematics after all. The Babylonians came up with square roots but certainly did not intend them for pianos. Then Pythagoras discovered the comma and messed up the circle of fifths. Today we have "mathematical interference symmetry" and "heavy mathematics" to thank for the only pure method of tuning pianos.

So I've decided to return to my naive and uniformed way of looking at things. I think it's best to look at Chas as a model of what you do and see what we can learn from it. If it helps you and anyone else to succeed with your tuning method then it's served its purpose. We would do well to recognize you follow in the tradition of Archimedes who explained the principle of the levers which underlie the symmetry of your beats.

What I can aspire to is a simple model in which the scale is stretched out across the octaves so that intervals sit between the partials. I think that can apply to both unequal and equal temperaments and I will work out how to do both one day.

I've learnt a lot from the debate.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#1799264 - 12/02/11 04:37 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Withindale]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi Ian,

..."On reflection, maybe we should not tune pianos by mathematics after all."...

Perhaps you are talking about ETD tunings, few cents deviations and stuff like that. In fact, I do not know of any aural tuner (like I am) that tunes pianos by mathematics. But maybe you are talking about one mathematical aspect, namely proportions, which in my view is what any instrument's tuning is about. Then, how and why proportions affect our tunings can always be understood and mastered to different degrees, with no contraindications.

..."So I've decided to return to my naive and uniformed way of looking at things."...

Is there a way we can return to naivety?

..."What I can aspire to is a simple model in which the scale is stretched out across the octaves so that intervals sit between the partials."...

One day I might ask you to lend me your definition. Thanks again and... keep in touch.

Best wishes, a.c.
.
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alfredo

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#1799277 - 12/02/11 06:11 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Withindale Offline
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Posts: 1795
Loc: Suffolk, England
Originally Posted By: alfredo capurso
But maybe you are talking about one mathematical aspect, namely proportions, which in my view is what any instrument's tuning is about. Then, how and why proportions affect our tunings can always be understood and mastered to different degrees, with no contraindications.


Yes, now you mention it, proportions.

Greek temples are models of perfection but their columns are not in strict mathematical proportion. The architects and builders adjusted their shape to allow for the way we see them.

Proportions and perception.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#1807749 - 12/17/11 04:48 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Hi.

Two links that I'm happy to share. The first is about symmetries, the second is about music analysis. The latter shows the Spiral Array, and also the paper (maths) is in the web.

Marcus du Sautoy: Symmetry, reality's riddle
http://www.ted.com/talks/marcus_du_sautoy_symmetry_reality_s_riddle.html

Engineer-Pianist Elaine Chew Talks About Using Mathematical and Software Tools to Analyze Music
http://www.youtube.com/watch?v=4GPwVNPuKuA&feature=player_embedded#!

Regards, a.c.
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#1807868 - 12/17/11 11:33 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
DoelKees Offline
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Registered: 05/01/10
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Loc: Vancouver, Canada
Originally Posted By: alfredo capurso

Hi.

Two links that I'm happy to share. The first is about symmetries, the second is about music analysis. The latter shows the Spiral Array, and also the paper (maths) is in the web.

Marcus du Sautoy: Symmetry, reality's riddle
http://www.ted.com/talks/marcus_du_sautoy_symmetry_reality_s_riddle.html

Engineer-Pianist Elaine Chew Talks About Using Mathematical and Software Tools to Analyze Music
http://www.youtube.com/watch?v=4GPwVNPuKuA&feature=player_embedded#!

Regards, a.c.






Those video's have nothing to do with piano tuning, chas or not.

Kees

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#1808754 - 12/19/11 03:52 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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..."Those video's have nothing to do with piano tuning, chas or not."

Kees,

perhaps we don't need to agree on what has to do with piano tuning and what not, perhaps every single piano tuner follows her/his own unique route.

