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More nifty 15/14 chroma scales

🔗Gene Ward Smith <gwsmith@svpal.org>

3/26/2003 12:45:33 AM

Nonkleismic[12]
rms error 3.320 cents

[126/125, 1728/1715]
[10, 9, 7, -9, -17, -9]
[1, 36/35, 7/6, 6/5, 49/40, 7/5, 10/7, 35/24, 49/30, 5/3, 12/7, 35/18]
[49/30, 35/18, 7/6, 7/5, 5/3, 1, 6/5, 10/7, 12/7, 36/35, 49/40, 35/24]

Circle of 6/5
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 7/5, 7/4] [1, 6/5, 7/5, 12/7]
[1, 7/6, 7/5, 7/4] [1, 6/5, 7/5, 12/7]
[1, 7/6, 7/5, 7/4] [1, 6/5, 7/5, 12/7]
[1, 7/6, 7/5, 49/30] [1, 6/5, 7/5, 12/7]
[1, 7/6, 7/5, 49/30] [1, 6/5, 7/5, 12/7]
[1, 7/6, 7/5, 49/30] [1, 6/5, 7/5, 12/7]
[1, 7/6, 7/5, 49/30] [1, 6/5, 7/5, 12/7]
[1, 7/6, 7/5, 49/30] [1, 6/5, 7/5, 8/5]
[1, 7/6, 7/5, 49/30] [1, 6/5, 7/5, 8/5]
[1, 7/6, 7/5, 49/30] [1, 10/9, 7/5, 8/5]

Alternative circle of 6/5
[1, 6/5, 3/2, 9/5] [1, 5/4, 3/2, 9/5]
[1, 6/5, 3/2, 5/3] [1, 5/4, 3/2, 5/3]
[1, 6/5, 7/5, 5/3] [1, 5/4, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 6/5, 7/5, 5/3] [1, 7/6, 7/5, 5/3]
[1, 10/9, 7/5, 5/3] [1, 7/6, 7/5, 5/3]

Superpythagorean[12]
rms error 6.410 cents

[64/63, 245/243]
[1, 4, -2, 4, -6, -16]
[1, 28/27, 8/7, 7/6, 9/7, 4/3, 35/24, 3/2, 14/9, 12/7, 7/4, 27/14]
[28/27, 14/9, 7/6, 7/4, 4/3, 1, 3/2, 8/7, 12/7, 9/7, 27/14, 35/24]

Circles of fifths
[1, 5/4, 3/2, 15/8] [1, 9/7, 3/2, 12/7]
[1, 5/4, 3/2, 15/8] [1, 9/7, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 9/7, 3/2, 12/7]
[1, 7/6, 3/2, 7/4] [1, 9/7, 3/2, 12/7]
[1, 7/6, 3/2, 7/4] [1, 9/7, 3/2, 12/7]
[1, 7/6, 3/2, 7/4] [1, 9/7, 3/2, 12/7]
[1, 7/6, 3/2, 7/4] [1, 9/7, 3/2, 12/7]
[1, 7/6, 3/2, 7/4] [1, 9/7, 3/2, 12/7]
[1, 7/6, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 7/6, 3/2, 7/4] [1, 6/5, 3/2, 8/5]
[1, 7/6, 3/2, 7/4] [1, 6/5, 3/2, 8/5]
[1, 7/6, 7/5, 7/4] [1, 6/5, 7/5, 8/5]

Alternative circles of fifths
[1, 9/7, 3/2, 27/14] [1, 5/4, 3/2, 5/3] [1, 5/4, 3/2, 15/8]
[1, 9/7, 3/2, 27/14] [1, 5/4, 3/2, 5/3] [1, 5/4, 3/2, 15/8]
[1, 9/7, 3/2, 27/14] [1, 5/4, 3/2, 5/3] [1, 5/4, 3/2, 7/4]
[1, 9/7, 3/2, 27/14] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 27/14] [1, 7/6, 3/2, 14/9] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 27/14] [1, 7/6, 3/2, 14/9] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 27/14] [1, 7/6, 3/2, 14/9] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 14/9] [1, 7/6, 3/2, 7/4]
[1, 6/5, 3/2, 9/5] [1, 7/6, 3/2, 14/9] [1, 7/6, 3/2, 7/4]
[1, 6/5, 3/2, 9/5] [1, 7/6, 3/2, 14/9] [1, 7/6, 3/2, 7/4]
[1, 6/5, 3/2, 9/5] [1, 7/6, 3/2, 14/9] [1, 7/6, 3/2, 7/4]
[1, 6/5, 7/5, 9/5] [1, 7/6, 7/5, 14/9] [1, 7/6, 7/5, 7/4]

Dominant sevenths[7]
rms error 20.163 cents

[36/35, 81/80]
[1, 4, -2, 4, -6, -16]
[1, 8/7, 6/5, 5/4, 4/3, 3/2, 8/5, 5/3, 7/4]
[8/5, 6/5, 7/4, 4/3, 1, 3/2, 8/7, 5/3, 5/4]

Circle of fifths
[1, 5/4, 3/2, 15/8] [1, 5/4, 3/2, 5/3]
[1, 5/4, 3/2, 15/8] [1, 5/4, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 5/3]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 8/5]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 8/5]
[1, 6/5, 7/5, 7/4] [1, 6/5, 7/5, 8/5]