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#1917868 - 06/23/12 10:34 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1540
Loc: Vancouver, Canada
Originally Posted By: alfredo capurso
I even wonder if 12 offsets, on paper, would work with UT models. I do not know... perhaps in practice?
It works quite well in theory and in practice.
Originally Posted By: alfredo capurso
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?

You do not understand, because you don't know what a cent is apparently.

Kees

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#1918256 - 06/24/12 09:37 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: DoelKees]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1540
Loc: Vancouver, Canada
Originally Posted By: alfredo capurso

#1917868 - Yesterday at 10:34 PM
Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]

Originally Posted By: alfredo capurso
I even wonder if 12 offsets, on paper, would work with UT models. I do not know... perhaps in practice?

DoelKees
1000 Post Club Member

..."It works quite well in theory and in practice."...

Originally Posted By: alfredo capurso
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?

..."You do not understand, because you don't know what a cent is apparently."...

Kees, I believe this new thread could house your educational too. By posting your understandings in here, you could explain at length what ever you think it is not understood.

Regards, a.c.

CHAS 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

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


Cent.

Kees

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#1918512 - 06/25/12 12:33 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: DoelKees]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 394
Loc: Boston, MA
I like how the replies get shorter and shorter here. wink

Probably the most effective route.

I sure would like to understand what mathematical basis Alfredo was going for here in his work. I can't understand the math in the paper because it's not correct/sufficient to explain what he qualitatively describes.

I do believe Alfredo understands something about tuning that most machine tuners do not understand. Only the best aural tuners have talked about tuning this way. There is something between machine tuning (the strict science of offset numbers) and aural tuning.. and it is a big gap for those who can hear: The difference between considering the entire partial bandwidth, instead of a point and considering all partials, instead of one at a time.

I see Alfredo going for this in his own way. There seems to be a point at which all partial expansions can be balanced to a point of best fit. Sometimes I would call this similar to Haye Hinrichsen's reduction of entropy.. but this does not describe what happens all of the time.

So aside from your confusing logic, a word of support Alfredo, for your non-reductionist ideas about tuning.

Now if you could just answer questions honestly and openly...
_________________________
www.tunewerk.com

Unity of tone through applied research.

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#1918681 - 06/25/12 10:54 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Tunewerk]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1540
Loc: Vancouver, Canada
Originally Posted By: alfredo capurso

Well, Tunewerk, the question may be when you reduce yourself, behaving as an anonymous slanderer who spends his time with obsessive s-talking. But, I believe you got one meaning for an s variable and deviating... behavior? wink
.

I don't think such posts are acceptable. Since it was not directed at me I'll just tell you to go wash your mouth with soap, rather than ask the moderator to ground you for a while.

Kees

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#1918742 - 06/26/12 02:22 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: DoelKees]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy
Originally Posted By: Grandpianoman
Hello Alfredo,

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

Originally Posted By: alfredo capurso

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.
.
Originally Posted By: Grandpianoman
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?
Originally Posted By: alfredo capurso

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.
.
Originally Posted By: DoelKees
Originally Posted By: alfredo capurso
I even wonder if 12 offsets, on paper, would work with UT models. I do not know... perhaps in practice?
It works quite well in theory and in practice.
Originally Posted By: alfredo capurso
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?

You do not understand, because you don't know what a cent is apparently.

Kees


Hi Grandpianoman,

Here is a short paper (below) that may explain exhaustively the meaning of my replies (above - let me know).

Look for: Fred Lieberman, WORKING WITH CENTS: A SURVEY.

Best wishes,

Alfredo

- . - . - . -

Kees, you may devote yourself to study and/or, if possible, post your comments in the …Comments thread.
.
_________________________
alfredo

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#1918877 - 06/26/12 11:12 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6331
Loc: France
I tried on Tunelab using those offsets on 12 tones, to see if when going up the scale by ear with similar progression, I obtained an even beating of 12 th and double octave.

It seem to work to some point, but I was not really sure.

Anyway when I use an ETD I tune "by ear" in the "marshmallow zone" of the ETD display.

BTW I have used an ETD with a display in Hz, makes you really aware of the pitch instability of the piano tones, in fact the cts display seem to show only apart of the tone, I mean you are more or less obliged to wait for the tone to be quiet to use the display.
(or there is an algorithm that helps to smoothen the display so it is easier to read).

I used that Dirk's software and the display is very fast, so I had to choose a moment in tone and to tune at that moment.

I was very surprised by the accuracy (progression of all intervals) in the end, when compared with that display.
To be complete I may say I tuned a vertical piano and Dirk's noticed to me that a few notes have really unstable and uneven partials (which explain the jumps in the beat curves of some intervals.

That is presented as a tool for pianists and amateurs, but frankly the result is straightforward with a very nice tuning. (and the price is not very high)

Someday other styles of tuning will be inserted based on even beatings or any pure interval wanted.



That software use an algorithm that sound logical, doing the same thing as the aural tuner that look for the nicest tone in the intervals he tunes. (simply as he can check for more intervals than an aural tuner the progressiveness is less skewed (with a favor for 5ths and octaves , seem to me, but no problems with octaves beating at the 2:1 level, which is what most tuners are doing)





Edited by Kamin (06/26/12 11:14 AM)
_________________________
Isaac OLEG - http://picasaweb.google.fr/PianoOleg pro

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#1919138 - 06/26/12 09:49 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1540
Loc: Vancouver, Canada
Originally Posted By: alfredo capurso

Kees, you may devote yourself to study and/or, if possible, post your comments in the …Comments thread.
.