Generally speaking, I'm with those who think that knowledge of arts and sciences is useful at any level; and when it comes to piano tuning, of course, I'm referring to common literature and my own experience. Now, the first video is about symmetries, the second is about music analysis and both subjects have been of great help to me. In particular the notion of symmetry was fundamental in regard to the temperament model that I'm sharing, be it theory or practice.

C.Ha.S. Model - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

..."Alfredo, you will get an apology from me if you can prove me wrong."...

The problem, Kees, is that you didn't prove yourself to be right, you gave no arguments nor evidences in regard to a long long series of statements and insinuations and all that, to me, sounds like true libel style. On this, I've had to inform Frank.

That said, I wanted to share one more video (only the esthetics) about Fibonacci numbers, the Golden section and logarithmic progressions in nature:

http://www.youtube.com/watch?v=PlxZpNP9zy8

There I found a link to a brief article where you read:

..."In 1999, retired mathematician Clement Falbo measured a series of nautilus shells at San Francisco's California Academy of Sciences, and he found that while they were indeed logarithmic spirals (like the golden spiral), their ratios ranged from about 1.24 to 1.43, with an average ratio of about 1.33 to 1, not even close to the 1.618... ratio of the Golden Spiral."...

http://www.shallowsky.com/blog/science/fibonautilus.html

As a matter of fact, 1.33.., i.e. 4:3 is our fourth ratio too.

Regards, a.c.

Edit: in the web, a paper by Clement Falbo: "The Golden Ratio - A Contrary Viewpoint".


Edited by alfredo capurso (12/19/11 05:11 PM)
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#1832101 - 01/26/12 06:05 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Hi All,

Last summer I contacted Professor Sander Germanus, director of the Huygens-Fokker Foundation. From his kind reply I understood that the Chas model would have been valued by their scientific coordinator Manuel Op de Coul. Today the paper is included in the Foundation's Tuning and Temperament bibliography:

http://www.huygens-fokker.org/docs/bibliography.html

This is a positive piece of news that I am happy to share.

Regards, a.c.
.
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alfredo

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#1840343 - 02/07/12 06:02 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi,

Two videos that have more to do with music, interpretation and two favorite composers. Thanks to two friends that pointed them out:

‪Alicia de Larrocha Mozart Concerto 27 in B Flat‬
http://www.youtube.com/watch?v=S_MEkfDA-x4&feature=share

‪Yuja Wang - Scriabin, Selections for Solo Piano‬
http://www.youtube.com/watch?v=nHO4Ucw9zL4&feature=related

Regards, a.c.
.
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alfredo

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#1889863 - 05/02/12 08:48 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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#1888755 - April 30, 2012 12:50 PM
Re: Ethics/Technicians/ Status [Re: Emmery]

Ken Knapp:

1000 Post Club Member

Registered: April 18, 2006
Posts: 1845
Loc: Pennsylvania

"Well, the moderator reports are beginning to roll in on this topic. It seems to happen every time.

I just get absolutely flabbergasted by how any discussion on ptg/non-ptg, rpt/non-rpt can escalate into insults, accusations, name calling, whatever. I don't care who you are or what side you're on. If you participate in this mud slinging you make yourself look foolish in the eyes of your customers when they read that stuff.

Maybe THIS particular topic hasn't degenerated into the cesspool some of the others have, but it's only a matter of time. I don't know what the answer is. Perhaps we should ban the very mention of the PTG, or RPT.

Some will think I've conveniently closed the topic when one side or the other looks better and thus stopped any chance of rebuttal. So don't forget to send me PM's accusing me of favoring one side or the other..
_________________________
Ken

- . - . - . -

Well, I'm very much surprised, actually bewildered as I would never have thought that the above topic needed to be closed down. And I'm very sorry to have to use this particular thread in order to express my disapproval.

..."If you participate in this mud slinging you make yourself look foolish in the eyes of your customers when they read that stuff."...

Ken, that may be your own opinion. But... who is "you"? Who has been "slinging"?

..."Maybe THIS particular topic hasn't degenerated into the cesspool some of the others have, but it's only a matter of time."...

