Thanks Bill, I will ask for a recording on a grand Bechstein 2.20m , just bought by the pianist. I hope he will agree.

Great overview, Alfredo!

Thank you Alfredo and Patrick. Patrick, I have known about the verbal descriptions from my music education but I rarely think in those terms. The one I dislike the most is the one that identifies the notes from 1-88.

Alfredo, thank you for the other systems. I had no knowledge of these. I prefer the Helmholtz system that I described, of course and that is what the PTG Journal and the exams use, so I am used to that and prefer it.

However, knowing about other means of identification is useful and constructive, the same as knowing another language very thoroughly is. It is an expansion of the mind. When we do not limit ourselves to just one way of thinking, that we understand what other people say, in their own way, we become a more enlightened person.

That is why I did not choose to argue with you on the other thread when I gave my opinion. Yes, I do have my own opinion about what well temperament can provide. No, I do not choose to tune any pianos in the CHAS method because I feel that it is virtually the same concept that I would have if I were to tune a piano in ET but I choose not to do that.

This does not mean that I object to what you attempt to accomplish and any of the mathematical understanding of it. You should pursue it, by all means.

The Cordier method is yet another idea and is essentially off topic for this thread but it is noted by me as yet another variant of ET (in which I am not really interested). However, the translation of what is said is interesting to me. I have not yet commented on my opinion of the text but I do wish to provide an accurate translation of it in North American English so that anyone who is interested in it may form their own conclusions.

That is how the piano makers talk to us about the notes, so to avoid any confusion. (when giving dimensions, for instance)

English translation of Cordier Octave Tuning

(The original French is in Italics and the English translation is in bold face for clarity)

Pour les prolongations vers octaves graves et aigues très simples , simplissime même :
To stretch the octaves in the the Bass and Treble is a very simple procedure, even extremely simple:


Cibles ou targets : sortie vers aigus : do3-do4 1bat/sec , do4-do5 2bats/sec , do5-do6 4bats/ sur les très bons pianos , un poil plus (5-6)
Objectives or Targets: Starting towards the Treble: C4-C5 1 beat per second, C6-C7 4 beats per second; on very good pianos, just a bit more, 5-6 beats per second.

sur les pianos moins bons (là il faut de l'oreille musicale pour bien juger) ,
On pianos of lesser quality, a very good ear for music is required.

ensuite accélération exponentielle des bats dans la dernière octave .... Bien entendu le tout TRES progressif entre les cibles !
Then, an exponential acceleration in the beats of single octaves in the High Treble...of course, everything must progress very evenly between the objectives.

Je suis tellement habitué que je peux régler dans l'absolu une octave prise au hasard wink Of course , contrôle systématique des quintes qui se forment au fur et à mesure et elles doivent être toutes sans battement !
I have so much experience that I can tune very accurately any octave taken at random (wink of course), check any of the 5ths that are formed as a result and they would all be found beatless!

Sur les très bon pianos 12° obtenues automatiquement sans battement presque jusqu'en haut ;
On very good pianos, 12ths (octave-5ths) are formed beatless automatically;

sur les autres pianos : bonnes jusque vers lab 60 après ça bat lentement entre plus ou moins 0,7 à 2 (ça dépend du piano),ensuite les bats se stabilisent (plafonnent).
On lesser quality pianos: good up to G#5, after that slowly progressing to between 0.7 and 2 beats per second (depending on the piano), then the beats stabilize (reach a maximum).

Entre fa3 et la3 je me sers des quartes (progressives , plus ou moins en les plafonnant suivant l'état de la quarte la2-re3 , plus ou moins lente , obtenue lors de la réalisation de la partition) en plus des octaves pour bien calibrer en combinant avec l'écoute des dixième jusque vers fa4 ...
Between F4 and A4, I reign in the beating of the 4ths (progressively but permitting only a certain maximum comparing them to the 4ths between F3 and A3, more or less slow, found when the division is created), [I do not know what is meant by the last six words but that is what it says] plus controlling the size (width) of the octave by also listening to the M10s up to about A4...