I kindly thank you for permitting me to do this.

Kees

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#1919218 - 06/27/12 12:35 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Offline
Full Member

Registered: 03/26/11
Posts: 394
Loc: Boston, MA
CHAS (chaz, n.; chaz*zed, to chazz, v.):

1. (n) A specific kind of equal temperament stretch tuning that aligns equal beating lower note 12ths and 15ths along a curve (as distinguished from Bill Bremmer's method of equal beating upper note 12ths and 15ths), while regarding all other intervals as well; not to the exclusion of the former.

2. (n) The theory that purportedly explains this more specifically, or any related theory that goes by this name.

3. (v) Any theory which uses the same tactics as CHAS and presents lengthy evidence to confuse the reader into a spindle of illogical fury, in order to eclipse the absence of any explanation whatsoever.

Syn.: Any equal temperament tuning methods that are already in wide use by the best aural tuners today, to put greater stretch into modern piano tuning to maximize harmonic alignment.

Any discussions relating to these subjects that confuse all of the above.



I'm confused. Are you? After all this work, talking about CHAS and trying to understand what it is, I confess, I still do not.

Is it supposed to be like a Jackson Pollock?.. I will 'get it' after staring for several hours in an alcohol-induced haze? But everyone 'gets it' in their own way?

Torsional plane? Helix structures? The golden ratio inscribed in the tuning? Nevermind that the number referenced is the sqrt {5}, not the actual golden ratio, which is [1 + sqrt {5} / 2].


Edited by Tunewerk (06/27/12 12:55 AM)
_________________________
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Unity of tone through applied research.

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#1919225 - 06/27/12 12:57 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Olek]
Grandpianoman Offline
2000 Post Club Member

Registered: 03/12/05
Posts: 2242
Loc: Portland, Oregon
Kamin, what 12 CHAS offsets are you referring to?

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#1919279 - 06/27/12 05:30 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Grandpianoman]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6331
Loc: France
Originally Posted By: Grandpianoman
Kamin, what 12 CHAS offsets are you referring to?



I dont recall exactly but I suppose I used the 12 first offsets as stated above : + 0.038 + 0.076 + 0.114 etc..

As it is (was ?) supposed to be linear, I thought I would get to a Chas temperament when making the 2 first octaves like that.


Edited by Kamin (06/27/12 05:33 AM)
_________________________
Isaac OLEG - http://picasaweb.google.fr/PianoOleg pro

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#1919330 - 06/27/12 08:25 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Chris Storch Offline
Full Member

Registered: 08/13/09
Posts: 171
Loc: Massachusetts
Hey! I'm post number 700! (are we any closer to figuring this out?)

Chris S.
Belmont, MA
_________________________
Chris Storch
Acoustician / Piano Technician

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#1997763 - 12/11/12 07:45 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Chris Storch]
alfredo capurso Offline
1000 Post Club Member

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

All, hello.

Yesterday, surfing the web, I've casually found one more work on Chas:

www.luciocadeddu.com/tesi/Cannas_triennale.pdf

Cagliari's is now the fourth Italian University (after Messina, Palermo and Milan's) involved with the divulgation of the Harmonic Temperament, and that is why I am very happy to share this news with (some of) you. For translating I often use Lexicool... In case, let me know if I can help.


Originally Posted By: Chris Storch
Hey! I'm post number 700! (are we any closer to figuring this out?)

Chris S.
Belmont, MA


Hi Chris, are you any closer to figuring Chas out?

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 (piano solo):
http://www.chas.it/index.php?option=com_content&view=article&id=64&Itemid=44&lang=en

With orchestra:
http://www.youtube.com/watch?v=SQ9BYCbJOfs
_________________________
alfredo

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#2048563 - 03/15/13 05:30 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

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

Tracing.

Re: Pro Tuners -Do you ever re-assess the ETD stretch? [Re: RonTuner]#2048118 - March 14, 2013 02:07 PM

Originally Posted By: alfredo capurso
Originally Posted By: RonTuner
Here on Pianoworld, we've read about at least three systems that claim to define that "perfect" piano tuning/stretch. There's a long thread on the C.H.A.S tuning, Dirk's software, and the OnlyPure approach...

What I have noticed while using multiple software platforms, and communicating with techs trying out different paths, is that our perception for what constitutes "the perfect stretch" is influenced by the particular approach we're currently using... It's almost as if our ears get trained to listen for the results that our approach place on a piano. This also applies to aural tuning that uses the same checks over and over on every piano. Something along the lines of "yup, my checks all work out fine, the piano is as good as it can get"

Where most of the approaches fail is dealing with the more difficult scales to tune - those smaller instruments that just are tough to make musical... Maybe I'll take a look at Dirk's to see how it deals with these!



Hi Ron,

Thank you for mentioning the model I'm sharing, as you say my tunings are the result of my approach to practical "intonation" and theoretical/numerical issues.

You also mention "checks" and throughout my own research (as an aural tuner) I have considered maximum beat-coherence and whole "in tune" resonance as my right and fair targets.