This surely is your own feeling, your own prediction.

..."I don't know what the answer is."...

That, in my view, cannot justify your act, though you are right, yours is not an answer nor a solution.

..."Perhaps we should ban the very mention of the PTG, or RPT."...

I do not think that would be a good solution either, though I'm not a Forum management expert... perhaps it could be enough to simply moderate individual abusers or reports that make no sense.

I was on the point of thanking Emmery for his topic and his elaborations, together with others, what I'm now forced to do from here.

Ken, as I find your decision incomprehensible and unjustifiable, I politely ask you to remedy by re-opening that Topic on Ethics/Technicians/ Status, so letting All people with dignity give their contribution.

Regards, a.c.
.
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alfredo

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#1893639 - 05/08/12 05:24 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Loc: Sicily - Italy

Hi Ken,

I was hoping in a reply, few words that could help me understand your decision. Now I hope you appreciate my attempt to let you know what I think, being on the other side, i.e. being one of many people that are ready to enjoy and contribute to this Forum.

You see, if the abrupt closing down of a topic was actually one of many options you have, that would not really be a problem for me, I'm able to accept (or not accept) a rule. What I find somehow disturbing is when you give moot reasons for justifying your act. I think that every adult customer...can use eyes and brain, so elaborating a unique way of thinking, and I find difficult to believe that you can truly anticipate the course of a topic... in time, what ever the subject may be.

You also wrote "I do not care who you are...", and on this I would actually like to tell you more: I too am an adult. When some facts or events are still within common sense and civil/human respect, I do not need to be convinced on what is best and what may get worse.

You mentioned an answer..., I suggest that you (or any other moderator) simply write: End of this Topic.

Regards, a.c.
.
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alfredo

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#1912014 - 06/11/12 06:02 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi,

Perhaps Loren, together with Tunewerk, would like to put some questions forward?

Regards, a.c.
.
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alfredo

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#1912166 - 06/12/12 03:02 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Originally Posted By: Tunewerk

"I'm posting here because I noticed both Doel and Phil have written in and offered contrary opinions on CHAS. I respect both of your thoughts and I'd like to hear more.

Alfredo was kind enough to explain CHAS in some detail to me. I listened and tried to clarify, but I am still confused as to what CHAS exactly is.

To my understanding from the paper and from speaking with Alfredo, CHAS is a way of looking at tuning, that all intervals can be proportional and progressive and that there can be an ideal stretch between the 15th and the 12th. However, for me this was not new, and has always been an integral principle in the nature of the mathematics of tuning. I know many tuners do not see this, so perhaps this is the addition to the tuning community?"

#1911874 - June 11, 2012 04:03 PM Re: Circular Harmonic System(C.HA.S) Tuning [Re: Tunewerk]

Phil D Offline
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Registered: January 15, 2010
Posts: 223
Loc: London, England

"This is pretty much exactly what it is. A mathematical exploration of the consequences of stretched octaves to ET. 12th-root-of-2 ET has a mathematical basis behind it, and so a set of theoretical beatrates and frequencies. But we don't tune this, we all know that. The way we tune is based on stretched octaves, and then a set of rules that allow us to set an equal temperament within those octaves. Many people, myself included, use an octave size that balances the octave, 15th and double octave. I set the temperament with equal-sized fifths and fourths, progressive 3rds and 6ths, then expand from there.

What the CHAS analysis does is allow us to see what should happen to all of the intervals. The paper is unfortunately very obtuse and difficult to understand, and as Alfredo seems to have a penchant for sacred geometry and other rather fringe fields, it does lose the reader very easily. (Sorry Alfredo, just the way I see it!)

However, in explanations on this board and in the practical application that he has found, there is real value. I wouldn't say that it is anything new. It's already been said many times that the delta-balancing equation is a direct equivalent to the Mindless Octave technique described by Mr Bremmer to stretch the octave so as to balance the 12th and double octave. However, Mr Bremmer is describing a practical technique. Alfredo has translated this into theory, which allows analysis that I don't think was done before.

