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43 augmented scales

🔗Gene Ward Smith <gwsmith@svpal.org>

1/16/2004 6:08:32 PM

Even after octave reducing, I'm getting 43 different scales. For these
scales, the period is octave-reduced to a value of 0, 1 or 2, and the
generator starts from 0 and goes however far it goes, which I then
call the complexity.

complexity 3 = Augmented[12]

{[1, 2], [1, 1], [1, 0], [2, 1], [2, 2], [1, 3],
[0, 3], [0, 2], [0, 1], [0, 0], [2, 0], [2, 3]}

complexity 5

{[0, 4], [1, 5], [0, 5], [1, 2], [2, 4], [2, 2],
[1, 3], [0, 3], [0, 2], [0, 1], [2, 0], [2, 3]}

{[0, 4], [2, 5], [1, 2], [1, 1], [2, 1], [2, 2],
[1, 3], [0, 3], [0, 2], [1, 4], [0, 0], [2, 3]}

{[0, 4], [1, 5], [1, 2], [1, 1], [2, 4], [2, 2],
[1, 3], [0, 3], [0, 2], [0, 1], [2, 0], [2, 3]}

{[2, 5], [1, 2], [1, 1], [1, 0], [2, 1], [2, 2],
[1, 3], [0, 3], [0, 2], [1, 4], [0, 0], [2, 3]}

{[2, 5], [1, 2], [1, 1], [1, 0], [2, 4], [2, 1],
[2, 2], [1, 3], [0, 3], [0, 2], [2, 0], [2, 3]}

{[0, 4], [0, 5], [1, 2], [2, 1], [2, 2], [1, 3],
[0, 3], [0, 2], [0, 1], [1, 4], [0, 0], [2, 3]}

{[0, 4], [1, 5], [0, 5], [1, 2], [2, 2], [1, 3],
[0, 3], [0, 2], [0, 1], [1, 4], [0, 0], [2, 3]}

complexity 6

{[0, 4], [2, 5], [1, 2], [1, 1], [2, 1], [1, 3],
[0, 3], [0, 2], [1, 4], [0, 0], [1, 6], [2, 3]}

{[1, 5], [2, 6], [0, 5], [1, 2], [1, 0], [2, 4],
[2, 2], [1, 3], [0, 3], [0, 1], [1, 4], [2, 3]}

{[0, 4], [1, 5], [2, 6], [2, 5], [1, 2], [1, 1],
[2, 2], [1, 3], [0, 3], [1, 4], [0, 0], [2, 3]}

{[0, 4], [0, 5], [2, 5], [2, 4], [2, 1], [2, 2],
[1, 3], [0, 6], [0, 3], [0, 2], [2, 0], [2, 3]}

{[0, 4], [1, 5], [2, 6], [1, 2], [1, 1], [2, 2],
[1, 3], [0, 3], [0, 1], [1, 4], [0, 0], [2, 3]}

{[0, 4], [0, 5], [2, 4], [2, 1], [2, 2], [1, 3],
[0, 6], [0, 3], [0, 2], [0, 1], [2, 0], [2, 3]}

complexity 7

{[0, 5], [2, 5], [1, 0], [2, 4], [2, 1], [2, 2],
[1, 3], [0, 6], [1, 7], [0, 3], [0, 2], [1, 4]}

{[0, 4], [2, 5], [1, 1], [2, 7], [2, 1], [1, 3],
[0, 6], [0, 2], [1, 4], [0, 0], [1, 6], [2, 3]}

{[0, 4], [1, 5], [0, 5], [1, 2], [1, 3], [1, 7],
[0, 3], [0, 2], [0, 1], [1, 4], [0, 0], [1, 6]}

complexity 8

{[1, 5], [2, 6], [0, 5], [1, 2], [2, 8], [2, 4],
[2, 2], [1, 7], [0, 3], [0, 1], [2, 0], [0, 7]}

{[0, 4], [2, 5], [1, 1], [2, 7], [0, 8], [2, 1],
[1, 3], [0, 6], [0, 2], [0, 0], [1, 6], [2, 3]}

{[0, 4], [1, 5], [2, 5], [1, 1], [2, 7], [0, 8],
[1, 3], [0, 6], [0, 2], [0, 0], [1, 6], [2, 3]}

{[0, 4], [1, 5], [1, 8], [2, 5], [1, 1], [2, 7],
[1, 3], [0, 6], [0, 2], [1, 6], [2, 0], [2, 3]}

