JI split

Just a thought:

Suppose I layer down a matrix, in 2D, and, likeso:

C D E F G A B C
24 27 30 32 36 40 45 48

C 24
D 27
E 30
F 32
G 36
A 40
B 45
C 48

And, assumedly, we can go further to 3D, 4D, 5D ect....

Can we also find the half way points, by:

(F+G)/2, or (F*G)^(1/2), or (F^G)&(1/2),
or (G^F)&(1/2).

This sort of "JI splitting" is possible for three notes, like so:

C
/ \
/ \
D-----B

For (C+D+B)/3 ect......

Sarn Richard Ursell wrote:

> Can we also find the half way points, by:
>
> (F+G)/2, or (F*G)^(1/2), or (F^G)&(1/2),
> or (G^F)&(1/2).

I think there is a simple wave equation where you put in all the waves and
figure the average. I'm not sure I understand all the formulas so could you
explain them. with examples just to make sure I get it. The principle
towards "means" has as strong a historical precedence. I feel it is as
important as Limits in the "organic" development of tunings. I love your
conceptual remarks as a contrast to my own rather conservative steps toward
development towards new materials. As far as multidimensional lattices the
Eikosany is a six dimensional figure that would look like a donut from 12
angles (according to Wilson) It is possible to take his centered pentad
lattice of the big E and rotate the factors into 72 figures. Another 72
would just be the mirror. The hebdomekontany
would occur in who know how many dimensions off hand and could possibly be
enough of a life work to take it all in!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

[Sarn Richard Ursell TD 183.7]

>Suppose I layer down a matrix, in 2D, and, likeso:
... [matrix omitted]
>Can we also find the half way points, by:

> (F+G)/2, or (F*G)^(1/2), or (F^G)&(1/2),
> or (G^F)&(1/2).

[and also for 3 or more notes] ...

My initial reaction is to ask why do this? My next reaction is to say
that and two notes X and Y will produces beats at (Y-X) and (X+Y) but
the minus one is generally far more important than the plus one.
I think that your table wouldbe much more interesting if you tabulate
the beats between the notes (i.e (Y-X) in each cell) rather than the
average. Do it once for JI and once for ET and the results will tell a
big story - in JI nearly all the beats are notes in the key (or at least
harmonic with them) while in ET they are not.

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