[tuning-math] A 7-limit planar temperaments list
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Mon, 22 Jul 2002 22:02:15 -0700
Here is a list of 7-limit planar temperaments, with complexity and rms
error less than 14, and badness calculated from that (as rms *
complexity^4, which are the right dimensions to correspond to linear
temperaments) less than 10000. I don't see much of interest in the ones
with badness over 5000, but they are listed in terms of increasing
badness and you can make your own judgments. Using Minkowski's basic
theorem from his geometry of numbers would help us these to be used to
get 7-limit temperaments.
4375/4374 (5)^4*(7)/(2)/(3)^7
[[1, 0, 0, 1], [0, 1, 0, 7], [0, 0, 1, -4]]
comp 8.514085954 rms .3862236561e-1 bad 202.9509048
generators [1200., 1902.005884, 2786.302406]
250047/250000 (3)^6*(7)^3/(2)^4/(5)^6
[[3, 0, 0, 4], [0, 1, 0, -2], [0, 0, 1, 2]]
comp 10.12074134 rms .2800947367e-1 bad 293.8693214
generators [400.0000000, 1901.922456, 2786.324561]
2401/2400 (7)^4/(2)^5/(3)/(5)^2
[[1, 1, 1, 2], [0, 2, 1, 1], [0, 0, 2, 1]]
comp 7.001210638 rms .1255441309 bad 301.6400406
generators [1200., 350.9775007, 617.6844971]
225/224 (3)^2*(5)^2/(2)^5/(7)
[[1, 0, 0, -5], [0, 1, 0, 2], [0, 0, 1, 2]]
comp 4.026020476 rms 1.484083173 bad 389.9080111
generators [1200., 1899.812912, 2784.171625]
64/63 (2)^6/(3)^2/(7)
[[1, 0, 0, 6], [0, 1, 0, -2], [0, 0, 1, 0]]
comp 3.320882425 rms 5.949512815 bad 723.5947437
generators [1200., 1911.692178, 2792.156018]
81/80 (3)^4/(2)^4/(5)
[[1, 0, -4, 0], [0, 1, 4, 0], [0, 0, 0, 1]]
comp 4.132030727 rms 3.443762373 bad 1003.892815
generators [1200., 1896.164845, 3366.344411]
32805/32768 (3)^8*(5)/(2)^15
[[1, 0, 15, 0], [0, 1, -8, 0], [0, 0, 0, 1]]
comp 9.459947973 rms .1320192291 bad 1057.285276
generators [1200., 1901.727514, 3368.705472]
126/125 (2)*(3)^2*(7)/(5)^3
[[1, 0, 0, -1], [0, 1, 0, -2], [0, 0, 1, 3]]
comp 4.396397238 rms 3.010264897 bad 1124.585345
generators [1200., 1899.984322, 2789.269735]
5120/5103 (2)^10*(5)/(3)^6/(7)
[[1, 0, 0, 10], [0, 1, 0, -6], [0, 0, 1, 1]]
comp 6.872898147 rms .5465065421 bad 1219.424726
generators [1200., 1902.888700, 2786.702752]
2460375/2458624 (3)^9*(5)^3/(2)^10/(7)^4
[[1, 0, 2, -1], [0, 1, 1, 3], [0, 0, 4, 3]]
comp 11.82008947 rms .7718361083e-1 bad 1506.635331
generators [1200., 1901.831749, -378.8994468]
28/27 (2)^2*(7)/(3)^3
[[1, 0, 0, -2], [0, 1, 0, 3], [0, 0, 1, 0]]
comp 3.320882425 rms 13.73919562 bad 1670.995600
generators [1200., 1924.441038, 2795.308127]
65625/65536 (3)*(5)^5*(7)/(2)^16
[[1, 0, 0, 16], [0, 1, 0, -1], [0, 0, 1, -5]]
comp 9.483876888 rms .2200495161 bad 1780.180537
generators [1200., 1901.707688, 2785.942745]
420175/419904 (5)^2*(7)^5/(2)^6/(3)^8
[[1, 0, 3, 0], [0, 1, 4, 0], [0, 0, 5, -2]]
comp 11.85680458 rms .9406410627e-1 bad 1859.065030
generators [1200., 1902.061943, -1684.389187]
6144/6125 (2)^11*(3)/(5)^3/(7)^2
[[1, 0, 1, 4], [0, 1, 1, -1], [0, 0, 2, -3]]
comp 7.012333797 rms .7993271605 bad 1932.746493
generators [1200., 1902.491206, -157.4631745]
