All;

I've implemented in scheme some of the stuff regarding the

generalized tetrachordality measure that went around a

while back.

My procedure finds the mean absolute deviation of a scale

from its transposition at 702 cents, first in scale order,

then in any order. Specifically, I do a brute force note-

to-note compare with all rotations of the notes of the

transposed scale in the former case, permutations in the

latter case, and return the minimum for each (source available).

Scales in ()s are degrees of 12-tET. Values are mean cents

deviation, rounded to the nearest cent.

Pentatonic Scale

(0 2 5 7 9) = 21, 21

1/1 9/8 4/3 3/2 27/16 = 18, 18

Diatonic Scale

(0 2 4 5 7 9 11) = 16, 16

1/1 9/8 5/4 4/3 3/2 5/3 15/8 = 16, 16

Diminished chord

(0 3 6 9) = 102, 102

Wholetone scale

(0 2 4 6 8 10) = 102, 102

Diminished scale

(0 2 3 5 6 8 9 11) = 50, 50

(0 1 3 4 6 7 9 10) = 102, 102

Minor scales w/'gypsy' tetrachord

(0 1 4 5 7 8 11) = 44, 44

(0 1 4 5 7 8 10) = 44, 44

(0 1 4 5 7 9 10) = 44, 44

The issues I'd like to bring to your attention are:

() Anybody care to compare results, or see

any obvious bugs? Debugging always appreciated.

() Different modes of a scale will give different

results, as with the diminished scale above. I

consider all "rotations", but I do not normalize

the rotations to their tonics to get modes. Maybe

I should? IOW, would we think omnitetrachordality

could be used find stable modes of a scale?

() Notice that the allowing permutations (2nd set of

values) never lowers the score. So I either have a

bug, or I don't need to fuss with permutations.

Normally, we could lower the meandev. between these

two...

(1 2 3 10 11 12)

(1 10 2 11 3 12)

By allowing permutations, vs. enforcing neighboring

order. However, maybe because I'm restricting myself

to transpositions, this sort of situation never arises.

Sound reasonable?

-Carl