Vers le grave utilisation :
1° des quartes jusque la1 env
2° des octaves dont il faut savoir apprécier la bonne lenteur (les quartes progressives et les quinte bien droites aident évidemment)
3° des quinte bien pures (du moins autant que le piano le permet à cet endroit)
4° écoute progressivité des sixtes et des tierces jusque vers le même La1 ; au delà 10° et 17° .

Towards the Bass, I use:
1. 4ths down to about A0 [??? (that is what it says, probably means A2)]; beyond that, M10s and M17s.
2.Octaves with a nice, slow roll (progressive 4ths and very just [pure, beatless] 5ths help to justify the width of the octave)
3. Very pure 5ths (at least as far as the piano will permit them)
4. Listen to the progression of the M3s and M6s down to about A0 [again, that it is what it says, I believe he means A2], beyond that, use M10s and M17s

Au delà la1 quintes bien pures et octaves cassées écoutées avec autant de priorité l'une que l'autre.
Beyond A0 [again, I think he means A2] very pure 5ths and broken octaves [I don't know what he means by "broken" but that is what it says, perhaps "open" or slightly wide)] with as much priority [as possible] of one over the other [I presume he means to favor the 5ths over the octaves]

Vers le grave 12° plus ou moins pures suivant qualité du piano . Pures sur les très bons , très très lentes sur les autres suivant état des cordes filées et qualité de la transition corde filées-cordes acier ... Là on rencontre souvent des discontinuités aux passages des cordes ... Preuve presque certaine de l'irrégularité de la progression de l'inh dans ce secteur ... :roll:

Towards the Bass, 12ths (octave-5ths) [are to be] more or less pure according to the quality of the piano. Pure on the very good ones, very, very slow [narrow] on the others following the state [amount of inharmonicity?] of the wound strings and the quality of the transition between plain wire and wound strings [make a suitable compromise according to how good or bad the break is]...There [at the break] one often finds a large discontinuity [dilemma] at the change of [one] string [type to another]...Almost certain proof of irregularity in the progression of inharmonicity in this area [of the piano]...

[Kamin]: About the 12ths stability , he stated :

Il est absolument clair que les 12° suivant leur état initial pourront donner l'impression d'une stabilité incertaine ... Seulement la 12° semble avoir au piano une assez grande plasticité suivant le lieu de la tessiture ...


It is absolutely clear that the 12ths (octave-5ths)following their initial state could give the impression of uncertain stability...Only the 12th seems to have a fairly large plasticity on the piano depending on the part of the scale. [I have no idea what the last paragraph means but that is a literal translation of what he said].

[Kamin]: [as he wrote it]It seem clear that depending of their initial condition the 12 ths may give the impression of some instability. But semm to me that the twelve, at the piano have a somewhat large plasticity, depending of the placement in the scale...


SO for what I understand my colleague is tuning a real Cordier (because of the speed of doubles and tripes octaves. he may have changed the sequence and sequence checks, but those bps rates speak to me as the Cordier sign (more or well accepted depending of the instruments). A recording is promised ....

Thank you for these translations.

Kamin is planning to recreate the tuning and record some pieces? Let's hope that the resulting tuning sounds good--it would be terrible if we found that the sound isn't good, after all of the attention Cordier has drawn and the time that you have given over to it.

Thank you very much, Bill, for your translation.

You wrote:... "The Cordier method is yet another idea and is essentially off topic for this thread but it is noted by me as yet another variant of ET (in which I am not really interested)."...

I'll write more about 1982 Cordier's ET variant in the Modern ETs thread.

Regards, a.c.

Hello.

Isaac, you wrote (April 06, 2010):

..."SO for what I understand my colleague is tuning a real Cordier (because of the speed of doubles and tripes octaves. he may have changed the sequence and sequence checks, but those bps rates speak to me as the Cordier sign (more or well accepted depending of the instruments). A recording is promised"....

It would be interesting to have the recording that was promised, also that colleague of ours may tell us whether he/she tunes three strings at the time or what. This could be relevant when having to count those beats.

