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#2206307 - 01/01/14 11:51 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1224
Loc: Sicily - Italy


...(((*20 HAPPY NEW YEAR 14*)))...


CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:

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
English - http://www.pdf-archive.com/2013/04/10/chas-prof-chiriano-english/

Chas Tunings (piano solo):

With orchestra:

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#2398307 - 03/15/15 07:58 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1224
Loc: Sicily - Italy
Originally Posted By Tunewerk
Alfredo, tuning a piano to a high level is in the end, an artistic process. Pianos and the inner ear have peculiarities, based on subjective perception, that isn't the domain of science.

I don't think anyone would deny that you are an artist of tuning after listening to the sound you've produced in recordings. However, it is arrogant to infer that intelligent technicians do not widely understand that ideal 12-TET tuning is based on more than one prime geometric curve other than (2/1)^x.

What you proclaim has been known formally since Stopper introduced the concept back in 1988. I'd argue he had to have had the same, or deeper, understanding to have realized the pure 12th was near the ideal solution in terms of bisecting the relevant curves. Yes, there are perhaps many still in the dark, but in the end these differences in practice are small.

If you really want to prove your case, a good idea might be to go back to your paper and correct the many errors in logic/proof that are there. I'm sure you can produce an excellent tuning, but I don't think you understand the basis behind what you are doing beyond the artistic sense. In the religious devotion to your idea, you seem to have become almost blinded in defense of what you regard as the only 'correct' solution.

The above quote was posted four days ago in "temperaments and tuning - why it matters for pianists".

Tunewerk, IMO it was off Topic. For me that came out of the blue and I do not think I want to engage on another discussion. See, perhaps if you manage to be less vague you will find others that are willing to add on.

As for my research, for those who want to know more, it is presented, described and discussed in this thread, and also here:


Sorry for all the 'noise' you may have to go through.

To All, have a nice Sunday.

Regards, a.c.

#2399407 - 03/17/15 06:58 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1224
Loc: Sicily - Italy

Hi Tunewerk,

Just to add some thoughts. Perhaps - in some way - you wanted to let me know that you have acknowledged the 'ideal' solution, and you did it.. in your way. In which case, this is to say that I did get it, and that I am sincerely glad for you.

You wrote also other things, on what was known before, about 'intelligent technicians', about errors in the Chas paper and about me, things that imo do not necessarily deserve a discussion.

Two passages though require some clarification.

The first, when you say "...pure 12th was near the ideal solution in terms of bisecting the relevant curves."

That still is. Both in theory and practice, pure 12th is near the ideal solution. Also other ratios happen to be 'near' the ideal solution, and we need to consider them, aiming at the beat curves we want when we actually tune a piano. This, I believe, is something that many expert aural tuners are well aware of, with or without theoretical background.

The second, where you write "...there are perhaps many still in the dark, but in the end these differences in practice are small."...

See, on the one hand, I do not think we need to promote approximation. Pianos, their dynamic nature together with the human/skill factor, already impose a fair amount of approximation; can't remember where I read this, but also in my experience 'small differences' can indeed make a big difference. On the other hand.. perhaps recently you have noticed how the ancient theoretical idea of 'pure' intervals and 'consonance' can affect our practical approach, and that (imo) is not at all a question of how 'intelligent technicians' are. This is to say that perhaps it is better not to digest a(ny) pure_interval ratio as if that was irrelevant, negligeable (in theory) or academic (in practice).

Last, I am not defending 'my solution', there is no need, I am simply trying to share it. If you are aware of other 'correct' solutions do not hesitate, start sharing.

Regards, a.c.

Edited by alfredo capurso (03/17/15 07:17 PM)
Edit Reason: Form

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