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#1912643 - 06/13/12 02:41 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Olek]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1723
Loc: Vancouver, Canada
Originally Posted By: Kamin
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.


What you write is gibberish to me. That's all I can say.

Kees

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#1912670 - 06/13/12 05:14 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Tunewerk]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy
Originally Posted By: Tunewerk
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?


Tunewerk, I see now that you have edited your post. I had written my reply already, which I'm now posting. I shall read your points and reply in turn.

Hi Tunewerk,

Thank you for your reply, I can now decode your intentions more clearly.

I was waiting for your questions but, which are the questions I did not answer? Please, if you can, list them.

You say I divert from thread to thread, and I have explained why for once I prefer so.

You say I become defensive, I simply try to get along with my feelings and nature and get to a steady point systematically.

You ask why 22 pages and you give yourself an answer. If you read them you would see it is 22 pages of answers in detail, mixed up with insinuations and insults.

Now you are asking for "nutshell clarity", yesterday you received and appreciated Phil's explanations and you wrote a panegyric about what I have been able to explain to you.

Now you agree with Kees Doel and choose to adopt his worst style.

Again you ask me to clarify my insights, although I have done that in private with you and extensively (your lament) here in PW.

Today you state that I "provide a whirlwind of nonsense", and that Chas paper being "largely nonsense" makes it "difficult to be specific about listing errors". I'd rather be informed on anything that makes no sense and about errors.

You end up writing: "You aren't fooling anyone by that, and rather exhausting those who try to listen". This to me sounds offensive and insinuating.

Please Tunewerk (what is your real name?), next time you chime in, taking my time and making this thread longer, please make sure you can list your questions and point out errors.

- . - . - . -

Gentlemen,

Yesterday it felt strange and I was puzzled. Today I can say it is all clear and sunny again.

Regards, a.c.

Edit: Tunewerk, in order to offer you a reply in detail, I'll have to spend some time tonight. I hope you do not mind.


Edited by alfredo capurso (06/13/12 05:33 AM)
_________________________
alfredo

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#1912686 - 06/13/12 06:22 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: DoelKees]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy
Originally Posted By: DoelKees
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


Kees, you talk about "evil" and I have told you I cannot stand your comments any longer. Please, if you do not want to be evil, share what ever opinion you have in a different thread.


Gentlemen,

I hope I'm wrong but... the end of the first paragraph of Kees' post may reveal, in my view, what this "game" is about.

Regards, a.c.
.
_________________________
alfredo

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#1912701 - 06/13/12 07:31 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Alfredo, there's no game among us. We are asking you to please be straightforward and stop playing your game, if you would.


Using the one solution from your equality:

(3−∆)^(1/19) = (4+∆)^(1/24), ∆ = 0.0021253899646

From your paper (p. 65):

(3−∆)^(1/19) = (4+∆)^(1/24) = 1.059486544350

The cent value of your new halfstep ratio is:

1200 log[2] (1.059486544350) = 100.03831844 cents, 'r'

r * 19 = 1900.72805; 1901.955 (pure) - 1900.72805 = 1.22695 cents narrow of pure (12th) CHAS

r * 24 = 2400.91964; 2400.91965 - 2400.000 (pure) = 0.91965 cents wide of pure (15th) CHAS

2^(1.22695 / 1200) = 1.000708965 beat ratio for the CHAS 12th
2^(0.91965 / 1200) = 1.000531352 beat ratio for the CHAS 15th

I wrote beat ratio to mean, multiply any top note fundamental frequency of a 12th or 15th by its 'beat ratio' and derive the theoretical BPS of that interval in CHAS. It's clear that 12ths and 15ths with a coinciding top note in CHAS do not beat at a 1:1 ratio.

