218edo: Difference between revisions

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^ this isn't patent val
^ this isn't patent val


It's great for 2.9.7.17 subgroup, and good for 2.9.5.7.11.17 subgroup.
Suggested subgroups: 2.9.7.17 and 2.9.5.7.11.17.


Tempers out 640000000000000000/635585924776181463 with patent 5, 7 and 9. This is the difference between three 7/4 ratios and sixteen 10/9 ratios stacked.
Also explore [[436edo]].
 
Commas using the 13-limit patent val:
 
3-limit: 1/1
 
5-limit: 20000/19683


Also explore [[436edo]].
7-limit: 4000/3969 65625/65536 245/243 2401/2400 60025/59049
 
11-limit: 4000/3993 12005/11979 16384/16335 4375/4356 78125/77616 896/891 67228/66825 1375/1372 6875/6804 5632/5625 385/384 94325/93312 15488/15435 75625/75264 15488/15309 3388/3375 1331/1323 6655/6561 65219/64800 43923/43904 73205/72576


Patent 13–limit commas include:
13-limit: 28672/28561 86240/85683 20480/20449 5600/5577 16807/16731 25000/24843 6125/6084 86625/86528 68992/68445 58080/57967 96800/95823 847/845 41503/41067 33275/33124 65219/64896 29575/29403 4225/4224 21632/21609 676/675 33124/32805 9295/9261 46475/45927 13013/12960 28561/28512


[[Category:Stub]]
[[Category:Stub]]

Revision as of 07:26, 23 September 2018

218edo, having a step size of 5.50458715596 cents, contains very accurate ratios, such as 7/4, 11/8, 9/7, 8/7, 9/8, 10/9, 11/10 and 17/16, and its step size can be approximated as 5.5 cents.

Bold numbers are off within less than 0.1 step size

fraction: 3/2 4/3 5/4 8/5 5/3 6/5 7/4 8/7 10/9 9/5 9/8 16/9
steps in 218edo: 128 90 70 148 161 57 176 42 33 185 37 181

^ this isn't patent val

Suggested subgroups: 2.9.7.17 and 2.9.5.7.11.17.

Also explore 436edo.

Commas using the 13-limit patent val:

3-limit: 1/1

5-limit: 20000/19683

7-limit: 4000/3969 65625/65536 245/243 2401/2400 60025/59049

11-limit: 4000/3993 12005/11979 16384/16335 4375/4356 78125/77616 896/891 67228/66825 1375/1372 6875/6804 5632/5625 385/384 94325/93312 15488/15435 75625/75264 15488/15309 3388/3375 1331/1323 6655/6561 65219/64800 43923/43904 73205/72576

13-limit: 28672/28561 86240/85683 20480/20449 5600/5577 16807/16731 25000/24843 6125/6084 86625/86528 68992/68445 58080/57967 96800/95823 847/845 41503/41067 33275/33124 65219/64896 29575/29403 4225/4224 21632/21609 676/675 33124/32805 9295/9261 46475/45927 13013/12960 28561/28512

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