Isaac (April 04, 2010)..."I've find that tuning [Cordier = pure fifths] so strong that he hide the piano "natural harmony", to my ears. As I've always have been tuning "in the piano spectra" as many tuners that state that "the piano tells you" , I perceive a too strong construction as something that push the envelope, but at the same time take precedence on what I perceive as "natural harmony" indeed that may sound obscure, it is may be only due to the very strong habit of hearing tempered intervals, but it is.

pppat (same day):..."Yes, same thing for me. Equal-beating 12ths/15ths seems like my upper tolerance limit, I get harmonically uncomfortable with a wider tuning than that (as you know through discussions here).

Neither am I sure why this is, but I'm glad I'm not the only one

PS my pure 12ths tuning is a little over a week old now, and it's settling in... with unisons adjusted, most 12ths are not pure anymore, but closer to equal-beating 12ths/15ths! I'm going to check the 2 weeks old pure 12ths tuning at the conservatory on tuesday, and see if the same thing is happening there."...

It would be nice to know from you, pppat, and about your tunings after some time was passed.

Regards, a.c.

CHAS Tuning MP3 (Granpianoman) on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

.

Hello.

Bill,

You have written more on My EBVT thread. I shall reply here, with my personal opinions, on some issues that may result misleading.

You say:...”We'll wait a few days for all of you to actually prove that you can reliably tell the difference and describe what it is about the EBVT III that offends you as compared to ET.”...

You and GP are then comparing EBVT and ET. Actually, in my opinion, you may be comparing a modern quasi-ET to an historical quasi-ET.

In fact, EBVT temperament has very small cents deviations from ET electronic values, probably smaller than many first/wrong ET attempts and smaller than what the piano itself is bound to produce with its own settlings. This temperament is then expanded through the use of equal beating 12ths and 15ths, which can be two ET scale constants as described and proved by the most recent ET theory.

The ET you are comparing EBVT with, is an ETD variation that can only refer to 12th root of two, our historical model. This ETD variation is likely based on an inharmonicity model, therefore it is not directly profiting from Modern ET theories.

So I ask: What is the point of your test? To guess which is which? Or which sounds better?

Then, you ought to decide if you would like EBVT to be valid, in that it can be “confused” with ET, or if you are going for “which sounds better”.

In the first case, there would be no need to fight a war against ET and you may then acknowledge ET's evolution and modern ET achievements.

In the second case, you ought to define your audience target and consequently adjust the tunings and recordings qualities, as well as specifying which ET you want to establish the EBVT supremacy on.

You write:...”We who are enjoying the pursuit of what we believe to be state of the art innovation in tuning concepts do not need to read comments from people who have already dismissed any such ideas purely on pre-conceived notions or beliefs.”...

You talk about innovation, about pre-conceived notions, but you may quietly ask yourself: what is my notion of Modern ET's innovations?

...”To those who have been seeking perfection in modern piano tuning merely by manipulating the amount of stretch in the octaves but still insisting on ET only, may I suggest that you have been "looking for love in all the wrong places".”...

I do not know who “those” are, nor if they exist. Personally, I have been seeking resonance and harmoniousness by looking for “natural” proportions, in that nature can be our reference, our common ground, more than individual preferences. And together with octaves, Chas is offering a Rule for tuning 4ths, 5ths, 12ths, 15ths and nicely progressive RBIs.

...”The idea that tuning theory reached its pinnacle with ET was popular in the late 20th Century. ET was the ultimate. The more perfected it could be, the better the music would be.”...

Not only that, Bill. The more harmonious and resonant our tuning could be, the better we all – composers and pianists, listeners and tuners - would enjoy music.

...”So, now in 2010, the May issue of the PTG Journal has two important and pages-long articles that say essentially that we have not yet found any ultimate solution at all. We haven't found the ultimate design for a piano and we haven't found the ultimate tuning for the piano.”...