"Systematic analysis of beats frequencies revealed a new differences constant, that is, a 1:1 beats ratio on harmonic partials 3 and 4. The order of sounds described here thus constitutes a set of proportional frequencies as a function of synchronic beats: a dynamic, stable and perfectly resonant system." (p. 58)

What are the set of 12ths and 15ths with a 1:1 beat ratio in CHAS?

y = ((1.000708965 * x) - x) / (1.000531352 - 1)

If you work through the frequencies, it seems the 15th with a top note at about 499.26 cents above its respective 12th, has a beat ratio of 1:1. That is to say: the only set of 12ths and 15ths that will have a beat ratio of 1:1 in CHAS, are the 12ths and 15ths that have a common bottom note - not exactly, but close.

Peer review, please, if I've made any mistakes...

This is just one example of how CHAS does not form any more of a 'perfect synchronic set' than any other theoretical alignment. Only one set of intervals can have a 1:1 beat ratio at a time.


Edited by Tunewerk (06/13/12 07:41 AM)
_________________________
www.tunewerk.com

Unity of tone through applied research.

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#1912742 - 06/13/12 09:24 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy

Tunewerk,

I see you have posted more, thank you very much. Just one thing, if you are on your own, perhaps you can address yourself with an "I"?

..."You asked for specifics, here is one thing that came to mind..

Thank you. As mentioned, I'll be able to sit down calmly later tonight but, if possible, could you post all things that possibly come to your mind, not just one example, so that you do not leave anything suspended, after a long run-up, and we both may be enabled to put an end to this game/no-game?

You see... you wrote: "There are errors in your mathematics..."... Thus, in any case I shall be ready to post sometime tonight, but I will wait until you write: "These are all the mathematical errors I could find".

You also wrote: "...and in your tuning instructions,...". Please, if you decide to specify, use the Chas Pre-tuning thread.

Regards, a.c.
.
_________________________
alfredo

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#1912967 - 06/13/12 04:44 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Alfredo, I'm not going to play your game. Answer the questions posed, or don't. It only reflects on your own credibility.

I think it's disrespectful how you treated most of the established technicians (Kent Swafford, Bill Bremmer) when they asked for answers. You are not holding a holy grail - so stop creating that appearance. That is how you do a disservice to those trying to understand.

If you want to pay me for my time to proof your whole paper and go into lengthy discussions about how I think this is unfounded or that is mathematically inaccurate, I can, but I don't think it would be worth the time. The paper is so full of confusion, where would one start? Errors among a heap of tangled yarns? The formation of the yarn itself is error.

Now, I believe that you have some genuinely deep understanding about tuning that I haven't seen many people reference, but you've taken your understanding and turned it into this massive theory that doesn't support actually what it claims to do. It will produce very good ET according to standard rules. This ET equally balances the stretch of the 15th and compression of the 12th: exclusively dealing with this compromise.

So, do I think the qualitative idea of CHAS will produce a great tuning? Yes. It takes Bill Bremmer's and Bernhard Stopper's ideas of the 12th together with the understanding of a unity in tuning.. as opposed to only looking at one interval, to the exclusion of balancing of the others.

Do I think the quantitative idea of CHAS means anything? Not much. You use mathematics to paint a picture of your qualitative idea, but the math is improperly used and the application, confused.

I don't know if it is even worth posting this.. does anyone else have opinions?
_________________________
www.tunewerk.com

Unity of tone through applied research.

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#1913005 - 06/13/12 05:46 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Tunewerk]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy
Originally Posted By: Tunewerk
Alfredo, I'm not going to play your game. Answer the questions posed, or don't. It only reflects on your own credibility.

I think it's disrespectful how you treated most of the established technicians (Kent Swafford, Bill Bremmer) when they asked for answers. You are not holding a holy grail - so stop creating that appearance. That is how you do a disservice to those trying to understand.

If you want to pay me for my time to proof your whole paper and go into lengthy discussions about how I think this is unfounded or that is mathematically inaccurate, I can, but I don't think it would be worth the time. The paper is so full of confusion, where would one start? Errors among a heap of tangled yarns? The formation of the yarn itself is error.

Now, I believe that you have some genuinely deep understanding about tuning that I haven't seen many people reference, but you've taken your understanding and turned it into this massive theory that doesn't support actually what it claims to do. It will produce very good ET according to standard rules. This ET equally balances the stretch of the 15th and compression of the 12th: exclusively dealing with this compromise.

