218edo: Difference between revisions
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'''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''' | '''Bold numbers are off within less than 0.1 step size''' | ||
| Line 12: | Line 12: | ||
| | 5/3 | | | 5/3 | ||
| | 6/5 | | | 6/5 | ||
| | 7/4 | | | '''7/4''' | ||
| | 8/7 | | | '''8/7''' | ||
| | 10/9 | | | 10/9 | ||
| | 9/5 | | | 9/5 | ||
| | 9/8 | | | '''9/8''' | ||
| | 16/9 | | | '''16/9''' | ||
|- | |- | ||
| | steps in 218edo: | | | steps in 218edo: | ||
| | | | | 127 | ||
| | | | | 91 | ||
| | 70 | | | 70 | ||
| | 148 | | | 148 | ||
| Line 34: | Line 34: | ||
|} | |} | ||
Suggested subgroups: 2.9.7.17 and 2.9.5.7.11.17. | Suggested subgroups: 2.9.7.17 and 2.9.5.7.11.17. | ||
Revision as of 18:43, 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: | 127 | 91 | 70 | 148 | 161 | 57 | 176 | 42 | 33 | 185 | 37 | 181 |
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