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

Kees

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.

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.
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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.

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.
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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.
.

Yes, it was very worthwhile posting and a good summary of my opinion also.

#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.
.

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.
.

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.
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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

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.

CHAS singing : [video:youtube]?v=uRu3CZfteyY[/video]

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.

Regards, a.c.
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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, do you realize both of these points are invalid/incorrect? I guess not, or you wouldn't have tried to make them.



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!



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.

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.
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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.

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

Kees