[tuning-math] Modified best 5-limit geometric list
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Tue, 23 Jul 2002 02:39:56 -0700
Here is another list, with the cutoffs changed to complexity and rms
error less than 20, and badness less than 3200:
32805/32768 (3)^8*(5)/(2)^15 shismic
[[1, 0, 15], [0, 1, -8]]
comp 9.459947973 rms .1616933186 bad 136.8857747
generators [1200., 1901.727514]
81/80 (3)^4/(2)^4/(5) meantone
[[1, 0, -4], [0, 1, 4]]
comp 4.132030727 rms 4.217730828 bad 297.5565312
generators [1200., 1896.164845]
2048/2025 (2)^11/(3)^4/(5)^2 diaschismic
[[2, 3, 5], [0, 1, -2]]
comp 6.271198982 rms 2.612821643 bad 644.4088670
generators [600.0000000, 105.4465315]
15625/15552 (5)^6/(2)^6/(3)^5 kleismic
[[1, 0, 1], [0, 6, 5]]
comp 9.338935129 rms 1.029625097 bad 838.6315482
generators [1200., 317.0796753]
1600000/1594323 (2)^9*(5)^5/(3)^13 amt
[[1, 3, 6], [0, -5, -13]]
comp 13.79419993 rms .3831037874 bad 1005.555381
generators [1200., 339.5088256]
128/125 (2)^7/(5)^3 augmented
[[3, 5, 7], [0, 1, 0]]
comp 4.828313736 rms 9.677665780 bad 1089.323984
generators [400.0000000, 91.20185550]
135/128 (3)^3*(5)/(2)^7 pelogic
[[1, 0, 7], [0, 1, -3]]
comp 4.132030727 rms 18.07773392 bad 1275.365360
generators [1200., 1877.137655]
2109375/2097152 (3)^3*(5)^7/(2)^21 orwell
[[1, 0, 3], [0, 7, -3]]
comp 12.77234114 rms .8004099292 bad 1667.723301
generators [1200., 271.5895996]
250/243 (2)*(5)^3/(3)^5 porcupine
[[1, 2, 3], [0, -3, -5]]
comp 5.948285733 rms 7.975800816 bad 1678.609846
generators [1200., 162.9960265]
78732/78125 (2)^2*(3)^9/(5)^7 hemisixths
[[1, -1, -1], [0, 7, 9]]
comp 12.19218236 rms 1.157498409 bad 2097.803242
generators [1200., 442.9792975]
256/243 (2)^8/(3)^5 quintal (blackwood?)
[[5, 8, 12], [0, 0, -1]]
comp 5.493061445 rms 12.75974144 bad 2114.877638
generators [240.0000000, 84.66378778]
393216/390625 (2)^17*(3)/(5)^8 wuerschmidt
[[1, -1, 2], [0, 8, 1]]
comp 12.54312332 rms 1.071949828 bad 2115.395301
generators [1200., 387.8196733]
3125/3072 (5)^5/(2)^10/(3) diesic
[[1, 0, 2], [0, 5, 1]]
comp 7.741412273 rms 4.569472316 bad 2119.954991
generators [1200., 379.9679493]
20000/19683 (2)^5*(5)^4/(3)^9 quadrafifths
[[1, 1, 1], [0, 4, 9]]
comp 9.785568434 rms 2.504205191 bad 2346.540676
generators [1200., 176.2822703]
648/625 (2)^3*(3)^4/(5)^4 diminished
[[4, 6, 9], [0, 1, 1]]
comp 6.437751648 rms 11.06006024 bad 2950.938432
generators [300.0000000, 94.13435693]
4294967296/4271484375 (2)^32/(3)^7/(5)^9 septathirds
[[1, 2, 2], [0, -9, 7]]
comp 18.57395503 rms .4831084292 bad 3095.692281
generators [1200., 55.27549315]
531441/524288 (3)^12/(2)^19 pythagorean
[[12, 19, 28], [0, 0, -1]]
comp 13.18334747 rms 1.382394464 bad 3167.444999
generators [100.0000000, 14.66378756]
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