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11-limit Haluska linear temperaments

🔗Gene Ward Smith <gwsmith@svpal.org>

3/30/2004 4:47:19 PM

By these I mean linear temperaments defined by three successive
Haluska commas.

[33/32, 36/35, 45/44]
[1, -3, 5, -1, -7, 5, -5, 20, 8, -20]
[[1, 2, 1, 5, 3], [0, -1, 3, -5, 1]]

[36/35, 45/44, 49/48]
[2, 3, 1, 7, 0, -4, 4, -6, 6, 16]
[[1, 2, 3, 3, 5], [0, -2, -3, -1, -7]]

[45/44, 49/48, 50/49]
[4, 2, 2, 10, -6, -8, 2, -1, 16, 21]
[[2, 4, 5, 6, 9], [0, -2, -1, -1, -5]]

[49/48, 50/49, 55/54]
[4, 2, 2, 10, -6, -8, 2, -1, 16, 21]
[[2, 4, 5, 6, 9], [0, -2, -1, -1, -5]]

[50/49, 55/54, 56/55]
[2, 6, 6, 0, 5, 4, -7, -3, -21, -21]
[[2, 3, 4, 5, 7], [0, 1, 3, 3, 0]]

[55/54, 56/55, 64/63]
[0, 5, 0, -5, 8, 0, -8, -14, -29, -14]
[[5, 8, 12, 14, 17], [0, 0, -1, 0, 1]]

[56/55, 64/63, 81/80]
[1, 4, -2, -6, 4, -6, -13, -16, -28, -10]
[[1, 2, 4, 2, 1], [0, -1, -4, 2, 6]]

[64/63, 81/80, 99/98]
[1, 4, -2, -6, 4, -6, -13, -16, -28, -10]
[[1, 2, 4, 2, 1], [0, -1, -4, 2, 6]]

[81/80, 99/98, 100/99]
[2, 8, 8, 12, 8, 7, 12, -4, 0, 6]
[[2, 3, 4, 5, 6], [0, 1, 4, 4, 6]]

[99/98, 100/99, 121/120]
[6, 10, 10, 8, 2, -1, -8, -5, -16, -12]
[[2, 4, 6, 7, 8], [0, -3, -5, -5, -4]]

[100/99, 121/120, 126/125]
[3, 5, 9, 4, 1, 6, -4, 7, -8, -20]
[[1, 2, 3, 4, 4], [0, -3, -5, -9, -4]]

[121/120, 126/125, 176/175]
[9, 5, -3, 7, -13, -30, -20, -21, -1, 30]
[[1, 1, 2, 3, 3], [0, 9, 5, -3, 7]]

[126/125, 176/175, 225/224]
[1, 4, 10, 18, 4, 13, 25, 12, 28, 16]
[[1, 2, 4, 7, 11], [0, -1, -4, -10, -18]]

[176/175, 225/224, 243/242]
[8, 1, 18, 20, -17, 6, 4, 39, 43, -6]
[[1, -1, 2, -3, -3], [0, 8, 1, 18, 20]]

[225/224, 243/242, 385/384]
[6, -7, -2, 15, -25, -20, 3, 15, 59, 49]
[[1, 1, 3, 3, 2], [0, 6, -7, -2, 15]]

[243/242, 385/384, 441/440]
[6, -7, -2, 15, -25, -20, 3, 15, 59, 49]
[[1, 1, 3, 3, 2], [0, 6, -7, -2, 15]]

[385/384, 441/440, 540/539]
[6, -7, -2, 15, -25, -20, 3, 15, 59, 49]
[[1, 1, 3, 3, 2], [0, 6, -7, -2, 15]]

[441/440, 540/539, 2401/2400]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]

[540/539, 2401/2400, 3025/3024]
[6, -7, -2, 15, -25, -20, 3, 15, 59, 49]
[[1, 1, 3, 3, 2], [0, 6, -7, -2, 15]]

[2401/2400, 3025/3024, 4375/4374]
[36, 54, 36, 18, 2, -44, -96, -68, -145, -74]
[[18, 28, 41, 50, 62], [0, 2, 3, 2, 1]]

[3025/3024, 4375/4374, 9801/9800]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]

[4375/4374, 9801/9800, 151263/151250]
[36, 54, 36, 18, 2, -44, -96, -68, -145, -74]
[[18, 28, 41, 50, 62], [0, 2, 3, 2, 1]]

[9801/9800, 151263/151250, 1771561/1771470]
[102, 210, 216, 222, 96, 56, -1, -88, -211, -124]
[[6, 11, 17, 20, 24], [0, -17, -35, -36, -37]]

[151263/151250, 1771561/1771470, 3294225/3294172]
[102, 210, 216, 222, 96, 56, -1, -88, -211, -124]
[[6, 11, 17, 20, 24], [0, -17, -35, -36, -37]]

[1771561/1771470, 3294225/3294172, 781258401/781250000]
[388, 658, 768, 821, 142, 128, -41, -64, -370, -352]
[[1, -113, -192, -224, -239], [0, 388, 658, 768, 821]]

[3294225/3294172, 781258401/781250000, 4882812500/4882786447]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]

[781258401/781250000, 4882812500/4882786447, 2541867610898/2541865828329]
[842, 1472, 1716, 1846, 378, 356, 13, -148, -806, -754]
[[2, -83, -146, -170, -182], [0, 421, 736, 858, 923]]