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Orwell[13] and Quadrafifhs[14]

🔗Gene Ward Smith <gwsmith@svpal.org>

3/22/2003 11:11:55 PM

It should be noted that the augmented triads in orwell, considered in
terms of septimal orwell, can be thought of as [1, 5/4, 14/9] as well,
a tempered ass triad, or whatever it should be called.

Orwell[13]

2109375/2097152
[1, 16/15, 1125/1024, 75/64, 5/4, 32/25, 512/375, 375/256, 25/16, 8/5,
128/75, 1875/1024, 15/8]
[25/16, 1875/1024, 16/15, 5/4, 375/256, 128/75, 1, 75/64, 512/375,
8/5, 15/8, 1125/1024, 32/25]

Generator = 75/64
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 25/16]
[1, 5/4, 25/16]
[1, 5/4, 25/16]
[1, 5/4, 25/16]
[1, 5/4, 25/16]
[1, 5/4, 25/16]
[1, 5/4, 25/16]

Quadrafifths[14]

20000/19683
[1, 81/80, 27/25, 10/9, 6/5, 100/81, 4/3, 27/20, 40/27, 3/2, 81/50,
5/3, 9/5, 50/27]
[27/25, 6/5, 4/3, 40/27, 81/50, 9/5, 1, 10/9, 100/81, 27/20, 3/2, 5/3,
50/27, 81/80]

Generator = 10/9
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]

Circles of fifths
[1, 5/4, 3/2] [1, 5/4, 3/2]
[1, 6/5, 3/2] [1, 6/5, 3/2]
[1, 6/5, 36/25] [1, 6/5, 36/25]
[1, 5/4, 3/2] [1, 5/4, 3/2]
[1, 6/5, 3/2] [1, 6/5, 3/2]
[1, 6/5, 3/2] [1, 6/5, 36/25]
[1, 6/5, 36/25] [1, 5/4, 3/2]