{[0, 4], [1, 5], [1, 8], [2, 5], [1, 1], [2, 7],
[2, 2], [1, 3], [0, 6], [0, 2], [2, 0], [2, 3]}

{[1, 5], [2, 6], [0, 5], [1, 2], [2, 8], [2, 4],
[2, 2], [1, 3], [1, 7], [0, 3], [0, 1], [2, 0]}

complexity 9

{[0, 9], [2, 6], [0, 5], [1, 8], [1, 2], [1, 0],
[0, 3], [0, 1], [1, 4], [1, 6], [2, 3], [0, 7]}

{[0, 9], [2, 6], [0, 5], [1, 2], [1, 0], [2, 4],
[0, 3], [0, 1], [1, 4], [1, 6], [2, 3], [0, 7]}

{[1, 5], [2, 6], [0, 5], [2, 8], [2, 4], [2, 2],
[1, 3], [0, 6], [1, 9], [1, 7], [0, 3], [2, 0]}

{[0, 9], [0, 5], [1, 2], [2, 8], [2, 4], [2, 7],
[1, 3], [1, 7], [0, 2], [0, 1], [1, 6], [2, 0]}

{[2, 6], [2, 9], [1, 8], [2, 5], [1, 0], [2, 1],
[2, 2], [0, 6], [1, 7], [0, 3], [1, 4], [0, 7]}

{[0, 4], [0, 9], [1, 8], [2, 5], [1, 1], [2, 7],
[1, 3], [0, 6], [0, 2], [1, 6], [2, 0], [2, 3]}

{[1, 5], [2, 6], [2, 9], [1, 8], [2, 5], [1, 0],
[2, 2], [0, 6], [1, 7], [0, 3], [1, 4], [0, 7]}

{[2, 9], [1, 8], [2, 5], [1, 0], [2, 1], [2, 2],
[1, 3], [0, 6], [1, 7], [0, 3], [0, 2], [1, 4]}

{[0, 4], [0, 9], [0, 5], [1, 2], [2, 4], [2, 7],
[1, 3], [0, 2], [0, 1], [1, 6], [2, 0], [2, 3]}

complexity 10

{[1, 5], [2, 6], [0, 5], [2, 8], [2, 4], [2, 10],
[2, 2], [1, 9], [1, 7], [0, 3], [2, 0], [0, 7]}

{[0, 4], [1, 5], [0, 10], [2, 5], [1, 1], [2, 7],
[0, 8], [1, 3], [0, 6], [0, 2], [0, 0], [2, 3]}

{[1, 5], [2, 6], [0, 5], [2, 8], [2, 4], [2, 10],
[2, 2], [1, 3], [1, 9], [1, 7], [0, 3], [2, 0]}

{[0, 4], [1, 5], [0, 10], [2, 5], [1, 1], [2, 7],
[0, 8], [1, 3], [0, 6], [1, 7], [0, 2], [0, 0]}

complexity 11

{[2, 9], [1, 8], [0, 10], [2, 5], [1, 0], [1, 11],
[2, 1], [1, 3], [0, 6], [1, 7], [0, 2], [1, 4]}

{[2, 6], [2, 9], [1, 8], [2, 5], [1, 0], [2, 10],
[0, 11], [2, 1], [2, 2], [0, 3], [1, 4], [0, 7]}

{[0, 5], [1, 0], [2, 4], [2, 7], [2, 10], [0, 11],
[0, 8], [2, 1], [1, 3], [1, 9], [0, 2], [1, 6]}

complexity 13

{[1, 13], [1, 5], [2, 6], [1, 8], [1, 0], [2, 10],
[0, 11], [2, 2], [1, 9], [0, 3], [1, 4], [0, 7]}

complexity 15

{[2, 9], [1, 8], [0, 10], [2, 5], [1, 0], [1, 11],
[1, 15], [2, 1], [0, 6], [1, 7], [0, 2], [1, 4]}

{[2, 9], [1, 8], [0, 10], [2, 5], [1, 0], [1, 11],
[0, 14], [1, 15], [2, 1], [0, 6], [1, 7], [1, 4]}

{[2, 9], [1, 8], [0, 10], [2, 5], [1, 0], [2, 13],
[1, 11], [0, 14], [1, 15], [0, 6], [1, 7], [1, 4]}