re: challenge

>Challenge: can a scale with 4 of them be as "tetrachordal" as Centaur?

S'thinks it's impossible.

-=carl

Paul

My precedent message was almost useless. Your answer was OK. I had read
only the begining. English is not easy for me. I stop often my reading (by
fatigue) if I think that I have understood essential. My remark for value
22 was insignificant : reason was a misinterpretation after too fast reading.

I'm glad that your subsequent message touch important divergence. But I
have a problem. It's hard to explain a new approach which is opposed to
common opinion of musicologists, acousticians, microtonalists, etc. It's
almost impossible, for me, in english. It's like boxing with gloves
attached. I have to decide if I will try in english. If yes, perhaps it
will be long.

For the moment, I would like to dissipate only a misunderstanding. When I
use the term "gamme" in french (that I translate by "scale") I don't refer
to the standard meaning which is much concerned with fixed notes, tuning,
acoustic, transposition, interfaces, etc.

As music is a human communication (and expression) I want to describe the
implicit conditions of intelligibity. The tonal segment of this
intelligibility depend mostly, in my opinion, of the only elementary
invariance of time & frequency thru acoustical channel which permit
algebrical structures (concerning time & frequency) to serve as paradigm in
(schematic) form recognition. If you name "ideal" the conception of
Zarlino, you have to go up for qualify mine's.

You presume, because I was speaking only of JI structure, that I reject
using of temperament. It will be odd after I had severely criticized, in
"Fétichisme du numérique et rationalité musicale" the use of obsessive
precision. You will never find number like 234.567891234567 in my texts.
It's absolutely ridiculous. There is no irrationality in perception. There
are two rationnal dimensions : rationality of widths (0 1 2 3 4 ..) and
rationality of sonances (2/1 3/2 4/3 ..). Actual mathematics join in real
field the two perceptive dimensions, inserting irrationality. It's good for
acoustical description of sonic matter. True tonal matter need a more
sophisticated mathematical approach respecting the concern of musical
apprehension. At end, If you think I reject temperament look at

http://www.aei.ca/~plamothe/jchal/jchalmers.htm

I stop here. I could write ten pages with fine shades in french in the time
I can write this approximation of my thoughts.

Pierre

--- In tuning@y..., Pierre Lamothe <plamothe@a...> wrote:

> You will never find number like 234.567891234567 in my texts.
> It's absolutely ridiculous.

It may just be laziness. I find it easier sometimes simply to use what the computer puts out than try to figure out how much I should round by. That way the other guy can decide how many digits to keep.