218edo
218edo, having a step size of 5.50458715596 cents, contains very accurate ratios, such as 7/4, 9/7, 8/7, 9/8, 10/9, 11/10 and 17/16 which are approximated within 0.55¢ deviation (10% the step size).
"218edo ~ 15601edo be NANOTONALS (Particulary I choose 218edo, because this EDO contains with much accurate the Ratios 7/4, 11/8, 9/7, 8/7, 9/8, 10/9, 11/10, 17/16 and very interesting accurate to the Pi Ratio [1981,7954 Cents Pi ; 1981,6514 Cents the 360\218edo]. 218edo contains a 'possible Comma' which is the Ratio 65207/65000). The size of 1\218 is 5,5046 Cents, but you can use the size of 5,5 Cents like a approximation too)."
The step size of 5.5045871559633 can be approximated as 5.5 cents, leading to a variation named 5.5cET (5.5 cent Equal-step Tuning) where the octave is reduced by 1 cent.
The following table shows the nearest matches for the interval, not the matches from the patent val. Bold numbers are off within less than 0.1 (10%) of the step size.
| Interval 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 |
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