I understand what you mean, when you mention "...those smaller instruments that just are tough to make musical...", and I happen to have stated that I have never had particular problems with that.

Since I believe you to be sincere, I think it is fair on my part submitting also a sample of my own tuning on a small piano, in fact the smallest Yamaha model. That was one single (my first) tuning on that worn and modest piano which had not been tuned for many years, during my stay in Paris (2010) when I first met Isaac. The site is the customer's (Sebastien Buchholz), he asked me to make a video...

"Almost" Chas, dissonances that we can still perceive clearly as dissonant, crispy as in my experience it can be (expecting more hysteresis), together with... what ever else you may notice in there.

Hmmm... I did not want myself to appear but... never mind, I apologise for that and for my casual improvisation.

http://s814.beta.photobucket.com/user/papafard/media/491_1437.mp4.html?sort=3&o=10

Regards, a.c.
.


Re: Pro Tuners -Do you ever re-assess the ETD stretch? [Re: alfredo capurso]#2048301 - March 14, 2013 08:29 PM

Originally Posted By: Olek

Shame on you, Alfredo wink

That said, the main result with your tuning approach is that there is always something we can refer to, whatever the scale and piano quality.

indeed very agreable. I noticed that something similar happens when the "pure 5th" sheme is tune, but sometime (with high iH probably" the piano tone turn to a cheap organ quality (Bontempi tone) that seems to be added, above the piano harmony.

The advantage of CHAS is that it takes in account what the piano proposes .While tending to or using a theoretical scheme, you are not addicted to a particular 10th beat rate, for instance.. the scheme itself inclued enough intervals to find its place (more or less correctly against theory) naturally.

But the temp sequence have to be respected (as the method, probably)

Greetings



Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm]#2048351 - March 14, 2013 10:08 PM

Originally Posted By: alfredo capurso

Hi Mwm,

As regard to theory and practice, I would never confuse a quip that tries to be clever with something serious, ideal-academical studies do have value, when they enable us to better describe our "world".

An ideal stretch does exist, throughout the compass, in theory as far theory can go, having to combine prime numbers in a scale, and in practice, every time we aim at harmoniousness and re-find our favorite theoretical references, on every single piano.

It does matter whether you consider ET's or a well temperament, in that the "tuning principles" are very different: 12 root of two rules the octave exponentially, Cordier's ET rules a fifth, Stopper's rules a 19th, the Chas model rules the whole 88 compass.

When you ask about any WT-expansion you touch one nerve centre of tuning, carefull because... it might be... panic, and you seem to understand that any WT ends up being a quasi-ET, the more you expand it, the closer to a modern ET. So, for any WT, the "best possible" seems to be when you can confuse the WT's theory with ET practice; the same does not apply to the set of rules I refer to.

Isaac,

Thank you for your comment, I share what you say.

But... you know me too well.. believe me.. I'm still ashamed!! blush

Regards, a.c.



Re: Pro Tuners -Do you ever re-assess the ETD stretch ? [Re: Mwm] #2048401 - March 15, 2013 12:13 AM

Originally Posted By: Phil D
When an aural tuner achieves the most pleasing compromise amongst all the pitches of the piano, he has made some value judgements along the way, according to what pleases him the most. Others would make different judgements, as they have different tastes.

Your analogy with a 'perfect ET' is false - there is no such thing as one single perfect ET. There is the theoretical ET, based upon A=440 and the 12th root of two ratio between semitones, but this is purely theoretical. There are, however, many actual ETs that can be tuned on a (well-scaled) piano, and this is what the aformentioned aural tuner will have tuned on the piano. An actual ET is one where there is an equal ratio between each semitone, and there is a nigh-infinite array of these that can be applied to a piano and it be pleasing.


Hi Phil,

Your post says [Re: Mwm].

I would like to add to what you said, but I'd go off topic there... May I ask you which analogy you are referring to?

Regards, a.c.
.
_________________________
alfredo

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#2049908 - 03/17/13 08:06 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
I was replying to Mwm's post at the bottom of the previous page, where he referred to 'perfect ET'.

I don't really appreciate having my words copied into this thread. It is inappropriate to quote me here, as what I said does not relate to this thread.
_________________________
Phil Dickson
The Cycling Piano Tuner

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#2050163 - 03/18/13 10:12 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
Originally Posted By: Phil D
I was replying to Mwm's post at the bottom of the previous page, where he referred to 'perfect ET'.

I don't really appreciate having my words copied into this thread. It is inappropriate to quote me here, as what I said does not relate to this thread.


Thanks for your reply, Phil, and I'm sorry to have copied your words in here, but I did it for two reasons: firstly, because many times I read some opinions that I find stimulating, but too many times I forget where I had read them; secondly, because I thought that what I was going to add would have been off topic at Mwm's, being it very much related to my own ideas on aural tuning, theoretical ET, perfect ET, 12 root of two, equal ratios, along some issues represented in that post of yours and in this thread.

Regards, a.c.
.
_________________________
alfredo

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#2051551 - 03/20/13 08:01 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

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

Hi Phil and All,

Just some thoughts in regard to what I have recently read in PW on equal temperament and tuning, in fact the fair incipit.

As an aural tuner I ask myself: am I tuning according to what pleases me the most? And... if I answered yes, to me that would sound as a simplification.