The value of this analysis is in seeing what happens to the size of all of the intervals if this balance is upheld. We're all aware that no interval stays the same width across the whole of the compass, and yet we tune the temperament with equal-sized fifths. What happens to them in the rest of the range is just a consequence of the octaves we tune. With the CHAS technique, the progression of the size of every interval is incorporated from the start. This means progressive 4ths and 5ths when setting the temperament. These intervals are then progressive throughout the compass, but the progression isn't simple - the progression of the 5ths inverts at a certain point in the tenor, depending on the piano. (the 5ths are always narrow, but they become less narrow as you move further from this point in either direction) This is essentially the only difference, but I think it is important as it is optimal.

We all strive for optimal tunings, and what we've done for many years is to improve on theory (12TET), and approached tunings optimised for each piano. CHAS describes this optimisation process, and in doing so gives us a much clearer picture of what it is we are doing, and an insight in what actually needs to happen for us to achieve the goal."

Quote:

Tunewerk: "I ran across what seemed to be mathematical errors in the paper and errors in the preparatory tuning instructions which confused me further.

Phil, it seems you understand it, so if you can explain it succinctly with a clear idea.. or mathematically, please do. I'd be grateful."

- . - . - . -

Phil: "Errors in the paper and in the instructions have put off a few others as well, it is a shame Mr Capurso hasn't managed to address them for you as of yet.

I hope I've explained how I see it to you well enough. You've struck me as a very analytic tuner keen to understand optimal tuning. And whereas the paper and presentation have thus far been far from optimal, I do think the tunings that can be produced using this technique are. How different they are in practice from well-executed ETs by other expert tuners, I am not sure. They're not hugely different, definitely. More research would be needed, which isn't something I've been inclined to do as of yet.

Forgive the rather unspecific nature of this post, I don't have all the facts to hand, I just wanted to talk about the concepts as I understand them."


Edited by alfredo capurso (06/12/12 12:05 PM)
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#1912329 - 06/12/12 12:04 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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#1911906 - June 11, 2012 05:17 PM Re: Circular Harmonic System(C.HA.S) Tuning [Re: Phil D]
Withindale Online content
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Registered: February 09, 2011
Posts: 430
Loc: Suffolk, England

Originally Posted By: Phil D
12th-root-of-2 ET has a mathematical basis behind it, and so a set of theoretical beatrates and frequencies.

- . - . - . -

Withindale wrote: "The mathematical basis for 12th-root-of-2 (1.059463094) ET is flawed in practice because it does not allow for inharmonicity.

CHAS (1.059486544) ET is a better mathematical model because it allows for inharmonicity and stretches all the semitones and octaves equally."
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alfredo

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#1912331 - 06/12/12 12:08 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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#1912141 - June 12, 2012 05:18 AM Re: Circular Harmonic System(C.HA.S) Tuning [Re: Weiyan]
alfredo capurso Online content
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Registered: July 10, 2007
Posts: 671
Loc: Sicily - Italy

Hmmm... I must admit I am quite puzzled. I said to myself... oh good, Tunewerk has replied.

Now that I've read the above post down to the end it feels strange. And I do not know if it is the tone, the punctuation or the sheer content of your reply, Tunewerk, or the way your outlook is being conveyed. Hmmm... I'm going to read it again.

Regards, a.c.
.
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alfredo

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#1912334 - 06/12/12 12:12 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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#1912159 - June 12, 2012 06:42 AM Re: Circular Harmonic System(C.HA.S) Tuning [Re: Weiyan]
alfredo capurso Online content
500 Post Club Member

Registered: July 10, 2007
Posts: 672
Loc: Sicily - Italy

Tunewerk wrote:

Hello Phil, Ian, Alfredo.

..."Thank you Phil for the most complete and honestly clear explanation I've seen yet for CHAS. With so much discussion around it, I had to assume people were seeing some basis in it."...