So, do I think the qualitative idea of CHAS will produce a great tuning? Yes. It takes Bill Bremmer's and Bernhard Stopper's ideas of the 12th together with the understanding of a unity in tuning.. as opposed to only looking at one interval, to the exclusion of balancing of the others.

Do I think the quantitative idea of CHAS means anything? Not much. You use mathematics to paint a picture of your qualitative idea, but the math is improperly used and the application, confused.

I don't know if it is even worth posting this.. does anyone else have opinions?


Tunewerk, you write like if you were running a temperature, it is quite embarrassing. I'm sorry for you, although your verbiage alone may eventually say it all, for others. All this is going to end very soon, I'm posting my reply to your editings and I'll reply on those last numbers you posted. That's it.

Oh... Please, you and the people you have mentioned may choose to go on with your crusade in a different thread.
.
_________________________
alfredo

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#1913046 - 06/13/12 06:52 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Tunewerk]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 625
Loc: Canberra, ACT, Australia
Originally Posted By: Tunewerk
Alfredo, I'm not going to play your game. Answer the questions posed, or don't. It only reflects on your own credibility.

I think it's disrespectful how you treated most of the established technicians (Kent Swafford, Bill Bremmer) when they asked for answers. You are not holding a holy grail - so stop creating that appearance. That is how you do a disservice to those trying to understand.

If you want to pay me for my time to proof your whole paper and go into lengthy discussions about how I think this is unfounded or that is mathematically inaccurate, I can, but I don't think it would be worth the time. The paper is so full of confusion, where would one start? Errors among a heap of tangled yarns? The formation of the yarn itself is error.

Now, I believe that you have some genuinely deep understanding about tuning that I haven't seen many people reference, but you've taken your understanding and turned it into this massive theory that doesn't support actually what it claims to do. It will produce very good ET according to standard rules. This ET equally balances the stretch of the 15th and compression of the 12th: exclusively dealing with this compromise.

So, do I think the qualitative idea of CHAS will produce a great tuning? Yes. It takes Bill Bremmer's and Bernhard Stopper's ideas of the 12th together with the understanding of a unity in tuning.. as opposed to only looking at one interval, to the exclusion of balancing of the others.

Do I think the quantitative idea of CHAS means anything? Not much. You use mathematics to paint a picture of your qualitative idea, but the math is improperly used and the application, confused.

I don't know if it is even worth posting this.. does anyone else have opinions?


Yes, it was very worthwhile posting and a good summary of my opinion also. thumb
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#1913048 - 06/13/12 06:54 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy

#1912614 - June 13, 2012 04:49 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Online blank

Registered: March 26, 2011
Posts: 181
Loc: Cambridge, 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."...

Edited by Tunewerk (June 13, 2012 08:51 AM)
- . - . - . -

Please, find my reply above. Now your editing, Tunewerk.

- . - . - . -

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

Thank you, Tunewerk (is this you real name?).

..."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"…

In my view, it is always better to separate tuning practice from theory and make a distinction between opinions and facts.

Theory: 12th root of two is the first ET formula, and it has little to do with piano tuning practice, as we tuners have experienced. Nevertheless, 12th root of two is still considered widely as our reference. Often we are told that the inadequacy of 12 root of two is due to inharmonicity. Chas model relates partial values to a sole "whole", which is based on ratios 1:1, 2:1, 3:1 and 4:1. This model addresses to "differences" from exact partial matchings, and enables to modify the scale theoretical values, as we happen to do in practice.

Practice: Thank you, Tunewerk, and I believe I'm not the only one. All aural tuners have good reasons for considering the entire piano with respect to all intervals. What I call "inter-modular" is not referred to practice.

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

Theory: Chas, as mentioned, puts forward the possibility to work with "differences", namely "delta-differences" which the variable "s" can modify. Thus I would not talk about "balanced dissonance", but variable beat-curves and progressions.