703125/702464 (3)^2*(5)^7/(2)^11/(7)^3
[[1, 0, 2, 1], [0, 1, 1, 3], [0, 0, 3, 7]]
comp 11.00411811 rms .1342982709 bad 1969.207103
generators [1200., 1901.822082, -505.2414545]
1029/1024 (3)*(7)^3/(2)^10
[[1, 1, 0, 3], [0, 3, 0, -1], [0, 0, 1, 0]]
comp 6.237538987 rms 1.350315689 bad 2044.035369
generators [1200., 233.4444416, 2785.016372]
49/48 (7)^2/(2)^4/(3)
[[1, 0, 0, 2], [0, 2, 0, 1], [0, 0, 1, 0]]
comp 3.733539376 rms 11.89893695 bad 2312.017448
generators [1200., 950.9775006, 2780.364245]
50/49 (2)*(5)^2/(7)^2
[[2, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 1]]
comp 3.891820298 rms 10.09659043 bad 2316.252253
generators [600.0000000, 1901.955001, 2777.569810]
3136/3125 (2)^6*(7)^2/(5)^5
[[1, 0, 0, -3], [0, 1, 0, 0], [0, 0, 2, 5]]
comp 7.348511491 rms .8057454012 bad 2349.607642
generators [1200., 1902.435257, 1393.797198]
245/243 (5)*(7)^2/(3)^5
[[1, 0, 0, 0], [0, 1, 1, 2], [0, 0, 2, -1]]
comp 5.914949368 rms 1.987070580 bad 2432.301564
generators [1200., 1904.876579, 440.9272508]
4000/3969 (2)^5*(5)^3/(3)^4/(7)^2
[[1, 0, 1, 4], [0, 1, 0, -2], [0, 0, 2, 3]]
comp 6.115596778 rms 1.784055755 bad 2495.535749
generators [1200., 1904.436192, 793.1568564]
10976/10935 (2)^5*(7)^3/(3)^7/(5)
[[1, 0, 2, -1], [0, 1, 2, 3], [0, 0, 3, 1]]
comp 8.434555688 rms .5771951599 bad 2921.268800
generators [1200., 1902.880572, -1139.661549]
5250987/5242880 (3)^7*(7)^4/(2)^20/(5)
[[1, 0, 0, 5], [0, 1, 3, -1], [0, 0, 4, 1]]
comp 11.71753460 rms .1695157602 bad 3195.619481
generators [1200., 1901.681064, -729.7186252]
2048/2025 (2)^11/(3)^4/(5)^2
[[2, 0, 11, 0], [0, 1, -2, 0], [0, 0, 0, 1]]
comp 6.271198982 rms 2.133360336 bad 3299.639851
generators [600.0000000, 1905.446531, 3370.920823]
875/864 (5)^3*(7)/(2)^5/(3)^3
[[1, 0, 0, 5], [0, 1, 0, 3], [0, 0, 1, -3]]
comp 5.590098759 rms 3.998747915 bad 3904.828359
generators [1200., 1904.145206, 2781.933305]
1728/1715 (2)^6*(3)^3/(5)/(7)^3
[[1, 0, 0, 2], [0, 1, 0, 1], [0, 0, 3, -1]]
comp 6.389007079 rms 2.386896737 bad 3977.105469
generators [1200., 1900.647644, 929.2070233]
128/125 (2)^7/(5)^3
[[3, 0, 7, 0], [0, 1, 0, 0], [0, 0, 0, 1]]
comp 4.828313736 rms 7.901781211 bad 4294.443852
generators [400.0000000, 1908.798145, 3375.669050]
525/512 (3)*(5)^2*(7)/(2)^9
[[1, 0, 0, 9], [0, 1, 0, -1], [0, 0, 1, -2]]
comp 4.914886013 rms 7.556420940 bad 4409.302991
generators [1200., 1892.089470, 2774.475078]
19683/19600 (3)^9/(2)^4/(5)^2/(7)^2
[[1, 0, 0, -2], [0, 2, 0, 9], [0, 0, 1, -1]]
comp 9.496383083 rms .5594506202 bad 4549.824682
generators [1200., 950.5282864, 2786.121192]
321489/320000 (3)^8*(7)^2/(2)^9/(5)^4
[[2, 0, 0, 9], [0, 1, 0, -4], [0, 0, 1, 2]]
comp 9.685150414 rms .5990398573 bad 5270.856574
generators [600.0000000, 1901.017355, 2786.179764]
4096000/4084101 (2)^15*(5)^3/(3)^5/(7)^5
[[1, 0, 0, 3], [0, 1, 0, -1], [0, 0, 5, 3]]
comp 11.01660696 rms .3957132811 bad 5828.704629
generators [1200., 1902.514624, 557.3000507]
686/675 (2)*(7)^3/(3)^3/(5)^2
[[1, 0, 2, 1], [0, 1, 0, 1], [0, 0, 3, 2]]
comp 6.011672792 rms 4.481232704 bad 5853.004182