Please Tunewerk, help me understand, are you interested in examining people or are you saying that "discussion" around it was much, perhaps out of proportion?

..."Alfredo, my apologies. I did not mean to insult you. I take ideas on their merit and mean no personal insult to anyone behind them."...

No need to apologize, what for, why should you? I'm trying to understand how you take ideas on their merit.

..."There are errors in your mathematics"...

Hmmm, I look forward to knowing more on that. And now, as a serious expert, you must show where.

..."and in your tuning instructions,…"

Hmmm, it's good if you can point out where.

..."which led me to believe that you didn't understand completely what you were trying to convey."...

Well, this is something original, on my idea's merit. You say: I do not "understand completely what" I (myself) am (was - would be) trying to convey?

..."With a lack of rigor, I lose energetic attention on the subject."...

You see, Tunewerk (is this your real name?) you say "lack of rigor" before proving it. Isn't this lack of rigor on your part? And would we be here if you had lost "energetic attention on the subject"? Hmmm...

..."I will be honest here in what I see: CHAS is an interesting attempt at organising theory,"...

Organizing theory? Is this what researchers do where you live, or new theories organize theory? You can be honest everywhere and specify what you intend to say.

..."...which can mean only positive things for the tuning community at large. However, it would do a greater service by being more transparent, instead of intentionally nebulous and obscure. Then others may contribute to a growing body of knowledge - and maybe add to your understanding, Alfredo."...

So, the problem now is not really "lack of rigor" but the fact that I make Chas theory (actually an attempt at organizing theory) nebulous and obscure, so the "body of knowledge" cannot grow and others cannot add to my understanding??? I'm astonished, I shall have a brake.
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#1912349 - 06/12/12 12:37 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hi Tunewerk,

Here is the second part of my reply.

Originally Posted By: Withindale

"The mathematical basis for 12th-root-of-2 (1.059463094) ET is flawed in practice because it does not allow for inharmonicity.

CHAS (1.059486544) ET is a better mathematical model because it allows for inharmonicity and stretches all the semitones and octaves equally."

- . - . - . -

Tunewerk wrote:

..."Withindale, the mathematical basis for 12th-R2 ET is flawed in theory, as well as practice, by disregarding the existence of other interval consonance in whole adoration for the octave."...

Tunewerk, I'm glad you have grasped that and Ian is right too. What you are stating (BTW, have you written any paper? And your Journal?) applies also to "whole adoration for 5ths" and "whole adoration for 12ths", it is good if you now agree on that.

..."I believe Alfredo understands this, and his attempt with CHAS is to tell others this, that the 12-tone frequency doubling model on the piano can also be seen as modulo 3, 4, 5, 7, 12, 16, 19, 24, etc. Is that true, Alfredo?"...

Thank you for your credit. Far beyond any fixed modulo "x", as I could explain to you privately, Chas theory is also based on "delta-differences" and represents a dynamic "s" adjustable scale. That is the meaning of the "s" variable.

..."If I am correct in reflecting this, then what you are trying to do is expand on Bernhard's concept of the 12th centrality into an understanding that the 12th is only one more consonance in the whole series. So, CHAS would be an overarching theory that includes Bernhard's understanding, and the rest of the whole series of harmonic consonances present in any 12-TET instrument."...

Yes, you could write "any any-TET". Hmmm... you stated (above) that Chas theory should be "more transparent", that it is "intentionally nebulous and obscure", yet you seem to understand something, although you ask others what their actual understanding is. Hmmm... If I were you, I would now concentrate on my own understanding. You seem to be grasping only the "static" part of the Chas theory and still be thinking in 12-modulo terms.

..."To this, I would say, well anyone with a physics or mathematics background already understood this."...

How funny, this reminds me of Bill, Bernard and J B Haldane's stages of new ideas acceptations... if memory serves that is the forth stage? Ian, how do you like that?

..."They would have been frustrated reading the old tuning texts, looking at one ratio, combination, or another.. since the people writing were limited in their depth of understanding; not being heavy theorists."...