Practice: I never tune "perfectly balanced dissonance" (see Preparatory Tuning), this is why Chas model suggests the adoption of a variable and enlargeable stretch.

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

Referring to inharmonicity, the "realization" you mention took place only after relating stretch to partials non-linearity, and that was on the theoretical side. In my practice, as mentioned, I went for chromatic beat rate progression and for satisfactory (to my ear) intonation. After many years I decided to make a model that would represent my approach and tuning experience more faithfully than the current reference, 12th root of two.

..."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."...

No Tunewerk, I'd rather have said: Not only the 12th is (tonal?) important, all intervals are related to stretch, in fact I was not thinking in terms of key-tonality, nor single intervals, but in terms of "whole". I actually look at all intervals relations as a whole and I am well aware that all intervals are stretch-related, not only 12ths. That is how I could draw the Chas form, believing that intervals are related as in a system of levers, believing that even one interval small approximation would have had consequences onto the whole.

..."However, your theory is a mess!"...

Hmmm... Is this verbiage familiar where you live, or academic?

..."I finally understood some of the things that you were talking about in your paper."...

I'm sincerely glad for you.

..."I plotted your model to visualize it's behaviour. Pages 66 - 74 contain various obvious consequences and parallels from your basic CHAS equality."...

Good, oh… you haven't told me yet if you like it better than 12th root of two, or say 19th root of three, will you?

..."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."...

Well, that is all I could do. The English translation on its own took months, in pair with a TEFL lecturer... Can you imagine going through the whole glossary? Then I agree on graphs, a better job could have been done.

..."Your parallels to the Railsback curve are illogical leaps that show you must not fully understand inharmonicity."...

Hmmm... Robert Scott also said that long ago. After some months he admitted that in his tuner, iH had been corrected empirically.

..."...'Graph 4' on p. 72 cannot be correct according to your model. The cent deviation from regular ET will remain constant."...

I'm not sure... Are you saying that the graph is not correct? It certainly is. Perhaps you want to expand?

..."That geometry you have drawn on p. 68 has no relevance to anything in your paper."...

This may well be an oversight of yours. That geometry is significant in that some interval ratios (of which you read on p. 67) are represented and related to the scale (steps in cents). That is what you read in the title of section 3.5, (p. 67): "Effect of ±DELTA on incremental ratios - x represents scale elements (spaced in cents), y represents incremental ratios of scale per degree elevation. List of scale degrees (in ascending order), of ratios, and of number of related elements:..."

..."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."...

Like any drawing, Tunewerk, that is a representation, and you have left behind the ordinate: there I could position the scale degrees. As mentioned, its meaning is precisely related to those delta-differences ratios. Nothing more, nothing less. I would be glad if you were able to represent those ratios (p. 67) in a way that can be meaningful for you.

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

I'm afraid you have lost me.

..."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."...

Really? Good, "almost... Chas" is what I too am able to tune. Jeff would say... Welcome aboard!

..."However, not by your theory."...

Oh, well, I was expecting to read about mathematical errors, now I think I've wasted my time once more.

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

Of course, this last question may well be rhetorical, perhaps like the alarming "mess" you have entertained me with, regarding Chas theory.

Today Chas is published by two Universities, from Palermo' (2009) and Milan' (2010). The latter' is named "Bocconi", see if you can find a link to this University. The article is signed by Professor Nicola Chiriano, he speaks good English. After this session, I invite you to write to him for any question about Chas model.

Tunewerk, your "expert" website happens to be just one page of sentences. No other page is linked there and your home address is missing. I hope you understand why I wondered (and that was not rhetorical) what you real name is.

- . - . - . -

Gentlemen,

Sorry for the quality of this page. Tomorrow this game-non-game will hopefully be over.

Regards, a.c.
.
_________________________
alfredo

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#1913151 - 06/13/12 10:41 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1723
Loc: Vancouver, Canada
Originally Posted By: alfredo capurso


..."Your parallels to the Railsback curve are illogical leaps that show you must not fully understand inharmonicity."...

Hmmm... Robert Scott also said that long ago. After some months he admitted that in his tuner, iH had been corrected empirically.