I used to tune my guitar that way, and I shall say that when I first tuned 13 pitches on a piano, I did try to do that according to what pleased me the most, I mean in relation to my "musical ear", but the result was quite terrible. Soon after I had to rationalize what actually pleases me and, above all, why some chords may not please me at all.

Later, I realized that "my taste" (read "my musical ear") showed to have some leeway practically on all bichords, and that leeway was not reducible "by ear" - i.e. on the bases of my taste - by tuning note by note.

Then I understood that I could not achieve "..the most pleasing compromise amongst all the pitches of the piano..", by making "..some value judgments along the way" basing on my taste, although I had consider myself able to "judge" when individual intervals sound "in tune". Evidently, it was complex chords making tuning more complex.

It was then that I started to come to terms with beats, and I discovered that my beat and rhythm perception was more precise and steady, say more severe and univocal than my musical taste; since then, I could not reduce the whole question to a simple matter of taste anymore, in that it was clear that my pleasure was strictly dependent on beats and on the way beats mix together.

I also noticed that by dealing with beats I was able to match my taste more consistently, and that would not happen by chance, but only when my tunings had rendered a precise order, like a geometrical regular form, a beat proportional order that made sense in terms of rhythm.

In my opinion, if musical "taste" is taken into account as the only parameter, perhaps even the same tuner may have "different tastes" from one day to the next - here referring to the ear's leeway I mentioned - without even knowing if the taste of the day depends on tiredness, on mood or something else.

If we consider rhythm (and sense of rhythm), instead, we can compare two or more beats and "judge" consistently, even objectively, their slower/similar/faster relation. In other words, our musical ear seems to have a more variable gradient than our sense of rhythm, which in fact appears to be fairly strict and shareable objectively. On this, I would really appreciate your (aural tuners and musicians') feedback.

I read: ..."there is no such thing as one single perfect ET."...

In regard to theory, we may all know how the centuries-old problem related to prime numbers has been considered irresolvable. The literature on this is quite abundant, and we may well acknowledge that the apparently "irresolvable problem" is the direct consequence of the theoretical approach to the scale, that is when (and every time) the theoretical scale is based on one pure interval.

That is (historically) where the idea of a (theoretical) compromise comes from, and when (in practice) we started thinking in terms of "pleasing compromise", instead of "optimum" or "ideal".

On my part, I would like to discover that perfect ETs can be many and that we are able (and allowed (?)) to tune ET along our individual taste, perhaps hoping to match the customer's.

As a matter of fact, my experience suggests a different conclusion, to the point that I cannot exclude the existence - in theory - of one single perfect ET.

For instance, I think about a cycloid, a purely theoretical form that we are enabled to represent also in practice. Be it theory or practice, we basically need to fix a point, draw a circle and make the circle rotate. There we can modify the length of the radius but only the scale will be different, the actual geometrical form and its intrinsic (and well shareable) proportions will be the same, two radius of a circle being always in 1:1 proportion.

It does not matter, really, if the actual circle we draw is going to be perfect, and I do not mean "perfect ET" in that sense, what matters is that we are (and always will be) able to replicate that form in force of (theoretically) correct constraints and some practical references. That is how, in this context, I understand theoretical perfection.

@Musical scale and ET ratios.

In theory we truly have a "nigh-infinite array" of ratios that we could well employ for gaining an exponential scale, but does it mean that in practice there are a "nigh-infinite array" of ET scales? Let's check.

Considering aural tuning and the state of the art, we can reasonably exclude all those theoretical ratios that would produce narrow octaves, so here we gain a first downward limit; then we could exclude all ratios that would produce wide fifths, here gaining the upward limit.

Still, in between 12 root of two and 7 root of 3/2 we may count a "nigh-infinite array" of ratios but, again, does it mean that we can only proceed tentatively (read "with no reference") throughout a "nigh-infinite array" of ETs? I don't think so, and in order to expand on this I will keep a distinction between theory and practice, yet attempting a reconciliation, in the idea that theory and practice together can enhance our work.

12 root of two is - historically - the first ET compromise between two intervals, and we ought to discard it not really because it is "purely theoretical"; it is not "pure theory" that makes our goal - sound and consistent ET aural tunings - vague and approximate, in this case it is wrong theoretical indications. We ought to discard this ET ratio in that, as an attempt for a theoretical "compromise", it favors one pure interval, the 2:1 octave, therefore it cannot represent a theoretical "optimum", nor a convenient reference.

And, on a strict theoretical ground, we may reasonably say the same about 7 root of 3/2, 19 root of three and any other pure-interval-based theoretical ratio.

By excluding all the above ratios we are still left with an infinite array of other theoretical ratios, all apparently suitable for ET and the ideal compromise. If anything though we may temporarily conclude that the "perfect ET" should not favor any pure interval.

How to further reduce the amount of ET ratios by using a criteria that makes sense, when our musical ear does not help anymore?

Of course, what follows is my own answer: look for the theoretically correct constraint, and I mean "theoretically correct" only when the constraint, as for our cycloid, can be replicated and demonstrated in practice.

Regards, a.c.
.
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#2062371 - 04/10/13 12:37 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: Olek]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1053
Loc: Sicily - Italy

Hello Isaac,

I do not see any Caesar.. whatever was shown is now and again your being, which I find astounding.