Hmmm... I would never say that previous researchers were "limited in their depth of understanding; not being heavy theorists". Previous researchers (including Cordier and Stopper) have all made the route to Chas model, all of them will have contributed. Yes, many centuries of frustration but... In my view, those ("anyone with a physics or mathematics background") that "already understood this" would simply have written a paper on ET, perhaps isolating Chas scale incremental ratio?

..."So seeing things rather in one dimension, they were confused when problems arose in other areas because they were only looking at one at a time."...

Which "other areas" are you referring to? Please, do not leave your thoughts suspended in the air and tell me: Were you too confused? Say that you Tunewerk were not confused (what on(?)), which other tuner or theorist have you shared your non-confusion with?

..."To me, it is wonderful that you would spread this awareness with CHAS, that tuning is a large model."...

Please, make "tuning" as large of a model as you like; you could try to make your model even larger than Chas "organizing" theory, but let me be the one who helps you with "what Chas represents", with what is still obscure for you. That is why I'm here.

..."This will help expand the one-dimensional understanding that's plagued tuners and the literature in the past."...

That's good, you are grasping at least one fact. When you can also grasp the dynamic // elastic \\ erratic meaning of the "s" variable, you'll be able to look at this model from all sides and you will find it even more... wonderful (though where I live, we cannot say "more wonderful" wink ).

..."My only problem is if you think this theory or understanding is exclusive to you, creating an environment that shuts off others' capacity to see that understanding within themselves - ..."...

I have no problems. When did you mature this last idea, do you feel that threat after my sharing? If anything, I see that some others are able to shut "off" their own "capacity" them selves. Don't you?

..."...or that existed always in the fabric of the universe."...

Well, I like your ending, I find it poetic although somehow flattering. Thank you, but I still am puzzled. In any case, are you ready to open out your capacities? Like Phil, Ian and Isaac and others are doing already, are you ready to help me (with my English and Institutions), help Bill and other examiners, Jerry and many RPT's and non-RPT's colleagues "to see that understanding within themselves"?

More than words and psychology, Tunewerk, I'm for dreams and pragmatism, and I serenely take around this contradiction.

Tunewerk added:

"PS - Phil, I noticed you wrote in another thread:

Originally Posted By: Phil D

"However, in his analysis he found an important fact about the beat rates of the 4ths and 5ths, and has developed a way to incorporate this into his tuning. I do think the approach is very difficult, and on this forum we've not seen a satisfactory scheme in order to tune it."

Tunewerk wrote: "Can you describe here what Alfredo has found, concerning 4ths and 5ths? Any other insights you have gleaned from his work?

I'd add to another CHAS topic, but they all get so wordy and out of hand, that I thought I'd just add it here."

- . - . - . -

Gentlemen,

I am not sure I am able to decode Tunewerk's outlook and intensions, nor his concrete background and theoretical knowledge.

I'd rather let him answer some questions (optional) and ask what is perhaps still nebulous or obscure for himself, so that concepts and facts may not get twisted further, in force of more wordy (as lamented) entertaining verbiage.

Very soon I will be posting also those explanations I wrote for Tunewerk, stay in touch.

To All, regards, a.c.

Edited by alfredo capurso (June 12, 2012 04:17 PM)
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#1912581 - 06/12/12 11:47 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
DoelKees Offline
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Registered: 05/01/10
Posts: 1540
Loc: Vancouver, Canada
Many people have argued in this tread with Alfredo, including some of the most respected authorities on the subject such as Kent Swafford, Bernhard Stopper, not to mention Bill Bremmer, who invented what in this thread is called "C.H.A.S".

All of these people have refuted chas as being either wrong or trivial. They have also stopped arguing with Alfredo as this is quite hopeless: he refuses to answer clear questions, he shows a shocking ignorance of basic tuning theory. He does not know what inharmonicity is. He does not know what a well-temperament is. He does not know what a 2:1 versus 2:4 octave is. He believes other tuners tune the octave to the 2:1 ration of fundamentals. Etc. etc.