Since Robert Scott has also thrown in the towel trying to argue with you, let me answer for him. He corrected and improved Young's formula for inharmonicity in his Tunelab software, using emprical data, long before you started the chas thread. This correction has always been documented in the Tunelab documentation, so your "after some month" comment is nonsensical.

Of course to appreciate the contribution of "an improvement over Young's formula" requires a basic understanding of what inharmonicity is, and to create that improvement (as RS has done) requires a deep understanding. You show again you do not have the basic understanding.

Kees

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#1913245 - 06/14/12 02:36 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: DoelKees]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy
Originally Posted By: DoelKees
Originally Posted By: alfredo capurso


..."Your parallels to the Railsback curve are illogical leaps that show you must not fully understand inharmonicity."...

Hmmm... Robert Scott also said that long ago. After some months he admitted that in his tuner, iH had been corrected empirically.

Since Robert Scott has also thrown in the towel trying to argue with you, let me answer for him. He corrected and improved Young's formula for inharmonicity in his Tunelab software, using emprical data, long before you started the chas thread. This correction has always been documented in the Tunelab documentation, so your "after some month" comment is nonsensical.

Of course to appreciate the contribution of "an improvement over Young's formula" requires a basic understanding of what inharmonicity is, and to create that improvement (as RS has done) requires a deep understanding. You show again you do not have the basic understanding.

Kees


Oh Kees, you misunderstand, or is it to make more noise? Please, again, stop it.
.
_________________________
alfredo

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#1913258 - 06/14/12 03:01 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Tunewerk]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy
Originally Posted By: Tunewerk
Alfredo, there's no game among us. We are asking you to please be straightforward and stop playing your game, if you would.


Using the one solution from your equality:

(3−∆)^(1/19) = (4+∆)^(1/24), ∆ = 0.0021253899646

From your paper (p. 65):

(3−∆)^(1/19) = (4+∆)^(1/24) = 1.059486544350

The cent value of your new halfstep ratio is:

1200 log[2] (1.059486544350) = 100.03831844 cents, 'r'

r * 19 = 1900.72805; 1901.955 (pure) - 1900.72805 = 1.22695 cents narrow of pure (12th) CHAS

r * 24 = 2400.91964; 2400.91965 - 2400.000 (pure) = 0.91965 cents wide of pure (15th) CHAS

2^(1.22695 / 1200) = 1.000708965 beat ratio for the CHAS 12th
2^(0.91965 / 1200) = 1.000531352 beat ratio for the CHAS 15th

I wrote beat ratio to mean, multiply any top note fundamental frequency of a 12th or 15th by its 'beat ratio' and derive the theoretical BPS of that interval in CHAS. It's clear that 12ths and 15ths with a coinciding top note in CHAS do not beat at a 1:1 ratio.

"Systematic analysis of beats frequencies revealed a new differences constant, that is, a 1:1 beats ratio on harmonic partials 3 and 4. The order of sounds described here thus constitutes a set of proportional frequencies as a function of synchronic beats: a dynamic, stable and perfectly resonant system." (p. 58)

What are the set of 12ths and 15ths with a 1:1 beat ratio in CHAS?

y = ((1.000708965 * x) - x) / (1.000531352 - 1)

If you work through the frequencies, it seems the 15th with a top note at about 499.26 cents above its respective 12th, has a beat ratio of 1:1. That is to say: the only set of 12ths and 15ths that will have a beat ratio of 1:1 in CHAS, are the 12ths and 15ths that have a common bottom note - not exactly, but close.

Peer review, please, if I've made any mistakes...

This is just one example of how CHAS does not form any more of a 'perfect synchronic set' than any other theoretical alignment. Only one set of intervals can have a 1:1 beat ratio at a time.


Hi Tunewerk,

From your post: ..."That is to say: the only set of 12ths and 15ths that will have a beat ratio of 1:1 in CHAS, are the 12ths and 15ths that have a common bottom note - not exactly, but close."...

