Matrices (digest 1166 topic 2)

Hi Graham (and tuning list at large),

Thanks for your exposition on the use of matrices to represent intervals and
scales (Digest 1166 Topic 2, Subject: Matrices for beginners). Tuning
systems are sometimes hard to visualize, so I always appreciate various ways
of representing them. (I've even resorted to gluing toothpicks together to
help conceptualize 5-limit just intonation. People now think I'm a "psycho"!)

At 04:15 PM 8/27/97 -0700, you wrote
>...
>A C major scale (not the only one) can be defined using t, s and p
>as follows:
>
> C D E F G A B C
> t+p t s t+p t p+t s
>
>This can be written using matrices:

Okay, just to prove I was following you, here's a correction:

You wrote You meant
---------------- ----------------
(C) (5 3 2) (C) (5 2 3)
(B) (5 3 1) (B) (5 1 3)
(A) (4 2 1) (A) (4 1 2)
(G) (3 2 1)(t) (G) (3 1 2)(t)
(F) = (2 1 1)(s) (F) = (2 1 1)(s)
(E) (2 0 1)(p) (E) (2 0 1)(p)
(D) (1 0 1) (D) (1 0 1)
(C) (0 0 0) (C) (0 0 0)

The s and p got confused on the second (top) half of the scale (G,A,B,C).
You wanted to end up with 5 minor tones (t=10/9), 2 diatonic semitones
(s=16/15), and 3 syntonic commas (p=81/80).

By the way, do you know a good way to visualize 4 dimensions, for things
like limit-7 just intonation? (My glued toothpicks only work for 3 dimensions.)

Thanks again,

--Mark
+------------------------------------------------------+
| Mark Nowitzky |
| email: nowitzky@pacificnet.net |
| www: http://www.pacificnet.net/~nowitzky |
| "If you haven't visited Mark Nowitzky's home |
| page recently, you haven't missed much..." |
+------------------------------------------------------+



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