All those people have given up arguing: It is fruitless to argue with a crackpot.

This is my opinion on chas, which I think is shared by just about anyone with knowledge on the subject. I distinguish myself by not giving up and cutting communication about the subject.

I think it is evil to ensnare unsuspecting aspirant tuners into this nonsense, and I think I make a positive contribution by pointing this out.

Kees

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#1912614 - 06/13/12 12:49 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Offline
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Registered: 03/26/11
Posts: 395
Loc: Boston, MA
Alfredo, your replies get more confusing and longer the more questions are posed. You don't answer the questions, but instead divert from thread to thread and become defensive. Why not answer the questions and save everyone time?

Your threads here are longer than any other I've seen. Why is 22 pages necessary? I'll venture a guess: because no one is being directly answered.

If you can provide nutshell clarity for what your theory is, I will certainly listen.

I have to agree with Kees posts here on p. 22 of this thread.

I have spoken here and kept up with effort to ask you deeper questions, in hopes to understand something new and to give you the benefit of the doubt. I hope you prove Kees and I wrong and clarify your insights, right here and right now.

Until then, it bothers me that to prop up your authority, you provide a whirlwind of nonsense. Your paper is largely nonsense, this is why it is difficult to be specific about listing errors. You aren't fooling anyone by that, and rather exhausting those who try to listen.

After having read through your paper once again tonight, I want to say that I believe that you understand many deep concepts about tuning.

These are:

- tuning with respect to the entire piano and all intervals (you call intermodular), i.e. 3rd, 8ve, 12th, 15th, not just 12th-R2

- the idea that perfectly balanced dissonance through careful aural tuning can build amazing resonance

- the realization that stretching near the 12th allows for a great inharmonicity match on most pianos and potential to unlock more resonance

It's clear, like many of us, that you've discovered the tonal importance of the 12th and it's relation to stretch. You have tried to encode that in theory.

However, your theory is a mess! I finally understood some of the things that you were talking about in your paper. I plotted your model to visualize it's behaviour. Pages 66 - 74 contain various obvious consequences and parallels from your basic CHAS equality. However, half of your graphs look like they were copy-pasted over lunch break and are missing some correct units as well as being smattered with Italian in the English translation. You might want to get on that.

Your parallels to the Railsback curve are illogical leaps that show you must not fully understand inharmonicity. 'Graph 4' on p. 72 cannot be correct according to your model. The cent deviation from regular ET will remain constant.

That geometry you have drawn on p. 68 has no relevance to anything in your paper. It doesn't prove scale symmetry. You have simply drawn circles at radii relative to their x-value, plotted within each other. This is meaningless.

You show data and then imply your meaning.. but your meaning is NOT a conclusion from the data!

Nevertheless, your findings on what creates a good tuning, I agree with. I found that after reading your paper, I could almost accurately call what I tune, CHAS. However, not by your theory.

I wonder who peer-reviewed this paper to allow it to be published under a university server?


Edited by Tunewerk (06/13/12 04:51 AM)
_________________________
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#1912631 - 06/13/12 01:56 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6360
Loc: France
well if I compare the attitude of Bernhard and Alfredo, one is providing a complete method to tune the harmonic set on the piano, the other protect its knowledge more.

the arguing there is not interesting, even me I can understand how the shape of hhe curve is automatically done. If the formula is not valid I dont see how it can be graphed. Thosrose approaches are on any case adbsorbing the iH, as does Cordier the first before an American had the idea to tune pure intervals ;-) allons enfants da patrie, le jour de gloire est arrive. .. sorry my milk is on the fire ! what do I say there.
ah yes wink too late it boils and get out of the can.

larn to recognize and create an optimal more or less auto settling strong harmonic set is in my opinion ideal for a beginner. learning to stretch properly is very difficult in comparaidon. It is also good fun and let you choose what you prefer in the end.

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