The ultimate tuning for the piano? That depends on what you are looking for. You can see, again with “Fluid piano”, that tastes and preferences may differ a lot. Though, when it comes to the semitonal scale we have longed-for, from Aristoxene to present days, you may well consider all the route, from pure fifths tuning to Chas ET.

...”If you want a real challenge, it will not be how to stretch so much or not stretch so much ET but how you can give each key signature its own definition and character yet still have the piano be able to perform all music the way that only ET is thought of as able to do.”...

You see, you talk about ET but maybe you have only experienced the historical ET and its ETD stretched variations. And to me it seems that your challenge is how much you can "magically" deviate from ET electronic values, “yet still have the piano be able to perform all music”. About cents deviations, isn't the piano "magic" enough?

...”I have done that with the EBVT III. Can you do better? If you can, I will be tuning your temperament and octave stretching style on the pianos I service as soon as you can write it out.”...

I think I've written my temperament out, both in theory and in tuning practice, but isn't you saying that you are not interested in ET? This is how I may be missing the sense of your comparison.

Regards, a.c.

CHAS Tuning MP3 - amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf


.

Hi alfredo,

I think what Bill means is that EBVT III and modern versions of ET, although part of the thinking will coincide, still goes for different ideals.

You speak of making the piano as resonant as possible, where Bill wants it as musical as possible. You might argue that a piano sounding as resonant and balanced as possible is making it musical, but I'm not really sure about that.

EBVT III challenges harmony in a way that I really like. It gives movement to the progression of harmony. I'm not as concerned about whether this is the ultimate way of creating progression, I just say that it's there. And that thing - putting energy into harmonic movement - simply cannot be done using a symmetrical tuning.

So, I enjoy playing EBVT III. My studio at the conservatory have both grands in EBVT III, and it has become the first choice practice room among the students. Even when other grands are tuned more recently, it has stayed that way. They speak of music having a certain clarity and mood when played on these instruments.

I haven't told them that they are playing a different temperament.

Alfredo,

In the mp3 attached to your signature (the CHas Tuning.mp3 recorded on the Steinway S) the player often chooses the interval of the M6th, or at least bits of pieces that emphasize the M6. Nothing unusual there. Nice M6's.

You say earlier in this thread that in tuning, you see the use of "m3d M6 as being useless in the end." But I have to ask, in the final tuning, is there a specific check that you do on M6's? Narrow or wide in certain ranges? Beating equally with other intervals? They seem to have a specific color in CHas. Or does their sound arise only accidentally, in a manner of speaking, as a result of paying more attention to the M12's and M15's?

Hello Jake, I'll reply asap.

Hello Patrick, you write:

...”I think what Bill means is that EBVT III and modern versions of ET, although part of the thinking will coincide, still goes for different ideals.”

Part of the thinking will coincide? To me, this sounds a bit vague, can you be more precise? From Bill I learn that he doesn't even want to know about modern versions of ET. Perhaps you are talking about your meanings.

Different ideals? Maybe, I talk about a "natural" ideal, Bill seems to talk about his own ideal.

I really wonder how Bill can still ignore modern versions of ET, and what follows is only one possible (rational) guess:

Bill (and not only him) may be convinced that ET is represented by the ETD stretched variations of 12th root of two (see PTG examination). Bill may then be interpreting some objective approximations, typical of ETD variations, as ET's limits. Then, Bill may think that in order to get color and emotions (what ETD misses?) we have to go through some “magic-out-of-tune” key-chords. Bill then refers his magic to those electronic cents deviations.

This may have convinced Bill that EBVT sounds nice in that EBVT is not ET, since ET (the ET he knows) goes to detriment of color and emotions. As a consequence, Bill is not acknowledging ET's evolution.

In my opinion, beyond any ideological position, Bill may click when he discovers that EBVT, compared to ETD values for ET, gives back a better approximation of Chas.

...”You speak of making the piano as resonant as possible, where Bill wants it as musical as possible.”...

Resonant, musical, harmonious, euphonious, colorful, motional, emotional....as a pro tuner I'd say “in tune”. A well tuned instrument opens to all the above. More than that, here I talk about a scientific Temperamental Theory, neither word-games nor magics.