Your... dévouement constant, à vouloir rationaliser et améliorer tous les moindres détails, votre désir d'une solution partageable et non la vaine gloire, et votre esprit grand ouvert, votre honnêteté et votre cœur, c'est ce que je vois... dear friend.

Alfredo
.
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#2062938 - 04/11/13 01:55 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1053
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Hi All,

I would like to thank a colleague from Canada, Ernest Unrau, for being so kind as to re-editing the English translation of the article written by Professor Chiriano on the Harmonic Temperament, and published by the Bocconi University (Milan - Italy).

I had some problems with the definition of the graphs and also some figures had mixed up; Ernest has fixed all that and provided a nice front page:

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

Below is the link to the original Italian version:

http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

This is the first time I use that pdf-archive, I hope it works.

Cheers, a.c.
.
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#2071284 - 04/26/13 07:38 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
hundenapf Offline
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Registered: 05/29/10
Posts: 2
I have read the entire thread over the last couple of days and have to admit that I am as confused about this topic as before.
I am comparing Cordier and Chas side by side in Pianoteq by loading their scala scales and find both of these stretched octave ETs more pleasing than "regular" ET with fixed octaves but beyond this sentiment of my personal taste as a simple musician I am lost and more confused than ever now but nevertheless would like to thank all involved for elaborating on this topic so deeply and passionately.

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#2071604 - 04/26/13 02:47 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1053
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Thank you, hundenapf, for sharing your appreciation.

For me it would certainly be interesting to be able to (aurally) evaluate Serge Cordier's temperament and Chas, in the way they are being proposed in Pianoteq. Do you think it might be possible? Even a short recording would do and perhaps a simple, slow execution of some chords would be enough.

As for "confusion", I will be happy to expand on any other issue that might be somehow obscure.

Regards, a.c.


Edited by alfredo capurso (04/26/13 06:00 PM)
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#2072102 - 04/27/13 12:47 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Tunewerk Offline
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Posts: 394
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This thread should really be omitted from discussion. Some of the best tuners in the world have asked questions, only to receive a charade in return. Inquiry has been met with condescention.

It's okay to be confused, hundenapf. Some of the best tuners and very bright minds have considered CHAS, trying to understand it deeper. As far as I know, everyone has come away confused.

I don't think it is okay at all to be condescending to someone asking genuine questions.
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#2076622 - 05/03/13 12:09 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
Originally Posted By: alfredo capurso

Hi All,

I would like to thank a colleague from Canada, Ernest Unrau, for being so kind as to re-editing the English translation of the article written by Professor Chiriano on the Harmonic Temperament, and published by the Bocconi University (Milan - Italy).

I had some problems with the definition of the graphs and also some figures had mixed up; Ernest has fixed all that and provided a nice front page:

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

Below is the link to the original Italian version:

http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

This is the first time I use that pdf-archive, I hope it works.

Cheers, a.c.
.
Originally Posted By: hundenapf
I have read the entire thread over the last couple of days and have to admit that I am as confused about this topic as before.
I am comparing Cordier and Chas side by side in Pianoteq by loading their scala scales and find both of these stretched octave ETs more pleasing than "regular" ET with fixed octaves but beyond this sentiment of my personal taste as a simple musician I am lost and more confused than ever now but nevertheless would like to thank all involved for elaborating on this topic so deeply and passionately.
Originally Posted By: alfredo capurso

Thank you, hundenapf, for sharing your appreciation.

For me it would certainly be interesting to be able to (aurally) evaluate Serge Cordier's temperament and Chas, in the way they are being proposed in Pianoteq. Do you think it might be possible? Even a short recording would do and perhaps a simple, slow execution of some chords would be enough.

As for "confusion", I will be happy to expand on any other issue that might be somehow obscure.

Regards, a.c.



I was going to forget: in case, please try to make sure your questions are genuine.

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 (piano solo):
http://www.chas.it/index.php?option=com_content&view=article&id=64&Itemid=44&lang=en

With orchestra:
http://www.youtube.com/watch?v=SQ9BYCbJOfs
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#2134767 - 08/18/13 10:38 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

Hi All,

Good news on the Chas divulgation's front: it seems that a major Institution in Europe is organizing the first 3-days seminar for in-house students and professionals... Once the dates are official I will be able to tell you more...

As a general news... :-) last July I moved to London, yes, so that I can get an idea about other tuning-standards and see if I can develop some new contacts, both in the academic and the professional environment.

I am sure you can imagine what the last two months have been, with so many things to organize and issues to sort out... and, I must admit, my energy is not like when I was 21... Anyway, now I am feeling quite settled, even more relaxed with my English, since very few people speak... English in London!! :-)

I look forward now to meeting some PW friends (oh, Isaac, London is only two hours away from Paris...?), be it only for a nice beer or anything concerning Chas. Phil, Ian, also a PM will do...

As promised, I start reporting (below) what I explained to a poster, when he kindly asked:

..."could you explain exactly what Chas is to me...

My first reply:

..."I thought I should start from a generic description; please tell me what may sound obscure, it could be due to my English or to some other reasons. I would be grateful if, at some stage, you could revise this explanation so that I can post it in PW, hoping that it will help the sharing.

The Chas model is the result of my empirical research. It all started from the idea that, at least in our tuning practice, it might be possible to achieve not only a "compromise" but a perfect sound scale, and that, perhaps only subsequently, it would be possible to describe this in theoretical terms as a temperament theory. It also started from the idea that even when we play or sing melodically we refer to and reproduce parts of a just, well-regulated whole, rather than a single, pure interval.

