739edo
| ← 738edo | 739edo | 740edo → |
739 equal divisions of the octave (abbreviated 739edo or 739ed2), also called 739-tone equal temperament (739tet) or 739 equal temperament (739et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 739 equal parts of about 1.62 ¢ each. Each step represents a frequency ratio of 21/739, or the 739th root of 2.
Theory
739edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.19.23.29.31.41.43 subgroup, tempering out 2001/2000, 59049/58880, 2945/2944, 1026/1025, 1161/1160, 564975/564224 and 2271564/2265625.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.467 | +0.154 | +0.592 | +0.691 | +0.779 | +0.609 | -0.312 | +0.593 | -0.355 | +0.126 | +0.142 |
| Relative (%) | -28.7 | +9.5 | +36.5 | +42.5 | +48.0 | +37.5 | -19.2 | +36.5 | -21.8 | +7.7 | +8.8 | |
| Steps (reduced) |
1171 (432) |
1716 (238) |
2075 (597) |
2343 (126) |
2557 (340) |
2735 (518) |
2887 (670) |
3021 (65) |
3139 (183) |
3246 (290) |
3343 (387) | |
Subsets and supersets
739edo is the 131st prime edo. 2217edo, which triples it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1171 739⟩ | [⟨739 1171]] | 0.1472 | 0.1472 | 9.06 |
| 2.3.5 | [38 -2 -15⟩, [-35 47 -17⟩ | [⟨739 1171 1716]] | 0.0759 | 0.1568 | 9.66 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 119\739 | 193.234 | 262144/234375 | Luna |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct