[tuning-math] 11-limit spacial temperaments list
- From: "genewardsmith" <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Sat, 27 Jul 2002 03:07:15 -0000
This may be the first time ever anyone has looked at spacial temperaments as
such, but even if it isn't I doubt there is much of a market. However, it's
useful to have them, and here is a list of everything satisfying complexity <
10, rms error < 20, and
badness < 10000. The ordering is by complexity, least to greatest.
33/32 (3)*(11)/(2)^5
[[1, 0, 0, 0, 5], [0, 1, 0, 0, -1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]]
comp 2.857236368 rms 18.60142732 bad 3542.232933
generators [1200., 1885.422018, 2764.728986, 3347.241179]
56/55 (2)^3*(7)/(5)/(11)
[[1, 0, 0, 0, 3], [0, 1, 0, 0, 0], [0, 0, 1, 0, -1], [0, 0, 0, 1, 1]]
comp 2.887939081 rms 10.36903038 bad 2082.947320
generators [1200., 1906.341694, 2801.423426, 3367.851086]
36/35 (2)^2*(3)^2/(5)/(7)
[[1, 0, 0, 2, 0], [0, 1, 0, 2, 0], [0, 0, 1, -1, 0], [0, 0, 0, 0, 1]]
comp 2.994519510 rms 17.48752667 bad 4210.795253
generators [1200., 1901.955001, 2810.698904, 4161.072022]
25/24 (5)^2/(2)^3/(3)
[[1, 1, 2, 0, 0], [0, 2, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]]
comp 3.025592935 rms 19.08172863 bad 4838.048328
generators [1200., 347.6988830, 3354.254274, 4136.746308]
45/44 (3)^2*(5)/(2)^2/(11)
[[1, 0, 0, 0, -2], [0, 1, 0, 0, 2], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0]]
comp 3.252337250 rms 12.45498136 bad 4532.323997
generators [1200., 1891.805670, 2766.860826, 3358.676575]
64/63 (2)^6/(3)^2/(7)
[[1, 0, 0, 6, 0], [0, 1, 0, -2, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]]
comp 3.320882425 rms 7.143746136 bad 2885.316848
generators [1200., 1909.101900, 2794.916460, 4159.920689]
100/99 (2)^2*(5)^2/(3)^2/(11)
[[1, 0, 0, 0, 2], [0, 1, 0, 0, -2], [0, 0, 1, 0, 2], [0, 0, 0, 1, 0]]
comp 3.652996092 rms 4.697903284 bad 3055.977200
generators [1200., 1903.569386, 2781.022118, 3369.453721]
49/48 (7)^2/(2)^4/(3)
[[1, 0, 0, 2, 0], [0, 2, 0, 1, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]]
comp 3.733539376 rms 9.638226848 bad 6991.990407
generators [1200., 949.3214630, 2778.953548, 4143.957775]
77/75 (7)*(11)/(3)/(5)^2
[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 2], [0, 0, 0, 1, -1]]
comp 3.811821523 rms 11.65840053 bad 9382.136804
generators [1200., 1905.751787, 2804.032044, 3365.661917]
55/54 (5)*(11)/(2)/(3)^3
[[1, 0, 0, 0, 1], [0, 1, 0, 0, 3], [0, 0, 1, 0, -1], [0, 0, 0, 1, 0]]
comp 3.814620480 rms 10.55929831 bad 8528.874811
generators [1200., 1906.422187, 2777.131166, 3367.833199]
50/49 (2)*(5)^2/(7)^2
[[2, 0, 0, 1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 0, 1]]
comp 3.891820298 rms 8.095281768 bad 7227.629199
generators [600.0000000, 1901.955001, 2777.569810, 4151.317943]
99/98 (3)^2*(11)/(2)/(7)^2
[[1, 0, 0, 0, 1], [0, 1, 0, 0, -2], [0, 0, 1, 0, 0], [0, 0, 0, 1, 2]]
comp 3.966980247 rms 4.745598368 bad 4662.202897
generators [1200., 1900.324226, 2785.679522, 3374.171224]
176/175 (2)^4*(11)/(5)^2/(7)
[[1, 0, 0, 0, -4], [0, 1, 0, 0, 0], [0, 0, 1, 0, 2], [0, 0, 0, 1, 1]]
comp 4.013858905 rms 2.093551491 bad 2181.193312
generators [1200., 1903.085976, 2790.209292, 3371.684758]
225/224 (3)^2*(5)^2/(2)^5/(7)
[[1, 0, 0, -5, 0], [0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 0, 1]]
comp 4.026020476 rms 1.577430795 bad 1668.515370
generators [1200., 1900.722983, 2783.324928, 4149.834958]
81/80 (3)^4/(2)^4/(5)
[[1, 0, -4, 0, 0], [0, 1, 4, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]]
comp 4.132030727 rms 5.635084765 bad 6787.630072
generators [1200., 1896.317430, 3364.336729, 4146.828764]
441/440 (3)^2*(7)^2/(2)^3/(5)/(11)
[[1, 0, 0, 0, -3], [0, 1, 0, 0, 2], [0, 0, 1, 0, -1], [0, 0, 0, 1, 2]]
comp 4.260379115 rms .8994907037 bad 1262.518976
generators [1200., 1901.430980, 2786.270044, 3367.341179]
385/384 (5)*(7)*(11)/(2)^7/(3)
[[1, 0, 0, 0, 7], [0, 1, 0, 0, 1], [0, 0, 1, 0, -1], [0, 0, 0, 1, -1]]
comp 4.322037437 rms 1.030496055 bad 1554.135766
generators [1200., 1901.354659, 2784.612746, 3367.124941]
126/125 (2)*(3)^2*(7)/(5)^3
[[1, 0, 0, -1, 0], [0, 1, 0, -2, 0], [0, 0, 1, 3, 0], [0, 0, 0, 0, 1]]
comp 4.396397238 rms 2.682546126 bad 4405.871537
generators [1200., 1901.955001, 2790.776728, 4152.129400]
121/120 (11)^2/(2)^3/(3)/(5)
[[1, 0, 1, 0, 2], [0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [0, 0, 0, 1, 0]]
comp 4.517667160 rms 4.072710005 bad 7663.984940
generators [1200., 1901.955001, -156.9226966, 3367.927957]
896/891 (2)^7*(7)/(3)^4/(11)
[[1, 0, 0, 0, 7], [0, 1, 0, 0, -4], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1]]
comp 5.006104786 rms 1.936418735 bad 6088.340810
generators [1200., 1903.925434, 2788.284144, 3369.893224]
540/539 (2)^2*(3)^3*(5)/(7)^2/(11)
[[1, 0, 0, 0, 2], [0, 1, 0, 0, 3], [0, 0, 1, 0, 1], [0, 0, 0, 1, -2]]
comp 5.187443078 rms .7484217537 bad 2811.338392
generators [1200., 1901.732843, 2785.955790, 3369.689857]
3025/3024 (5)^2*(11)^2/(2)^4/(3)^3/(7)
[[1, 0, 0, 0, 2], [0, 1, 0, 1, 2], [0, 0, 1, 0, -1], [0, 0, 0, 2, 1]]
comp 5.895318737 rms .1081738857 bad 770.2982011
generators [1200., 1901.955001, 2786.170613, 733.4354526]
1375/1372 (5)^3*(11)/(2)^2/(7)^3
[[1, 0, 0, 0, 2], [0, 1, 0, 0, 0], [0, 0, 1, 0, -3], [0, 0, 0, 1, 3]]
comp 6.019980961 rms .5552206980 bad 4389.764646
generators [1200., 1901.851244, 2785.575886, 3369.229406]
9801/9800 (3)^4*(11)^2/(2)^3/(5)^2/(7)^2
[[2, 0, 0, 0, 3], [0, 1, 0, 0, -2], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]]
comp 6.558685862 rms .2935901386e-1 bad 356.3080343
