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Heavy duty hemis

🔗Gene Ward Smith <gwsmith@svpal.org>

3/22/2003 2:11:00 PM

The "Hemis" in question are some high-complexity temperaments with
generators half of a consonance, with scales for which 36/35 is a
chroma. As expected, hemififths is the star of the show because it has
only two wolf fifths out of the 34. When checking it out, bear in mind
it is a highly accurate temperament with an rms error of 0.585 cents.

Hemififths[34]

[2, 25, 13, 35, 15, -40]
[1, 28/27, 21/20, 15/14, 49/45, 9/8, 8/7, 7/6, 32/27, 49/40, 56/45,
80/63, 9/7, 21/16, 4/3, 112/81, 7/5, 10/7, 81/56, 3/2, 32/21, 14/9,
63/40, 45/28, 49/30, 27/16, 12/7, 7/4, 16/9, 90/49, 28/15, 40/21,
27/14, 63/32]
[56/45, 32/21, 28/15, 8/7, 7/5, 12/7, 21/20, 9/7, 63/40, 27/14, 32/27,
81/56, 16/9, 49/45, 4/3, 49/30, 1, 49/40, 3/2, 90/49, 9/8, 112/81,
27/16, 28/27, 80/63, 14/9, 40/21, 7/6, 10/7, 7/4, 15/14, 21/16, 45/28,
63/32]

Circle of generators, 49/40 generator

[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 54/35, 9/5] [1, 6/5, 54/35, 12/7]
[1, 9/7, 54/35, 9/5] [1, 6/5, 54/35, 12/7]

Hemiweurschmidt[25]

[16, 2, 5, -34, -37, 6]
[1, 49/48, 25/24, 35/32, 28/25, 8/7, 7/6, 49/40, 5/4, 32/25, 64/49,
48/35, 7/5, 10/7, 35/24, 49/32, 25/16, 8/5, 49/30, 12/7, 7/4, 25/14,
64/35, 48/25, 49/25]
[25/24, 7/6, 64/49, 35/24, 49/30, 64/35, 49/48, 8/7, 32/25, 10/7, 8/5,
25/14, 1, 28/25, 5/4, 7/5, 25/16, 7/4, 49/25, 35/32, 49/40, 48/35,
49/32, 12/7, 48/25]

Generator circle for 28/25

[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, 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, 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, 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, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 35/24, 7/4] [1, 6/5, 35/24, 12/7]
[1, 5/4, 35/24, 7/4] [1, 6/5, 35/24, 12/7]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 12/7]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 12/7]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 12/7]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 128/75] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 128/75] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 128/75] [1, 7/6, 35/24, 5/3]
[1, 128/105, 35/24, 128/75] [1, 7/6, 35/24, 5/3]
[1, 128/105, 35/24, 128/75] [1, 7/6, 35/24, 5/3]

Hemithirds[37]

[15, -2, -5, -38, -50, -6]
[1, 50/49, 21/20, 16/15, 15/14, 35/32, 28/25, 8/7, 75/64, 25/21, 6/5,
49/40, 5/4, 32/25, 21/16, 4/3, 75/56, 175/128, 7/5, 10/7, 147/100,
112/75, 3/2, 32/21, 25/16, 8/5, 80/49, 5/3, 42/25, 128/75, 7/4, 25/14,
64/35, 28/15, 15/8, 40/21, 49/25]
[15/14, 6/5, 75/56, 3/2, 42/25, 15/8, 21/20, 75/64, 21/16, 147/100,
80/49, 64/35, 50/49, 8/7, 32/25, 10/7, 8/5, 25/14, 1, 28/25, 5/4, 7/5,
25/16, 7/4, 49/25, 35/32, 49/40, 175/128, 32/21, 128/75, 40/21, 16/15,
25/21, 4/3, 112/75, 5/3, 28/15]

Circle of generators, 28/25 generator

[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[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, 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, 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, 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, 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, 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, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]

Hemikleismic[23]

[12, 10, -9, -12, -48, -49]
[1, 25/24, 21/20, 35/32, 8/7, 125/108, 6/5, 5/4, 63/50, 21/16, 48/35,
25/18, 36/25, 35/24, 32/21, 63/40, 8/5, 5/3, 125/72, 7/4, 64/35,
40/21, 48/25]
[35/24, 8/5, 7/4, 48/25, 21/20, 125/108, 63/50, 25/18, 32/21, 5/3,
64/35, 1, 35/32, 6/5, 21/16, 36/25, 63/40, 125/72, 40/21, 25/24, 8/7,
5/4, 48/35]

Generator circle for 35/32 generator

[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[1, 5/4, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 6/5, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 128/105, 35/24, 7/4] [1, 7/6, 35/24, 5/3]