It works quite well in theory and in practice.

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

Kees

Cent.

Kees

I like how the replies get shorter and shorter here.

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...

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

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.
.

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)

I kindly thank you for permitting me to do this.

Kees

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].

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.

Hey! I'm post number 700! (are we any closer to figuring this out?)

Chris S.
Belmont, MA

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.




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

Tracing.

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



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



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



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



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.
.

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.
.

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.
.

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
.

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.
.

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.

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.

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.

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