If beats are the effect of combinations of fundamentals and partials in time, if beats can truly define the color, the character, the tension of any chord, then beats deriving from all sound relations and combinations must have a proportional order. I hypothesized that this could have been the key to a self-ordering sound whole.

Today in the Chas formula, (3 - ∆)^(1/19) = (4 + s*∆)^(1/24), s =1 establishes the 1:1 delta-proportion which defines the incremental ratio of the logarithmic scale; delta, (referred to differences from 3:1 and 4:1 partial matchings) represents the function that the "s" factor can "adjust". This is how the Chas model enables proportional beat curves to be drawn for all chromatic intervals.



When I began tuning, I had learned that ET thirds should be progressive, fifths should be narrow, fourths wide, and octaves (if possible) beat-less. With this in mind, I first tried to obtain smooth and coherent progressive thirds, but there was no way to do this, not even within the first temperament octave. Fourths and fifths could beat in a similar fashion, but I found them to be disordered. Then I opened to the idea that perhaps fourths, fifths and octaves too needed to be progressive. Some years later I understood that fourths and fifths could not be progressive in a monotone beat curve: those curves needed to be dual.

The last step was understanding that we cannot achieve any form unless we establish the correct premises (see Chas Preparatory Tuning in PW) and take into account the piano's overall dynamics. Only then did I notice that 12ths and 15ths, as the overall result of beats proportion, were beating at the same rate (edit: today I should write "...beating similarely"), though one was narrow and the other wide; then I realized that those two intervals may well have functioned as the single constant for our correct ET scale. In other words, I was able to achieve the form and the formula only after ordering all beats proportions and progressiveness, by taking account of the piano adjustments.



The basic Chas algorithm, (3 - ∆)^(1/19) = (4 + ∆)^(1/24), uses 3 and 4, which are the (natural) values of the partials relative to 12ths and 15ths, together with 19 and 24, which are the number of steps/keys (starting from zero) where we find 12ths and 15ths positioned in a semitone keyboard.

Once I had the formula, I thought that its simplest form did not represent what I needed: the possibility to adjust the preparatory beat rate progressions dynamically, according to the requirements of the piano. So I added the "s" variable, an arbitrary parameter that makes it possible to change the delta value and (potentially) gain infinite incremental ratios and microtonal adjustments. 


Thus Chas combines all intervals by managing and proportioning differences from pure ratios. The (logarithmic) scale incremental ratio is determined by the delta factor (which stands for differences), and by the "s" variable that stands for our (arbitrary) rational. 


By studying theory, I learned that all previous models had been developed on the basis of some unjustifiable assumptions: firstly, that pure ratios only (2:1, 3:2, 5:4) could have perfect consonance and harmony; secondly, that the temperament module needed to encompass only 12 semitones (13 notes), all the other intervals being tuned with the help of copied octaves; thirdly, that in order to gain the best compromise we should "slice" the frequencies of the scale and keep one theoretical pure ratio (2:1 for the octaves, see also Cordier's pure fifths and Stopper's pure 12ths). It was also believed that combining primes 2, 3 and 5 in the same scale was simply impossible.



Instead, what happens now is that partial 3's delta can bend, say modify fourths (4:3), fifths (3:2) and octaves (2 = 3/2*4/3); in a combined balancing action, partial 4's delta too can stretch all those intervals, plus thirds (5:4) and the double-octave. Partial 4 also reaches the two-octave compass and so interrelates all octaves.



As in practice, every interval now has its own unique theoretical beat curve and maximum beats coherence within the whole. Chas employs both linear and logarithmic beat proportions: in general, differences on exact partial matchings progress logarithmically, like the scale frequencies; differences on 12ths and 15ths, in the way they are related (with constant equal (opposite-in-sign) values), express the linear proportion (1:1 (when s = 1)).

So, as a temperament theory, Chas modifies the approach to the definition of the scale frequencies. Instead of "slicing" frequencies, we can manage all differences (that is what we do in practice), down to any zero beating "pure" interval. Chas proves that an ideal sound whole does exist and, if the premises we set were to be correct, we may actually experience it."

- . - . - . -

Regards, a.c.


Edited by alfredo capurso (08/18/13 10:55 AM)
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#2148399 - 09/11/13 06:44 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
Originally Posted By: alfredo capurso

Hi All,

Good news on the Chas divulgation's front: it seems that a major Institution in Europe is organizing the first 3-days seminar for in-house students and professionals... Once the dates are official I will be able to tell you more...



Hi,

Now the dates have been fixed, the seminar will take place on the 19th, 20th and 21st of November 2013 at the ITEMM, Le Mans (France):

http://www.itemm.fr/site2/page.php?pp=2961

I am glad because three days is enough time for covering both theory and practical tuning evidences, and partecipants can receive specific training and perhaps even tips on tuning-hammer techniques and variable tuning curves.

The number of partecipants is restricted, I will post more details as soon as I can.

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

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

With orchestra:
http://www.youtube.com/watch?v=SQ9BYCbJOfs
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#2168449 - 10/19/13 11:00 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
All... Hello,

The post quoted below was waiting for more feedbacks, more exactly there:

When I wrote: “...What I’m stating is: even thinking to non-iH tones, traditional ET pseudo-model can not give you progressive intervals...

