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Isaac, Alfredo:

Very good example - the difference is highly noticeable. The CHAS tuning sounds uniform, yet open.

What would be the "standard tuning" of the file that CHAS is compared to?

Jeff,

What would pure 12ths in the mid-range break down to octave-wise, in your experience? 6:3's, or somewhat narrower?

This as a practical question, given different inharmonicity and scaling problems. I can do the math theoretically (as I know you can), but what's your 'hands-on' experience?

Isaac,

could you give a more specific explanation? 2:1 octaves and 3:2 fifths sounds good in theory. Did you invent a new instrument or something? :-D

Pat, in mine (experience) , less than 6:3 , a very quiet octave in fact .

Thanks for the quote, Alfredo, and I do agree on what you wrote here.

I'm also been following your work (mainly due to Isaac's kind updating), and I really like your concept. I will try it out.

Which brings me to a thought. Would it be a good idea to summon this method in a separate thread? The preparatory setting, the idea of stretch and so on. These threads have had a rather vivid posting rate, and the basic information gets somewhat hidden in here.

Just a thought. Being a math person myself I find the principles for your way of tuning interesting, I would certainly try it if I got the reference litterature in a more compact form.

By the way, I think this forum is great for the curious ones. Always something new to try, new challenges, helpful hints, and so on. It's really good to have this community-style exchanging of ideas going on!

Yeah, all the good information is so difficult to find amongst all the nitpicking and defending! A summary of techniques would be so very useful, if you have the time or the inclination!

Alfredo, you did mention wanting somebody with the english skills to help you write something about this technique. Perhaps I can be this person, if you would like to work together on producing a usable tuning sequence etc.

..."Perhaps I can be this person, if you would like to work together..."...

Yes N a M, what a nice offer, thank you, I'm looking forward. I'll be back home in a week's time, otherwise I'd be willing to start tonight, were the circumstances appropiate.

..."It's really good to have this community-style exchanging of ideas going on!"...

It is my pleasure too, glad that you are curious, Pat.

Regards, a.c.

Not a Mongoose:

Did you see the CHas Preparatory Tuning thread? I created a preliminary list of the major qualities of CHas there, and Alfredo made corrections. It might serve as a point of departure. These is a sequence of steps in that thread, too. Not a conventional (Anglo-American?) sequence, exactly, since Alfredo doesn't set a one octave bearing, but it may let you construct something closer to a conventional sequence.

Just a passing note. I just read that A.J. Ellis, whose essays on pitch and tuning are often cited here, was one of the sources for Shaw's Dr. Higgins in "Pygmalion" and thus for "My Fair Lady." Henry Sweet, who studied with Ellis, appears to have been the main source, however.

Had no idea.

You should read the introduction to Pygmalion for the exact details. For that matter, it is worth reading the entire play, including the epilog.

Bill, thank you for your explanation. I'm replying here since we talk about ET, music and theory, though I do not consider my self a musicologist.

You say:...“Yes, Alfredo, it means that he (Rameau) changed his mind about what he was interested in. The temperament he used was a modified meantone and it was VERY unequal and that was typical of his time.”...

We may as well say that Rameau changed not only his “interest”, he changed his entire approach to intervals and temperament issues.

...“Just like Bach, he decided at one point that he wanted a temperament that was more accessible to all keys.”...

You call that “accessibility” which to me sounds indefinite, I'd call it “in tune”, i.e. the sense of the intervals proportions that we can share. In other words, they were looking forward to getting reed of any “wolf”, they were simply asking for maximum euphonicity.

...“The theory of ET had always been there, since the time of Pythagoras and even before that among the ancient Chinese way before the common era.”...

This may be a simplification. The “idea” of equal size semitones is very ancient, but the practice for progressive intervals was not. Not even today, and you yourself seem to confirm. And more: the octaves then were theorized “pure”. It was only last century when some models opened to stretched theoretical octaves. Have you noticed?

...“But did you also read that just because he (Rameau) thought about ET did not mean he could tune it and he could not. Rameau was known for many temperaments, including some quasi ETs but not ET itself. He did not discover a way to tune ET accurately.”...

I'm not surprised. The temperament was based on one octave module, then theoretical octaves were “pure”, the 2:1 octave's ratio was favoured, not having been mixed with all the others, so the first ET theory was not practicable. In fact, I still don't know about which ET you talk about. And I find strange how your theoretical interest and understanding can suddenly drop, strange how you do not seem to notice the route towards the harmonic resonances of the sound whole, and strange how you do not seem to bother about a significant difference between the first ET and modern approaches.

...“It would be quite highly manipulative in my view, to take that one phrase that you found to suggest that 11 years after he wrote about the effects of interval sizes on emotions, he took a tranquilizer and tuned his pianos in ET after that.”...

It looks like the issue is bounced back (ok), but to me your quotation sounded exploitable. Anyway, why do you talk about tranquillizers? Interval size is one matter, cacophony is a different matter. Wouldn't one need a tranquillizer when surrounded by “wolfs”?

...“What I was actually looking for was a list of descriptions of the effects of various key signatures that composers themselves wrote. They are in Owen Jorgensen's publications somewhere but I thought I might find them on the web and they may be but I cam across that phrase by Rameau.”...

Today you could get more theoretical knowledge available, beyond “a phrase” you could come across.

...“It described quite well what I was referring to in the interpretation of the Schubert Impromptu. You can hear Rubinstein play it and if you like that, fine but I for one, have heard it performed in an amazing way that I will never forget.”...

Fair enough. That phrase was exploitable and you've heard an amazing version of Schubert Impromptu that you'll never forget. But in any case, what has this got to do with colour and emotions.

