215edo
| ← 214edo | 215edo | 216edo → |
215 equal divisions of the octave (abbreviated 215edo or 215ed2), also called 215-tone equal temperament (215tet) or 215 equal temperament (215et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 215 equal parts of about 5.58 ¢ each. Each step represents a frequency ratio of 21/215, or the 215th root of 2.
The equal temperament tempers out 4000/3969 and 65625/65536, and the patent val provides the optimal patent val for the 53 & 162 temperament (ditonic extension) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and supports hemififths.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +1.30 | -1.20 | +2.34 | +2.60 | +1.24 | +2.26 | +0.10 | +1.09 | -1.70 | -1.94 | +2.42 |
| relative (%) | +23 | -21 | +42 | +47 | +22 | +41 | +2 | +20 | -30 | -35 | +43 | |
| Steps (reduced) |
341 (126) |
499 (69) |
604 (174) |
682 (37) |
744 (99) |
796 (151) |
840 (195) |
879 (19) |
913 (53) |
944 (84) |
973 (113) | |
Subsets and supersets
Since 215 factors into 5 × 43, 215edo contains 5edo and 43edo as its subsets.