...”You might argue that a piano sounding as resonant and balanced as possible is making it musical, but I'm not really sure about that.”...

What do you mean by “musical”?

...”EBVT III challenges harmony in a way that I really like.”...

That is good. I quite like it too, as an ordinary listener.

...”It gives movement to the progression of harmony.”...

Movement to the progression of harmony? What do you mean? And compared to what?

...”I'm not as concerned about whether this is the ultimate way of creating progression, I just say that it's there. And that thing - putting energy into harmonic movement - simply cannot be done using a symmetrical tuning.”...

Sorry, together with “progression of harmony”, what do you know about “symmetrical tuning”? I would like you to be a “symmetry” expert and I hope you are not improvising. And if I may suggest, try to be concerned about ultimate harmony, nature's harmony.

...”So, I enjoy playing EBVT III. My studio at the conservatory have both grands in EBVT III, and it has become the first choice practice room among the students. Even when other grands are tuned more recently, it has stayed that way. They speak of music having a certain clarity and mood when played on these instruments.”...

Clarity and mood, OK Patrick, but yesterday you wrote:...”EBVT III brings color to the keys. Harmonic motion, not clarity”.

Please, make up your mind, all this sounds like verbal contortions. And sorry, I'm not a student. Which is the tuning on the other grands?

You see Patrick, talking about tuning while mixing different levels of expertize is quite a non-sense, it can eventually be confusing and you can see in the EBVT thread what it is leading to. You are a pianist and a teacher, I am a piano technician. I do have an idea about piano conditions in schools and conservatories, and about common “in tune”standards, so I can understand your liking EBVT. Yet I would hopefully discuss the meaning of a handful of cents with Bill himself and/or experienced colleagues, while to you (teacher) I'd only say: would you like a demonstration of Chas tuning? Or: can I help you with Chas theory?

...”I haven't told them that they are playing a different temperament.”...

Is it that mysteries go along with magics? Today you may duly tell your students, that is a fairly close approximation of a modern ET Theory.

Nice reading about symmetries:

SYMMETRY AND COMPLEXITY
The Spirit and Beauty of Nonlinear Science
by Klaus Mainzer (University of Augsburg, Germany)
http://books.google.it/books?id=Gr3TEgy5...p;q&f=false

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

.

He means ET has the permutation group on the 12-tone set as symmetry, EBVT does not.
Therefore in a harmonic progression in ET all chords have the same quality,
but not in EBVT (or most well temperings). So if in a V-I cadence in C, GB is wider
than CE, the cadence is enhanced as we now also hear the resolution of a poor third
into a better third.

Interestingly the neutral harmonic progressions of ET are also present in meantone,
where we have a restricted symmetry group over a limited set of keys. During the
MT period there was no real harmony, so one could argue one of the reasons the well-temperaments became popular is that they also enhanced harmonic contrast.

Does your CHAS theory have anything to say about major thirds? These have always been
the major focus of unequal temperaments, and in my opinion make or break a temperament.

Kees

Thank you, Kees, for helping with what Patrick may have meant.

Patrick is relating “ symmetrical tuning” with “putting energy into harmonic movement“.

You say:...”So if in a V-I cadence in C, GB is wider than CE, the cadence is enhanced as we now also hear the resolution of a poor third into a better third.”...

For example you say: G4-B4 is wider than C4-E4? And you mean EBVT? 12th root of two ET? Or?

Before I reply thoroughly, may I ask you whether you are a musician, and/or a theorist, a piano tuner? And/Or?

Regards, a.c.

Let me reword then.

If (if!) GB is wider than CE, in a V-I cadence in C,the cadence is enhanced.
GB is wider than CE in for example Werckmeister III, Lehman-Bach, EVBTIII,
but not in 1/4' meantone or ET (stretched or not).

I am all 3, but not a pro at piano practical tuning yet.