generators [600.0000000, 1901.942581, 2786.331654, 3368.843848]
5632/5625 (2)^9*(11)/(3)^2/(5)^4
[[1, 0, 0, 0, -9], [0, 1, 0, 0, 2], [0, 0, 1, 0, 4], [0, 0, 0, 1, 0]]
comp 6.993059136 rms .2430345239 bad 4064.470495
generators [1200., 1902.129577, 2786.808340, 3369.064493]
2401/2400 (7)^4/(2)^5/(3)/(5)^2
[[1, 1, 1, 2, 0], [0, 2, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 0, 0, 1]]
comp 7.001210638 rms .1009378214 bad 1697.929473
generators [1200., 350.9685108, 617.6855869, 4151.277988]
4000/3993 (2)^5*(5)^3/(3)/(11)^3
[[1, 2, 0, 0, 1], [0, 3, 0, 0, -1], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0]]
comp 7.277091769 rms .4609639205 bad 9407.109365
generators [1200., -165.9852708, 2785.912380, 3368.915093]
160083/160000 (3)^3*(7)^2*(11)^2/(2)^8/(5)^4
[[1, 0, 0, 0, 4], [0, 2, 0, 0, -3], [0, 0, 1, 0, 2], [0, 0, 0, 1, -1]]
comp 8.009661546 rms .1093194687 bad 3603.863536
generators [1200., 950.9520900, 2786.387123, 3368.712970]
200704/200475 (2)^12*(7)^2/(3)^6/(5)^2/(11)
[[1, 0, 0, 0, 12], [0, 1, 0, 0, -6], [0, 0, 1, 0, -2], [0, 0, 0, 1, 2]]
comp 8.318381546 rms .2154655877 bad 8581.675756
generators [1200., 1902.164272, 2786.650868, 3368.943828]
4375/4374 (5)^4*(7)/(2)/(3)^7
[[1, 0, 0, 1, 0], [0, 1, 0, 7, 0], [0, 0, 1, -4, 0], [0, 0, 0, 0, 1]]
comp 8.514085954 rms .4939105833e-1 bad 2209.726294
generators [1200., 1901.970692, 2786.247899, 4151.309660]
41503/41472 (7)^3*(11)^2/(2)^9/(3)^4
[[1, 0, 0, 1, 3], [0, 1, 0, 0, 2], [0, 0, 1, 0, 0], [0, 0, 0, 2, -3]]
comp 8.658539469 rms .1810507469 bad 8810.966005
generators [1200., 1901.922750, 2786.182918, 1084.258868]
131072/130977 (2)^17/(3)^5/(7)^2/(11)
[[1, 0, 0, 0, 17], [0, 1, 0, 0, -5], [0, 0, 1, 0, 0], [0, 0, 0, 1, -2]]
comp 8.760551242 rms .1254478302 bad 6473.219372
generators [1200., 1902.082652, 2786.470618, 3369.041318]
496125/495616 (3)^4*(5)^3*(7)^2/(2)^12/(11)^2
[[1, 0, 0, 0, -6], [0, 1, 0, 0, 2], [0, 0, 2, 0, 3], [0, 0, 0, 1, 1]]
comp 8.950239742 rms .1701889922 bad 9774.730881
generators [1200., 1901.809793, 1393.008192, 3368.566607]
43923/43904 (3)*(11)^4/(2)^7/(7)^3
[[1, 0, 0, 3, 4], [0, 1, 0, 3, 2], [0, 0, 1, 0, 0], [0, 0, 0, 4, 3]]
comp 9.113321395 rms .9348367894e-1 bad 5876.506598
generators [1200., 1901.925304, 2786.274940, -1484.226778]
180224/180075 (2)^14*(11)/(3)/(5)^2/(7)^4
[[1, 0, 0, 0, -14], [0, 1, 0, 0, 1], [0, 0, 1, 0, 2], [0, 0, 0, 1, 4]]
comp 9.183316130 rms .1339543440 bad 8748.920624
generators [1200., 1902.050698, 2786.516624, 3369.087298]
151263/151250 (3)^2*(7)^5/(2)/(5)^4/(11)^2
[[1, 0, 0, 1, 2], [0, 1, 0, 0, 1], [0, 0, 1, 0, -2], [0, 0, 0, 2, 5]]
comp 9.621494742 rms .1438141844e-1 bad 1185.808221
generators [1200., 1901.953231, 2786.325998, 1084.404501]
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