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altering a Pythagorean set by 64/63s & 33/32s

🔗D.Stearns <stearns@xxxxxxx.xxxx>

10/3/1999 3:37:17 AM

While growing bleary eyed by chipping away at revising an old score, I
just noticed this pretty interesting example of an a fairly unusual
scale (a pretty wrongish Lydian at 1/1, 8/7, 9/7, 7/5, 32/21, 12/7,
27/14, 2/1) that is also a strictly proper scale (I came about this
scale by ear without giving the possible ins and outs of its
construction a seconds thought).

By rotating this scale to its best approximation of a I - VII, and
calling the 147/80 an 11/6 (thereby altering the Pythagorean set by
64/63s & 33/32s), it offers a better view of the interesting array of
3s, 7s, & ~11s that this scale contains:

1/1, 9/8, 81/64, 21/16, 3/2, 27/16, 11/6, 2/1
1/1, 9/8, 7/6, 4/3, 3/2, 18/11, 16/9, 2/1
1/1, 28/27, 32/27, 4/3, 16/11, 128/81, 16/9, 2/1
1/1, 8/7, 9/7, [7/5], 32/21, 12/7, 27/14, 2/1
1/1, 9/8, 11/9, 4/3, 3/2, 27/16, 7/4, 2/1
1/1, 12/11, 32/27, 4/3, 3/2, 14/9, 16/9, 2/1
1/1, 12/11, 11/9, 11/8, [10/7], 18/11, 11/6, 2/1

Dan

PS - If everything were consistent here, the 7/5 & 10/7 would be
108/77 & 77/54, e.g., 729/512 & 1024/729 diminished and augmented by
the combined commas (2079/2048).