This post of mine is to say why I had to take part to this, simply because you, Tunewerk, wrote a statement: ..."There are errors in your mathematics"...

Now, in your post I see no errors in the mathematics of mine. Instead, you show clearly how scale numerical values can well be derived from Chas algorithm. In contextual terms, your operations prove Kees Doel wrong, confirming once more that this ET model is effective. Two days ago you wrote:

..."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 - "...

You see, unfortunately I don't think I can solve your problems, even when you seem to mix up the meaning of simple words, like "theory" and "understanding". See, 12th root of two is a lame-born theory, nevertheless we can hear lovely tunings, thanks to the understanding of many many aural piano tuners.

..."This is just one example of how CHAS does not form any more of a 'perfect synchronic set' than any other theoretical alignment. Only one set of intervals can have a 1:1 beat ratio at a time."...

Please, allow me one recommendation: next time you refer to Chas algorithm, remember to include the "s" variable and specify its value. That's all.

Thank you.

Regards, a.c.
.
_________________________
alfredo

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#1913283 - 06/14/12 04:32 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7540
Loc: France
are not the cts to be used in Chas formula different from the cts used for the usual ET (I mean, are they compatible ? can cts even used ? I thought that only Hz could be used in such computations ?

Sorry for the naive question
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#1913559 - 06/14/12 05:19 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Olek]
Tunewerk Offline
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Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Kamin, yes, any logarithm can be used to measure any exponential expansion. It's a really good question and hard to visualize.

Using traditional cents as a measure gives reference to something we know. That's why I used it here, anyway.

Cents are like inches or centimeters for frequency doubling. Changing them would be changing the unit of measure which would make cross-comparison difficult.
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#1913912 - 06/15/12 09:25 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7540
Loc: France
CHAS singing :
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#1915778 - 06/19/12 02:00 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Olek]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy

Hi Isaac,

Nice posting... That's quite something.

Sorry about your last question, but I didn't want to carry out anonymous insinuations, I do not wish to be a "peer" of an anonymous poster that acts like a craven hypocrite slanderer. Those numbers prove only that cents relative approximations are not being considered, either due to ignorance or bad faith, you decide.

And I've never heard of tones producing lower partials than the fundamental; in fact partials (where I live) seem to go in ascending scale order; thus, in my view, expecting top-note coincident 12ths and 15ths going down the numerical scale is pure nonsense. Oh... If you were to know of fundamental tones that have lower partials... please let me know, because then I may have to revise the Chas model. wink

Regards, a.c.
.

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

Chas Tunings:
http://www.chas.it/index.php?option=com_content&view=article&id=64&Itemid=44&lang=en
_________________________
alfredo

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#1915823 - 06/19/12 04:20 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
Alfredo, do you realize both of these points are invalid/incorrect? I guess not, or you wouldn't have tried to make them.

Originally Posted By: Alfredo
Those numbers prove only that cents relative approximations are not being considered, either due to ignorance or bad faith, you decide.


Do you understand how cents measurements work? If I was to use 'CHAS' relative cents, everything would line up at zero! We would derive no comparison from that, nevermind that types of cents values are irrelevant for obtaining beat rates.

If we used 'relative' cents for inharmonicity measurements, the inharmonicity would magically disappear!

Originally Posted By: Alfredo
And I've never heard of tones producing lower partials than the fundamental; in fact partials (where I live) seem to go in ascending scale order; thus, in my view, expecting top-note coincident 12ths and 15ths going down the numerical scale is pure nonsense.


Well, let's see.. a top note coincident pair of 12ths and 15ths seems to exist plenty fine in my universe:

The 4th partial of the 15th and the 3rd of the 12th below the top note, aligning with the fundamental of the top note, forms a top note pair.

If you look back at my previous posts, and those of others.. I see only one thing happening: them being extremely patient with you, while you continue to peddle your theory without answering questions. You only have created more of a 'smoke screen', which seems to mirror the level of logic in your paper.

There seems to be only one slanderer: you, in defense of your opaque, indecipherable theory.
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#1915853 - 06/19/12 05:09 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy

Tunewerk (or whoever you are), as you prefer but, sorry, where do you think you are?

