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13-limit yantra temperaments

🔗Gene Ward Smith <gwsmith@svpal.org>

3/20/2004 9:41:36 PM

I took this up to the 2000th 13-limit yantra. Hanson/catakleismic
seems pretty important, so does the 35th temperament on the list,
which is a 494-et system with generators [1/2, 86/494] (the second
being a 44/39 interval.) Less complex systems follow one after
another, but supersupermajor does alright for itself, along with
wuerschmidt and the two versions of miracle.

[2, 1, -1, 1, 2, -3, -7, -5, -4, -5, -1, 1, 6, 9, 3]
[[1, 1, 2, 3, 3, 3], [0, 2, 1, -1, 1, 2]] [10, 10]

[0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 9, 0, 10, 0, -14]
[[4, 6, 9, 10, 13, 14], [0, 0, 0, 0, 1, 0]] [11, 11]

[2, 3, 6, -2, 6, 0, 4, -10, 2, 6, -15, 3, -26, -6, 28]
[[1, 2, 3, 4, 3, 5], [0, -2, -3, -6, 2, -6]] [12, 12]

[1, -1, 3, -1, 3, -4, 2, -5, 1, 10, 1, 11, -13, -3, 14]
[[1, 2, 2, 4, 3, 5], [0, -1, 1, -3, 1, -3]] [13, 13]

[1, -1, 3, -1, -2, -4, 2, -5, -7, 10, 1, -1, -13, -17, -3]
[[1, 2, 2, 4, 3, 3], [0, -1, 1, -3, 1, 2]] [14, 14]

[1, -3, 5, -1, -4, -7, 5, -5, -10, 20, 8, 2, -20, -30, -10]
[[1, 2, 1, 5, 3, 2], [0, -1, 3, -5, 1, 4]] [15, 15]

[4, 2, 2, 10, -2, -6, -8, 2, -18, -1, 16, -12, 21, -13, -44]
[[2, 4, 5, 6, 9, 7], [0, -2, -1, -1, -5, 1]] [16, 16]

[0, 0, 0, 0, 10, 0, 0, 0, 16, 0, 0, 23, 0, 28, 35]
[[10, 16, 23, 28, 35, 37], [0, 0, 0, 0, 0, 1]] [17, 18]

[1, -1, -2, -1, 1, -4, -6, -5, -2, -2, 1, 6, 4, 10, 7]
[[1, 2, 2, 2, 3, 4], [0, -1, 1, 2, 1, -1]] [19, 20]

[1, 4, -2, -1, -4, 4, -6, -5, -10, -16, -16, -24, 4, -4, -10]
[[1, 2, 4, 2, 3, 2], [0, -1, -4, 2, 1, 4]] [21, 22]

[1, 4, -2, 11, 8, 4, -6, 14, 9, -16, 12, 4, 38, 30, -13]
[[1, 2, 4, 2, 8, 7], [0, -1, -4, 2, -11, -8]] [23, 23]

[2, 8, 8, 12, 4, 8, 7, 12, -1, -4, 0, -20, 6, -18, -30]
[[2, 3, 4, 5, 6, 7], [0, 1, 4, 4, 6, 2]] [24, 24]

[4, 2, 2, -4, 8, -6, -8, -20, -2, -1, -16, 11, -18, 15, 42]
[[2, 4, 5, 6, 6, 9], [0, -2, -1, -1, 2, -4]] [25, 26]

[6, 10, 10, 8, 26, 2, -1, -8, 19, -5, -16, 23, -12, 36, 60]
[[2, 4, 6, 7, 8, 11], [0, -3, -5, -5, -4, -13]] [27, 27]

[3, 5, 9, 4, 17, 1, 6, -4, 16, 7, -8, 21, -20, 14, 44]
[[1, 2, 3, 4, 4, 6], [0, -3, -5, -9, -4, -17]] [28, 29]

[9, 5, -3, 7, 11, -13, -30, -20, -16, -21, -1, 7, 30, 42, 12]
[[1, 1, 2, 3, 3, 3], [0, 9, 5, -3, 7, 11]] [30, 32]

[8, 8, 8, 8, 8, -6, -10, -15, -17, -4, -9, -11, -5, -7, -2]
[[8, 13, 19, 23, 28, 30], [0, -1, -1, -1, -1, -1]] [33, 33]

[13, 9, 1, 19, 7, -16, -35, -15, -37, -23, 13, -17, 50, 16, -46]
[[1, 4, 4, 3, 7, 5], [0, -13, -9, -1, -19, -7]] [34, 35]

[9, 0, 9, 9, 9, -21, -11, -17, -19, 21, 21, 21, -6, -8, -2]
[[9, 14, 21, 25, 31, 33], [0, 1, 0, 1, 1, 1]] [36, 36]

[4, -3, 2, -4, 3, -14, -8, -20, -10, 13, 1, 18, -18, 1, 25]
[[1, 2, 2, 3, 3, 4], [0, -4, 3, -2, 4, -3]] [37, 38]

[8, 1, 18, 20, 27, -17, 6, 4, 13, 39, 43, 59, -6, 9, 19]
[[1, -1, 2, -3, -3, -5], [0, 8, 1, 18, 20, 27]] [39, 44]

[10, 2, 24, 25, 36, -20, 10, 5, 20, 50, 51, 76, -13, 12, 32]
[[1, 5, 3, 11, 12, 16], [0, -10, -2, -24, -25, -36]] [45, 46]

[4, 9, -8, 10, -2, 5, -24, 2, -18, -44, -8, -38, 56, 24, -44]
[[1, 1, 1, 4, 2, 4], [0, 4, 9, -8, 10, -2]] [47, 47]