Kees

No, I'm fine, thanks, I don't need that. Fact is, when you throw that kind of lines in my face, I couldn't be less interested.

Hello Patrick,

I'm afraid you have misunderstood my words. With those lines I meant to say:

1- I find inadequate trying to fill up an expertize gap through posts
2- I do not find difficult to understand how you may enjoy one tuning or another
3- I would like to discuss about fine tuning with experienced colleagues
4- I'd be happy to give you, pro teacher, a demonstration of Chas tuning
5- I'll be happy to deepen with you any issue on Chas theory

I apologize for any other meaning you may have picked up, most probably due to my English (?).

Hello Jake,

You say:...”In the mp3 attached to your signature (the CHas Tuning.mp3 recorded on the Steinway S) the player often chooses the interval of the M6th, or at least bits of pieces that emphasize the M6.”...

I should not think that was intentional. The player, Alessandro Petrolati, piano technician and lecturer at University of Macerata, after witnessing Chas tuning was kindly asked to play anything he wanted, possibly with a slow rhythm.

...”You say earlier in this thread that in tuning, you see the use of "m3d M6 as being useless in the end."...

Would you report my own words, so that I can contextualize them? Personally, I do not use those tests, but beat-coherence, i.e. the increment of the beat rates for chromatic intervals must make sense in proportional terms (a:b=b:c=c:d=etc.) and must be smooth.

...”But I have to ask, in the final tuning, is there a specific check that you do on M6's?”...

Generally, I check the progressiveness of M6's and other intervals on Pre-form tuning, on center strings, from about F2 to C6.

...”Narrow or wide in certain ranges? Beating equally with other intervals?”...

M6ths are never narrow, nor equally beating with other intervals. Chas form has only two equal beating intervals: 12ths (narrow) and 15ths (wide) all along the keyboard. All other intervals have their unique beat rates. If anything this, in my opinion, ends up adding color and character to each single key signature.

...”They seem to have a specific color in CHas. Or does their sound arise only accidentally, in a manner of speaking, as a result of paying more attention to the M12's and M15's?”...

Chas tuning is not an expansion of the temperament section, it is an ordered, inter-modular form (we could say a whole or a set), so nothing really can be accidental. In Chas form everything is consequential, all intervals contribute to the form, which is the result of (attention to) all intervals beat rates.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.

Alfredo:

My apologies--it was Kamin who spoke of not paying much attention to M3's and M6's, here: http://www.pianoworld.com/forum/ubbthreads.php/ubb/showflat/Number/1343718/Searchpage/8/Main/86822/Words/m3d+M6+as+being+useless/Search/true/Re:%20CIRCULAR%20HARMONIC%20SYSTEM%20-.html#Post1343718

But I was glad to read your response about checking M6's, which I do like the sound of in CHas. Someone else was asking about your M3's, and I'd like to hear what you have to say, too. One of the criticisms of ET is of course its widely stretches M3's. I must admit I haven't determined if M3's are more narrow in CHas than in ET. (I still want create some elementary graphs to compare the widths of the intervals in various temperaments. There are of course many charts that list the data, but I'd like to create simply several sets of lines, marked like rulers, with one group marking off the widths of M5's in each temperament, another group marking the width of octaves, another the width of M3's, and then M10ths, and M12ths, etc. Or would I be reinventing the wheel--have these been drawn up already?)

I didn't mean, by the way, that the pianist was intentionally playing a lot of M6's to demonstrate the sound--it seemed more that the interval was attractive to him in CHas, so he found himself playing it. Or at least I found myself noticing and liking the color of the interval in CHas as he played...

Cheers.

With regards to the size of the M3 in CHAS, it is wider than 12th-root ET. This is because the octave is wider, and a wider octave causes wide intervals to get wider. However, if you tune an ET using an octave size similar to CHAS - between 4:2 and 6:3, then the M3s will have pretty much the same width. The RBIs progress in almost exactly the same way as normal ET, it is the size of the octaves, 4ths and 5ths that progress in a different way.

