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Nineteen notes, 49/48 chroma

🔗Gene Ward Smith <gwsmith@svpal.org>

3/24/2003 7:52:55 PM

Semisixths[19]
rms error 5.053 cents

[1, 4, -9, 4, -17, -32]
[1, 28/27, 15/14, 10/9, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7,
3/2, 14/9, 8/5, 5/3, 12/7, 9/5, 28/15, 27/14]
[8/5, 28/27, 4/3, 12/7, 10/9, 10/7, 28/15, 6/5, 14/9,
1, 9/7, 5/3, 15/14, 7/5, 9/5, 7/6, 3/2, 27/14, 5/4]

Circle of major and minor tetrads generator 9/7
[1, 5/4, 3/2, 7/4] [1, 49/40, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 49/40, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 56/45, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 56/45, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 56/45, 40/27, 12/7] [1, 6/5, 40/27, 12/7]
[1, 56/45, 40/27, 12/7] [1, 6/5, 40/27, 12/7]
[1, 56/45, 40/27, 12/7] [1, 6/5, 40/27, 12/7]
[1, 56/45, 40/27, 12/7] [1, 6/5, 40/27, 12/7]
[1, 56/45, 40/27, 12/7] [1, 6/5, 40/27, 12/7]
[1, 56/45, 40/27, 12/7] [1, 6/5, 40/27, 12/7]
[1, 56/45, 40/27, 12/7] [1, 6/5, 40/27, 12/7]

Circle of alternative tetrads generator 9/7
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 40/27, 9/5] [1, 7/6, 40/27, 5/3] [1, 7/6, 40/27, 12/7]
[1, 9/7, 40/27, 9/5] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 80/49] [1, 8/7, 40/27, 12/7]
[1, 32/25, 40/27, 16/9] [1, 8/7, 40/27, 80/49] [1, 8/7, 40/27, 12/7]

Magic[19]
rms error 4.139 cents

[1, 4, -9, 4, -17, -32]
[1, 25/24, 15/14, 10/9, 7/6, 6/5, 5/4, 9/7, 4/3, 25/18, 35/24,
3/2, 14/9, 8/5, 5/3, 12/7, 9/5, 15/8, 27/14]
[10/9, 25/18, 12/7, 15/14, 4/3, 5/3, 25/24, 9/7, 8/5,
1, 5/4, 14/9, 27/14, 6/5, 3/2, 15/8, 7/6, 35/24, 9/5]

Circle of major and minor tetrads generator 5/4
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 40/27, 12/7] [1, 6/5, 40/27, 12/7]
[1, 5/4, 40/27, 12/7] [1, 25/21, 40/27, 12/7]
[1, 5/4, 40/27, 12/7] [1, 25/21, 40/27, 12/7]
[1, 5/4, 40/27, 12/7] [1, 25/21, 40/27, 12/7]
[1, 60/49, 40/27, 12/7] [1, 25/21, 40/27, 12/7]

Circle of alternative tetrads generator 5/4
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 27/16] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 27/16] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 27/16] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 27/16] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 16/9] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 16/9] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 16/9] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 16/9] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]
[1, 9/7, 40/27, 16/9] [1, 8/7, 40/27, 5/3] [1, 8/7, 40/27, 12/7]

Meantone[19]
rms error 3.665 cents

[1, 4, 10, 4, 13, 12]
[1, 21/20, 15/14, 9/8, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2,
14/9, 8/5, 5/3, 12/7, 9/5, 15/8, 27/14]
[12/7, 9/7, 27/14, 10/7, 15/14, 8/5, 6/5, 9/5, 4/3,
1, 3/2, 9/8, 5/3, 5/4, 15/8, 7/5, 21/20, 14/9, 7/6]

Circle of major and minor tetrads
[1, 5/4, 3/2, 7/4] [1, 49/40, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 49/40, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 49/40, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 7/4]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 60/49, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 60/49, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 60/49, 3/2, 12/7] [1, 6/5, 3/2, 12/7]
[1, 60/49, 72/49, 12/7] [1, 6/5, 72/49, 12/7]

Circle of alternative tetrads
[1, 21/16, 3/2, 49/27] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 49/27] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 21/16, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 5/3] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 80/49] [1, 8/7, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 8/7, 3/2, 80/49] [1, 8/7, 3/2, 12/7]
[1, 9/7, 72/49, 9/5] [1, 8/7, 72/49, 80/49] [1, 8/7, 72/49, 12/7]