You (edit: Robert Scott) answered back:

”Nonsense. Of course the intervals are progressive for non-IH tones. Just play any cheap electronic piano (I say "cheap" to make sure it does not simulate inharmonicity, which the expensive ones do). The beat rate of 3rds, 4ths, 5ths, etc. will be prefectly progressive. They will all increase as you go up the scale. (Unless you are inventing a new defintion for the word "progressive" too.)”

I think you are right, one of us is saying nonsense. In my opinion, if you were familiar with beats you could never say that. Give me a little time, and I’ll help you with precise reference brands and 4ths and 5ths reference intervals. In the meanwhile please, keep your definition of “progressive” but notice that RBI beat-rate progression can also be rough or smooth. A rough-hewn RBI progression will leave disorder amongst SBI, what some aural tuners may well know.

- . - . - . -

In these days (thank you, guys) I have read other comments on electronic keyboards and temperaments, Robert. Oh... four years have gone!!


#1217935 - June 16, 2009 10:52 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS


Originally Posted By: alfredo capurso

Robert, thank you.

In one previous posts of yours you wrote:

“I don't know what false assumptions you are attributing to ET. As far as I know, ET does not make any assumptions at all.”

Have I succeded to explain you that?

You say:

“Clearly you have in mind a definition of the word "inharmonicity" that is different from what the rest of the world means by "inharmonicity".

Have I talked about iH definition? No, I have and I am talking about the reference model on which basis iH’s effects have been calculated.

About the case of a pipe organ you wrote:

“It has harmonics. Those harmonics are true. They are locked to the fundamental. If air pressure changes, then the pitch of the pipe will change, but so will all its harmonics, and they will remain locked. That is the definition of zero inharmonicity.”

Please tell me, when you say “It has harmonics…..that is the definition of zero inharmonicity”, what are the harmonics values you are/they were referring to, when fixing zero iH?

“Whether or not 12ths and 19ths sound good does not change this fact.”

Whether or not 12ths and 19ths sound good, this may change our reasoning about traditional ET pseudo-model V iH.

“You certainly can and do get progressive intervals from the traditional no-stretch ET model,…”

Do you mean, on a pipe organ? By the way, are you an aural tuner?

…“Now when it comes to instruments that have inharmonicity, like the piano, nobody uses the traditional no-stretch ET model. So you are criticizing a model that nobody uses for the piano anyway.”…

I am criticizing traditional ET pseudo-model because it is a lame reference model, with or without iH.

When I wrote: “...What I’m stating is: even thinking to non-iH tones, traditional ET pseudo-model can not give you progressive intervals...

You answered back:

”Nonsense. Of course the intervals are progressive for non-IH tones. Just play any cheap electronic piano (I say "cheap" to make sure it does not simulate inharmonicity, which the expensive ones do). The beat rate of 3rds, 4ths, 5ths, etc. will be prefectly progressive. They will all increase as you go up the scale. (Unless you are inventing a new defintion for the word "progressive" too.)”

I think you are right, one of us is saying nonsense. In my opinion, if you were familiar with beats you could never say that. Give me a little time, and I’ll help you with precise reference brands and 4ths and 5ths reference intervals. In the meanwhile please, keep your definition of “progressive” but notice that RBI beat-rate progression can also be rough or smooth. A rough-hewn RBI progression will leave disorder amongst SBI, what some aural tuners may well know.

When you said:

“...Some say that the octaves should be beatless 4:2 octaves. Some say they should be slightly wide of just. And they are both right.”

I retourned you my opinion:

“In my opinion, they are both – you choose the word – bewildered? Lost? Puzzled? Disconcerted? Mixed up?”

You answered back saying:

”I would say they are entitled to their own opinion.”

Ok, generally speacking I quite agree, but I’m not writing about an opinion festival. Chas model’s interweaves prime numbers and relates scale’s frequencies on the basis of a new ET theory, a theory deriving from a dynamic approach to beats. In other words, Chas model proves how proportional beats can define an infinite number of scale’s ratios, quite the opposite of what has always been done.

You finally say:

"IH experts" as if IH was some deep notion, accessible only to a few. It is an objective physical measurement that anyone can make with the proper equipment. They do not have to be an expert. By way of analogy,…”

I am referring to those technicians able to make laboratory measurements and calculations with sophisticated technology. Masons still work with a tape (God bless them), land-surveyors don’t anymore. As you may notice, I’m treating a semitone ratio that, compared with traditional ET pseudo-model, differs 0.00002.., and produces an A5 octave difference of 0.2337..

Tooner, thanks for your commitment.

You say:

“I have been able to learn a great deal from this Forum. Others have corrected errors when they find them. By doing so, it maintains the integrity of the vast knowledge that can be found in past posts. I feel an obligation to help correct errors, also. Your paper and posts are in error because of your misunderstanding of iH.”

I feel a similar tipe of obligation, this is way I would ask you to be very responsible and utterly precise when you say “your paper is in error”, as I would also ask you to acknoledge that I do not ignore iH, I precisely think it should be calculated by using a correct reference model.