I would recommend Scala (free software) for that. It comes with just about every tuning
anyone has ever thought of, and you just type the offsets from ET to define a new temperament. It allows you to plot sizes of any interval you want in any format
you can imagine. It also allows you to tune MIDI files (good for quick checks).
http://www.huygens-fokker.org/scala/

Kees

I've played around with Scala some. I'm just wanting to create simple line drawings that put the widths of the M3's, M5's etc of the major temperaments, particularly the various meantones and wells, side by side. Which means that I just need to sit down and look at the charts and do it...

In Scala: Analyse-->Tone circle. Set generator to 7 (fifths). Then hit "Temperament Radar" button and you can see M3's m3's and P5's plotted in a circle of fifths.

Kees

Hello Kees,

I'm glad to learn that you are a musician, a theorist and a tuner practicer.

You say:...”if in a V-I cadence in C, GB is wider than CE, the cadence is enhanced as we now also hear the resolution of a poor third into a better third.”...

This may result from the approach to consonance and dissonance in those times, and from having to interpret and manage the “wolf”. Also, I would think that the degree of desirable enhancement can only be subjective.

...”Interestingly the neutral harmonic progressions of ET are also present in meantone, where we have a restricted symmetry group over a limited set of keys.”...

Saying “neutral harmonic progressions of ET...”, you may refer to equal size semitones, accessibility to all keys and overall harmony. Say that “neutral” was then the goal, unfortunately 12th root of two ET did not get it. In fact that model stretches 5ths and 3rds in favor of pure octaves. The 2:1 ratio determines a module restricted to 12 tones, so the temperament is not expandable beyond the octave (Research report, section 4.3).

In 12th root of two ET, thirds are theoretically the same size, though in stretched octaves practical tuning, beat-wise, they are not (I'm not sure this was a point).

You say:...”During the MT period there was no real harmony, so one could argue one of the reasons the well-temperaments became popular is that they also enhanced harmonic contrast.”...

Yes, It may also be argued that once we started seeking harmony we needed to contrast the wolf, so well-temperaments where enhanced. May harmony and shareability have called for ET (and ET's evolution)?

Patrick stated: “...putting energy into harmonic movement - simply cannot be done using a symmetrical tuning.”...

I wondered then about “energy” and “harmonic movement”, how they were related, and whether Patrick referred “symmetrical tuning” to theory or tuning practice, Patrick himself may say.

In Chas theory “energy”, “harmonic movement”, and “symmetry” are referred to beats and to their dynamic proportions and synchronism.

Chas is not a 12-tone nor a 19-tone set, as it is not related to zero-beating, pure intervals (Research report, section 3.4 ).

You ask:...”Does your CHAS theory have anything to say about major thirds?”...

What to say? With a classical approach, Chas 3rds on paper may result wider, but it goes in favor of minor 10ths. Actually in Chas all intervals (and tensions) are maximally related by the multiple, combined action of all partials. In fact, partial 3's delta acts on 4ths and 5ths, partial 4's delta acts on 3rds and 6ths. The octave then is a sub-module and the set symmetries can be defined purely in terms of beats and beat-coherence (Research report, section 3.5).

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Gracias! I spent about two hours trying to map out a meantone last night. Entering the data took about two minutes. Trying to line up text boxes indicating the distance between the M3's while fitting them all in a single line took up the rest of the time. You may have saved me from much pain and suffering.

I assume music is subjective, perhaps you believe there is a divine music and tuning independent of mankind? A respectable point of view, held through the ages by tuning theorists, but not very common nowadays.


No I mean that a V-I sounds the same in F major and C major in meantone as well as in ET. In MT the semitones are very different. Listen to a chromatic scale in 1/4' MT, e.g. Sweelinck's chromatic fantasia. This tuning has strong melodic effects too.

Yet as long a you avoid the wolf all keys sounds the same in MT.

Thanks for the other clarifications.

Kees

Hello Kees,

To me saying: I would think that the degree of desirable enhancement can only be subjective.

You reply...”I assume music is subjective, perhaps you believe there is a divine music and tuning independent of mankind?”...