generators [1200., 1907.336788, 130.2063806]
33075/32768 (3)^3*(5)^2*(7)^2/(2)^15
[[1, 1, 0, 6], [0, 2, 0, -3], [0, 0, 1, -1]]
comp 7.823970640 rms 1.622557336 bad 6080.074498
generators [1200., 349.7544516, 2784.112225]
405/392 (3)^4*(5)/(2)^3/(7)^2
[[1, 0, 1, -1], [0, 1, 0, 2], [0, 0, 2, 1]]
comp 5.199938690 rms 8.419825102 bad 6155.962460
generators [1200., 1888.775891, 789.3913963]
3645/3584 (3)^6*(5)/(2)^9/(7)
[[1, 0, 0, -9], [0, 1, 0, 6], [0, 0, 1, 1]]
comp 6.872898147 rms 2.773231799 bad 6187.935855
generators [1200., 1897.216978, 2783.549864]
2100875/2097152 (5)^3*(7)^5/(2)^21
[[1, 0, 2, 3], [0, 1, 0, 0], [0, 0, 5, -3]]
comp 12.52322351 rms .2532643498 bad 6229.290561
generators [1200., 1901.704334, 77.19380915]
1323/1280 (3)^3*(7)^2/(2)^8/(5)
[[1, 0, 0, 4], [0, 1, 1, -1], [0, 0, 2, 1]]
comp 5.199938690 rms 8.527334761 bad 6234.565687
generators [1200., 1888.607610, 445.9928964]
67108864/66976875 (2)^26/(3)^7/(5)^4/(7)^2
[[1, 0, 0, 13], [0, 2, 0, -7], [0, 0, 1, -2]]
comp 13.68011660 rms .1803880478 bad 6317.815729
generators [1200., 951.1207079, 2786.557165]
15625/15552 (5)^6/(2)^6/(3)^5
[[1, 0, 1, 0], [0, 6, 5, 0], [0, 0, 0, 1]]
comp 9.338935129 rms .8406854315 bad 6394.740953
generators [1200., 317.0796754, 3368.695142]
16875/16807 (3)^3*(5)^4/(7)^5
[[1, 0, 0, 0], [0, 1, 3, 3], [0, 0, 5, 4]]
comp 9.567898928 rms .7767030640 bad 6509.105851
generators [1200., 1901.307749, -583.6772476]
102760448/102515625 (2)^21*(7)^2/(3)^8/(5)^6
[[2, 0, 0, -21], [0, 1, 0, 4], [0, 0, 1, 3]]
comp 13.89893287 rms .2141059337 bad 7990.142647
generators [600.0000000, 1902.288028, 2786.613436]
250/243 (2)*(5)^3/(3)^5
[[1, 2, 3, 0], [0, 3, 5, 0], [0, 0, 0, 1]]
comp 5.948285733 rms 6.512214090 bad 8152.596693
generators [1200., -162.9960265, 3371.413598]
458752/455625 (2)^16*(7)/(3)^6/(5)^4
[[1, 0, 0, -16], [0, 1, 0, 6], [0, 0, 1, 4]]
comp 10.00226449 rms .8352030642 bad 8359.598450
generators [1200., 1903.280492, 2787.462472]
589824/588245 (2)^16*(3)^2/(5)/(7)^6
[[1, 0, 4, 2], [0, 1, 2, 0], [0, 0, 6, -1]]
comp 11.93226425 rms .4664233339 bad 9455.221767
generators [1200., 1902.165950, -969.5993818]
256/243 (2)^8/(3)^5
[[5, 8, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
comp 5.493061445 rms 10.41828523 bad 9485.365527
generators [240.0000000, 2795.336213, 3377.848405]
------------------------ Yahoo! Groups Sponsor ---------------------~-->
Free $5 Love Reading
Risk Free!
http://us.click.yahoo.com/NsdPZD/PfREAA/Ey.GAA/wHYolB/TM
---------------------------------------------------------------------~->
To unsubscribe from this group, send an email to:
tuning-math-unsubscribe@xxxxxxxxxxxxxxx
Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
____________________________________________________________
To learn how to configure this list via e-mail (subscribe,
unsubscribe, etc.), send a message to listar@xxxxxxxxxxxxx
with the subject line "info tuning-math". Or visit the
website: < //www.freelists.org/list/tuning-math > .
Other related posts:
- » [tuning-math] A 7-limit planar temperaments list