I don't think we need to agree, you know I'm not for DO unisons. Remember that you can start a different thread when ever you like. There you may share your understandings and write about whatever model and paper, even carrying on with your style and expertise.

You see, here again you confirm your arguments. I acknowledge everything that you have been able to write, now I kindly ask you (don't worry, this is not a question) to let me enjoy my sharing with colleagues (meaning real, name and surname piano tuners). Numbers and techniques should not represent a threat, in fact anyone is allowed to any individual preference, and beats... will always be there, well available.

Perhaps you prefer a particular type of climate, please, see that there is room for any climate.

Regards, a.c.
.
_________________________
alfredo

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#1915895 - 06/19/12 06:16 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 410
Loc: Boston, MA
I'm not trying to prove a point or start a thread, I'm trying to make sense of yours. That's why I was here - trying to understand you.

You so far have not specifically answered a single question. You just criticized my questions, to which your criticisms were objectively incorrect.

I see that you prefer a 'climate' of those who don't question or ask you anything objective, but instead accept CHAS with wide-eyed faith.

If you call objective questioning and analysis, not accepting of other 'climates', then you are right! It calls for a clear answer, which you have not been able to provide.

I would think it would be safe to assume at this point, that you cannot provide an answer because it is not there. You must not have an analytic understanding of what you propose in CHAS, only qualitative 'feelings' of what your tuning provides.

That is valid, so you should just state that, and avoid all the superfluous theory that will deceive and mislead people.
_________________________
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#1915927 - 06/19/12 07:48 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1723
Loc: Vancouver, Canada
Originally Posted By: alfredo capurso
Sorry about your last question, but I didn't want to carry out anonymous insinuations, I do not wish to be a "peer" of an anonymous poster that acts like a craven hypocrite slanderer. Those numbers prove only that cents relative approximations are not being considered, either due to ignorance or bad faith, you decide.

A cent is a frequency ratio of 2^(1/1200) and that's all there is to it.

Kees

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#1916903 - 06/21/12 07:15 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Grandpianoman Offline
2000 Post Club Member

Registered: 03/12/05
Posts: 2345
Loc: Portland, Oregon
Hello Alfredo,

Are there 12 offsets for etd's that we can try for CHAS? thanks, GP

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#1917164 - 06/22/12 10:18 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Grandpianoman]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy

Hi GP,

Nice question, straightforward and not wordy. There is one precise reason why I'm not making an effort in that direction, related to the fact that I would not be 100% sure about how those offsets would work in general. ETD's are not standardized (yet) and 12 offsets (probably) are not enough for Chas. The best solution (for my serenity) would be a "take" of all the offsets for one precise ETD, relative to one precise piano, directly from my tuning. Thinking how keen you are... I wish I could have answered yes.

Thank you for your consideration.

Regards, a.c.
.
_________________________
alfredo

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#1917298 - 06/22/12 02:29 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Grandpianoman]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 625
Loc: Canberra, ACT, Australia
Grandpianoman, CHAS is an ET-type tuning so it does not have specific offsets for an EDT that you would find in an UT tuning, such as EBVT. All 12 notes will offset in theory by zero. However, since the tuning is stretched slightly beyond normal 2-root-1/12 then the offsets will fan out progressively by about 0.1 cent or so for each semitone depending on the piano and the amount of stretch required.

To put this in another way, a normal ET tuning with an aggressive stretch starting though the mid-treble range will result in something like a CHAS tuning from my understanding. Something like a SAT tuning with a decent DOB added perhaps.


Edited by Chris Leslie (06/22/12 02:59 PM)
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#1917406 - 06/22/12 06:03 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7540
Loc: France
Not exactly Chris, the nearest approximation would be to obtain an even beating between 12th and 15th all along the scale.