Well, in guessing my believes you may say “divine” meaning a precise category. In that case I do not think there is a divine music, nor a divine tuning. You can indeed say music be subjective, like this all world might be, but then I need to make some distinctions.

In this world there are some phenomenons that we can regularly observe. From their regularity we try to gain a Rule, from their loyal reproducibility we try to achieve a shareable Law.

I think of music mostly as production of sound and rhythm.

Sounds and resonance phenomenons are related by fairly precise proportions, which are manifest in nature, and therefore not strictly subjective.

A vibrating string is observable in quite objectives terms, and so is resonance. From objective observations we could see that in a vibrating string all partial sounds are ordered in a well known, precise sequence, the harmonic series.

From the harmonic series we may have learned the harmonic mean, one kind of average.

Then, I tend to think that my/your/our (musical) ear can well be related to/calibrated on fairly precise sound proportions. More than “divine”, I would then think in terms of “natural” harmony or “matter's harmony”, referring to those proportions which are independent of mankind and yet to a certain extent shareable, since they may already reside in most of us. Has it ever happened that you could agree with someone else on a poor, flat or sharp pitch? It has happened to me.

Rhythm as a notion, is even more objective than pitch and both are translatable into frequencies.

My research went for an order, both from sounds and rhythm, namely the beat rate (or beat-frequency, period, coherence time), two vibrating strings can steadily reproduce, what may then be said an “intrinsic” order.

Off course, words like objective and intrinsic are strictly related to investigation tools and subjective urges, first of all the urge to share some feelings and meanings.

Back to temperament and the enhancement of a V-I cadence, thinking to the dozens of artistic, compromise-type WT available, I prefer Chas*, simply because through my tuning I can enjoy all pitches and all keys, I can feel light (partial sounds), energy (resonance) and harmony (in tune) without having to be combed against poor and better intervals.

(*) The “s” variable of Chas algorithm (Research report, section 3.3) opens to any sort of subjective preference - on this you may find the kite analogy, in this thread. Thinking “dynamic” has helped me not to take a prejudiced position and overtake the objective Vs subjective antinomy. As a theorist, you may appreciate that.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.

The kite analogy was posted here in June 04, 2009 - 05:30 PM

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Regards, a.c.
.

Thanks Alfredo for that elaboration. I am encouraged to bring up yet another matter.

Does CHAS have anything to do with difference tones? As you probably know
apart from the series of partials, when two notes sound together the difference
of their fundamentals is also produced. A common trick used in pipe organs; you can get
a 32' pipe from two 16' pipes tuned a just 5th apart.

Now in conventional ET the difference tone of a M3 is about 80cent off, quite gross.
Also when sounding e.g. a just C6-E6-G6 the 3 difference tones are C4 (twice) and C5
but in ET you get C4-82cent, C4+67cent, and C5-6cent which is a disgusting mess.

Kees

Hello,

...”Does CHAS have anything to do with difference tones?”...

I have not calculated Chas difference tones.

Resonance enhancement may result from the relation between fundamental frequencies, partial frequencies and beats periods.

Chas manages to relate and proportion scale frequencies and beats periods with one (scale incremental) ratio. It is my opinion that this double-ring* relation opens to synergy and may determine a self-exciting system.

...”As you probably know apart from the series of partials, when two notes sound together the difference of their fundamentals is also produced. A common trick used in pipe organs; you can get a 32' pipe from two 16' pipes tuned a just 5th apart.”...

Are you familiar with pipe organs?

...”Now in conventional ET the difference tone of a M3 is about 80cent off, quite gross.
Also when sounding e.g. a just C6-E6-G6 the 3 difference tones are C4 (twice) and C5 but in ET you get C4-82cent, C4+67cent, and C5-6cent which is a disgusting mess.”...

Yes. That looks pretty bad. Are those figures theoretical or real? I haven't had a chance to measure Chas-ET real frequencies, so I'm not able to release any figure in cents. Sorry.

(*) Maybe I should say double-spiral.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.