You kindly wrote:

“The iH of other notes can be determined by multiplying 0.10000 times (2 ^ (1/8)) ^ (the number of semitones above C3). A3 is 9 semitones above C3. So the iH of A3 = 0.1 * (2 ^ (1/8)) ^ 9.”…

This formula is the base of all your calculations. So I ask you: how wide are you calculating the semitone? What partial values would you expect with “zero inharmonicity”?

Certainly you will have red where our cello-expert writes: “…the outstanding symmetry of the 19th root of three ET can still be preserved with proper consideration of inharmonicity.” What do you think he meant, saying “…proper consideration of inharmonicity”?

Bill, Kent,

I will contribute to what you are saying asap, thank you.

Regards, a.c.
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#2168474 - 10/19/13 11:52 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Online   content
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Registered: 03/14/08
Posts: 6331
Loc: France
Hi Alfredo, very nice to read that.

Chas have been yet "understood" and recognized by some French tuners, that tried it, due to the preparatory sequence publication.

As I told you yet may be it made me recognize the high consonant spot it produce, I believe it is to the point I can "tune CHAS" directly, based on the energy perceived in the octave.

Now a feel preparatory tuning is an extremly strong "launching ramp" for all the scale.
It raise the "impression of justness" making it easy for the mind to grasp (as for other instruments as I noticed, they adjust very naturally to Chas)

Having done that possibly it is just me, but I wished more variety and also to avoid too fast beating major intervals in medium range for some pianos.

I will then certainly use a "partial CHAS" being aware of the consonance but allowing it to express itself only above c5 for instance.

That is me, certainly, in any case I always use the "launching ramp" system, the main reason being the settling of pitches is taken in account that way (Pitch raise are easier when the method have been learned).

I tend to compress the temperament zone those days , and do so within a CHAS framing that have been installed at a point or another.
That make a zone which is a little compact and the rest can correctly fall in place with the Chas consonance in the ear.

You told me that CHAS, (as ET , to simplify) is a "goal" We are lucky the instruments seem to grasp on it easily, naturally and even seem to stay there long term for whatever reason.

I find it funny to hear CHAS in simple octaves, and it works more of course when more of the piano is yet tending or tuned in CHas mode.

SO , we do not need extra large hands or comparaisons of 12-15, to use it.

I do not know if you agree, in any case the temperament have to be the launching ramp so your beat progression method have to take place anyway.

I will be very pleased to mee again. Let's see if I can go to le Mans for a "hello" .

I may say that your explanations based on numbers and theory may relates more to acoustics than to piano tuning, hence the way the tuning community is not at easy with.

Hopefully those are things that are more easy to practice than to understand the theory 'for me)

ALl the best

Isaac

P.S Alfredo, there is an argument you may have heard and you may have adequate answer to.
CHAS is a tuning mode for pianos or instruments having iH.
It is a way to take iH in account, without sacrificing to the cycle of 5ths and ET "rules".

SO it is perfectly suited for pianos, and I am unsure it will work as musically on an organ (as octaves motion will be more perceived)

As I am a piano tuner this suit me perfectly.

PPS this is a "CHAS" attempt, on a 1838 Pleyel pianino played with a cello - I gave that link yet.

https://docs.google.com/file/d/0B6GjQDkF_AMQWDBacURRZjY5OHc/edit?usp=sharing

Having done that for a choir and barocco ensemble on a Stein Forte, I noticed also how easily the justnesse blended/ eventually putting a little aside the "original" tone of the instrument, if you see what I mean (it does not squeak as a door needing oil)


Edited by Olek (10/19/13 12:29 PM)
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#2172209 - 10/26/13 06:38 AM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6331
Loc: France
ALfredo, something is wrong with your link

The dates are visible but the content of the training not.

http://www.itemm.fr/site2/page.php?pp=2961

Can you please provide it ? I could translate if you want, and send it to the ITEMM.



Edited by Olek (10/26/13 06:39 AM)
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#2172281 - 10/26/13 10:33 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

Thank you, Isaac, I will try to email my contact this afternoon, but I am not sure I'll get a reply before next week.

This below is the "Prochains Stages" page:

http://www.itemm.fr/site2/index.php

I hope to be able to add on that (and on your other post) in a short time.

Buon weekend, a.
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#2191374 - 12/02/13 11:26 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

Hi All,

A brief report about the last event at the ITEMM... I met different level students, various teachers, one researcher (on temperaments) and one piano manufacturer. It was exiting and rewarding, though here I'd like to share what was new to me, i.e. a different approach to the construction of a piano:

http://www.stephenpaulello.com/

I haven't heard this piano "live" yet, but it makes me very very curious.

Regards, a.c.
.
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#2191442 - 12/02/13 01:04 PM Re: CIRCULAR HARMONIC SYSTEM - CHAS [Re: alfredo capurso]
pyropaul Online   content
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Posts: 132
Loc: Montreal
Originally Posted By: alfredo capurso

Hi All,

A brief report about the last event at the ITEMM... I met different level students, various teachers, one researcher (on temperaments) and one piano manufacturer. It was exiting and rewarding, though here I'd like to share what was new to me, i.e. a different approach to the construction of a piano:

http://www.stephenpaulello.com/

I haven't heard this piano "live" yet, but it makes me very very curious.

Regards, a.c.
.


Antoine Herv plays one in his on-line Jazz lessons. See http://www.youtube.com/watch?v=R6S8RCKRIoY for example. Very very nice sound.

Paul.

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