...“The fact that Rameau later attempted to explore ET was not pertinent although I did consider adding that I thought his change of mind was an interesting twist. That interesting twist does not change the fact that interval sizes do affect the emotions.”...

You say Rameau's “twist”, I'd say acknowledgement. Sincerely, I think that a massive quantity of clichés are being loaded onto a tuning technique, as if the technical result itself – (O) an enjoyable tuning - was not enough. In my opinion, any arbitrary out-of-tune interval can only hurt our “ear” and our emotions. How about a professional dancer wearing an non-equal costume, the one I like, skin-contact silk and jute, would that help his/her emotions?

...“Patrick may also be able to come up with some other examples as he learns to play according to temperament and show us how ET affects his mood in one way but the EBVT affects it differently.”...

May I ask you which ET? Rameau's ET? A Modern ET? Again it gets turbid and I feel confused, you talk about ET, but you continuously notice reverse well, then you would expect Patrick to tune what you call true ET, but you do not acknowledge modern ETs, maths having little to do with music (?). Is there a point I'm missing?

Regards, a.c.

.

Bill, in Chas thread you wrote:..."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."...

Leave my own way aside, when we talk about ET we are talking about "nature's way" and its ordered proportions. This can help to understand why a geometric progression is (aurally) so strongly appealing.

..."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."...

The point is that Chas, Cordier's ET, Stopper's ET must not be confused with 12th root of two ET, i.e. the first model based on natural proportions. Then, whether you call Chas ET model "Chas" or "what Bill Bremmer feels being virtually the same concept that he would have if he were to tune a piano in ET", does not really matter.

And after all, the simple acknowledgment of modern variants of ET would merely prove your enlightenment. You could now start referring to your own opinions and ET in very precise terms, so avoiding confusion amongst your/our colleagues.

BTW, is saying "method for tempering" equal to saying "temperamental theory", in North American English?

Regards, a.c.

Edit: Recently I read: "some temperaments are more equal than others", quite funny, (O) very true.

Well, the pythagorean tuning is also based on natural proportions. It could be argued that the 12th root of 2 is not based on natural proportions because it is based on an irrational number (it cannot be described by a ratio made of whole numbers).

But the point I really want to make is that the 12th root of 2 ET is different than the others that are mentioned because it cannot be tuned aurally on a real piano. It defines pitches without regard to inharmonicity. And that is also the problem with the published CHAS theory. Although there is an aural sequence for tuning CHAS, which takes into account inharmonicity, the CHAS theory does not. If we divide “marrow from bone” CHAS theory is very similar to 12th root of 2 theory because it is based on a fixed ratio, but CHAS tuning is not. They are two different things just as 12th root of 2 theory is different from tuning ET with aurally pure octaves.

And please do not resume that deceptive "shell game" about what a theory is and what a model is.

Jeff sorry, on "deceptive games" I cannot help you.

The article linked below may better explain what I mean when I talk about nature's proportions and logarithmic scales:

Mario Livio: "The golden number: nature seems to have a sense of proportion":

http://findarticles.com/p/articles/mi_m1134/is_2_112/ai_98254967/?tag=content;col1

Together with this article there is plenty of literature in the web on the same issue.

Regards, a.c.

I believe that whatever the iH is we tune in it because it is the source for the real tone we hear.

It may not have to do much with the model itself. Instruments with inharmonic tones have been tuned to pure 5ths Cordier. Indeed the speed of 3ds may have raised a lot, but if the idea is to obtain relations between beats, iH is not playing a so large role in the effect, not more than with a standard tuning.

When you talk about proportions, such as semitone ratios, inharmonicity cannot be ignored in a meaningful discussion.

Frankly, I suggest that no. Inharmonicityy play a role in the particular tone of the instrument ,and also in its ability to be tuned more or less open (hence based on a 4:2 on beat octave)

It may play a role in a discussion, but if you try to tune with pure double or triple frequencies (in Hz) you get nowhere.


The piano have its tone, and that is what is tuned, that is what I mean. Ih is giving us problems because its uneven progressivness is in the way on pianos with less than good scales. The stretching of the intervals above the basic ih correction give us some "room" to reconciliate these, that is one of the main reason why it is used, to me.

Ih will adbsorb some of the beating and create others.

We need to "decompress" the piano, to open the tone, so we are not annoyed by iH.

But it can be also a bad habit !

If you are interested in iH and its relation to tuning, do you know what the are the iH level of grands or verticals of differnt brands , and how they change the way you tune them ?

Yes I do. I have a collection of measured iH curves and a database application to see the effects of different tuning schemes. Aurally I notice the difference in stretch when comparing 12ths to 4:2 octaves and 4:1 double octaves depending on the size of the piano. But starting in the direction of finding the best stretch for a given piano has led me in a different direction when actually tuning.

I am tuning more and more by playing three notes at a time and striving for the best sound or resonance. This also gives quite a bit of stretch. After tuning the temperament, with the color of the 4ths and 5ths I want, I then tune octaves by including the fifth down from the top note. When I can then tune 12ths, I again include the 5th from the top note. There are plenty of other checks, of course.

Jeff,

You write:..."After tuning the temperament, with the color of the 4ths and 5ths I want, I then tune octaves by including the fifth down from the top note. When I can then tune 12ths, I again include the 5th from the top note."...

This sounds interesting. Could you let us listen to a recording of your tuning (slow playing of chromatic intervals)?

Have you tried Chas Preparatory Tuning?

Regards, a.c.

.

Yes Jeff, I agree with Alfredo - I think this is interesting, too. Any new field reports from your experiment with three notes?