[2, -4, 30, 22, 16, -11, 42, 28, 18, 81, 65, 52, -42, -66, -26]
[[2, 3, 5, 3, 5, 6], [0, 1, -2, 15, 11, 8]] [48, 49]

[4, -8, 14, -2, -14, -22, 11, -17, -37, 55, 23, -3, -54, -91, -41]
[[2, 3, 5, 5, 7, 8], [0, 2, -4, 7, -1, -7]] [50, 52]

[3, 17, -1, -13, -22, 20, -10, -31, -46, -50, -89, -114, -33, -58, -28]
[[1, 1, -1, 3, 6, 8], [0, 3, 17, -1, -13, -22]] [53, 57]

[6, -7, -2, 15, 38, -25, -20, 3, 38, 15, 59, 114, 49, 114, 76]
[[1, 1, 3, 3, 2, 0], [0, 6, -7, -2, 15, 38]] [58, 61]

[6, -7, -2, 15, -34, -25, -20, 3, -76, 15, 59, -53, 49, -88, -173]
[[1, 1, 3, 3, 2, 7], [0, 6, -7, -2, 15, -34]] [62, 63]

[24, 20, 16, 60, 56, -24, -42, 12, 0, -19, 70, 56, 113, 98, -28]
[[4, 6, 9, 11, 13, 14], [0, 6, 5, 4, 15, 14]] [64, 66]

[6, 5, 22, -21, 14, -6, 18, -54, 0, 37, -66, 14, -135, -42, 126]
[[1, 0, 1, -3, 9, 0], [0, 6, 5, 22, -21, 14]] [67, 93]

[12, 34, 20, 30, 52, 26, -2, 6, 38, -49, -48, -5, 15, 72, 69]
[[2, 4, 7, 7, 9, 11], [0, -6, -17, -10, -15, -26]] [94, 111]

[36, 73, 89, 119, 127, 32, 40, 64, 68, 2, 24, 25, 26, 27, -1]
[[1, -4, -9, -11, -15, -16], [0, 36, 73, 89, 119, 127]] [112, 122]

[36, 54, 36, 18, 108, 2, -44, -96, 38, -68, -145, 51, -74, 170, 307]
[[18, 28, 41, 50, 62, 65], [0, 2, 3, 2, 1, 6]] [123, 138]

[2, -57, -28, 46, 81, -95, -50, 66, 121, 95, 304, 399, 226, 331, 110]
[[1, 1, 19, 11, -10, -20], [0, 2, -57, -28, 46, 81]] [139, 142]

[22, 48, -38, -34, -54, 25, -122, -130, -167, -223, -245, -303, 36,
-11, -61]
[[2, 7, 13, -1, 1, -2], [0, -11, -24, 19, 17, 27]] [143, 435]

[78, 72, -12, -96, -216, -67, -238, -422, -631, -230, -472, -768,
-228, -562, -392]
[[6, 15, 19, 16, 14, 7], [0, -13, -12, 2, 16, 36]] [436, 457]

[208, 147, 58, -76, -81, -250, -492, -840, -898, -278, -685, -732,
-414, -442, 1]
[[1, -30, -20, -6, 15, 16], [0, 208, 147, 58, -76, -81]] [458, 475]

[873, 790, 1894, 2792, 2986, -775, 551, 1405, 1502, 2180, 3750, 4010,
1286, 1374, -2]
[[1, 104, 95, 225, 331, 354], [0, -873, -790, -1894, -2792, -2986]]
[476, 526]

[150, 180, 60, -60, -270, -63, -326, -614, -983, -366, -762, -1293,
-376, -980, -712]
[[30, 47, 69, 84, 104, 112], [0, 5, 6, 2, -2, -9]] [527, 949]

[141, -225, -2, 586, -356, -684, -399, 441, -1086, 627, 2139, 6, 1652,
-992, -3400]
[[1, -12, 24, 3, -53, 38], [0, 141, -225, -2, 586, -356]] [950, 965]

[79, 517, 374, -20, 457, 636, 371, -305, 432, -583, -1835, -852,
-1350, -101, 1655]
[[1, 35, 221, 161, -5, 197], [0, -79, -517, -374, 20, -457]] [966, 979]

[184, 556, 242, 430, 340, 454, -133, 45, -142, -999, -925, -1268, 370,
59, -415]
[[2, 43, 125, 58, 100, 81], [0, -92, -278, -121, -215, -170]] [980, 1012]

[96, -60, 418, 166, -56, -318, 393, -69, -444, 1139, 593, 92, -980,
-1704, -808]
[[2, 9, 1, 31, 17, 4], [0, -48, 30, -209, -83, 28]] [1013, 1153]

[441, 135, 848, 1196, -166, -810, 106, 370, -1895, 1590, 2310, -885,
424, -3604, -5000]
[[1, -55, -15, -106, -150, 25], [0, 441, 135, 848, 1196, -166]] [1154,
1216]

[79, -348, 786, 1510, 563, -735, 1024, 2120, 600, 2802, 4710, 2595,
1520, -1328, -3640]
[[1, -19, 93, -202, -390, -143], [0, 79, -348, 786, 1510, 563]] [1217,
1328]

[872, 391, 2366, 3509, 3752, -1405, 1302, 2545, 2720, 4396, 6795,
7265, 1666, 1778, -5]
[[1, -211, -93, -574, -852, -911], [0, 872, 391, 2366, 3509, 3752]]
[1329, 2000]