But to get to the Chas tuning the piano have to be tuned a little large on the center string. Anyway that method works perfectly well (using pure 12 th on center string for instance, it will temper in the Chas final product when unisoned)
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#1917456 - 06/22/12 07:35 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Olek]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 625
Loc: Canberra, ACT, Australia
Originally Posted By: Kamin
Not exactly Chris, the nearest approximation would be to obtain an even beating between 12th and 15th all along the scale.

But to get to the Chas tuning the piano have to be tuned a little large on the center string. Anyway that method works perfectly well (using pure 12 th on center string for instance, it will temper in the Chas final product when unisoned)



Since GP asked for offsets I put my reply into an ETD perspective.


Edited by Chris Leslie (06/22/12 07:35 PM)
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http://www.chrisleslie.com.au

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#1917492 - 06/22/12 08:50 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Grandpianoman Offline
2000 Post Club Member

Registered: 03/12/05
Posts: 2345
Loc: Portland, Oregon
Alfredo, Chris, Kamin, thanks for the explanations.

My next question....do 12 offsets only work with UT's?

Alfredo, will you be here for the PTG Convention?

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#1917497 - 06/22/12 09:01 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Grandpianoman]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 625
Loc: Canberra, ACT, Australia
GP, the twelve offsets are relevant only to UTs. For ET the non-iH offsets would be all zero!
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#1917530 - 06/22/12 10:42 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Chris Leslie]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1723
Loc: Vancouver, Canada
Originally Posted By: Chris Leslie
GP, the twelve offsets are relevant only to UTs. For ET the non-iH offsets would be all zero!


Not quite. CHAS specifies equal beating octave+fifth and double octave, without imposing 2:1 octaves, leading to a stretch even without inharmonicity. There is a large discussion on this in the context of tuning some electronic piano (in which Alfredo participated) here.

You can thus compute the offsets on an imaginary zero inharmonicity piano and get:

! CHaS.scl
!
CHaS s=1
12
!
100.038318440222
200.076636880444
300.114955320666
400.153273760888
500.19159220111
600.229910641332
700.268229081554
800.306547521776
900.344865961998
1000.38318440222
1100.42150284244

As you can see the offsets are much smaller than the offsets generated by inharmonicity, so largely irrelevant for real piano tuning.

Kees

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#1917665 - 06/23/12 09:47 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1061
Loc: Sicily - Italy

Hmmm... Perhaps "largely irrelevant" or "relevant" is to be related to approximations?

Hi GP,

I even wonder if 12 offsets, on paper, would work with UT models. I do not know... perhaps in practice?

In fact, the 2:1 theoretical ratio, every 12 steps, would "double" differences-from-pure-ratio values. Then, if I understand correctly (...not sure at all), in order to expand the tuning beyond 12 UT's values, ETD's adopt an "iH model" (empirically re-shaped (?)) that (in practice) enables to correct and "regularize" the overall tuning curve, also compensating the 2:1 "doubling" effect?

I'm sure Robert Scott would be able to tell us more, as Robert has good knowledge of how ETD's can work, perhaps how different degrees of approximation can make a difference amongst ETD's?

On top of that, I'll have to rectify (in the near future) the ideas concerning the Chas target and principle... As Isaac mentioned, equal beating 12ths/5ths is (in practice) one close approximation that we can consider, when setting the premises.

Regards, a.c.
.
_________________________
alfredo

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#1917674 - 06/23/12 10:19 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7540
Loc: France
The iH model is just using the iH recorded with the notes of the piano, then use a decision on which interval may be beating more than the other.

The model is the problem of ETD , from what I understand, unless an iterative computation can be used that take in account maximum possibilities and choose which is nearer the wanted preferences.

That is how Dirk's tuner is working and I find it providing a very progressive tuning , less "model imprint" than I haver seen previously.
Those choice does not use an octave as model but the whole piano, more or less, so in the end it sticks more to consonance (or lessening of partials beating) than the others ETD have used.

If we use the partial match to compute a tuning, as it can be done with Verituner, the problem would be to weight the 2 prominent beats from the 5ths the 12 th, the 3ds etc..

Because what we hear in the end induce all the partials, some more than others but I believe it can be simplified only up to some point.
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