701edo
| ← 700edo | 701edo | 702edo → |
701 equal divisions of the octave (abbreviated 701edo or 701ed2), also called 701-tone equal temperament (701tet) or 701 equal temperament (701et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 701 equal parts of about 1.71 ¢ each. Each step represents a frequency ratio of 21/701, or the 701st root of 2.
Theory
701edo is consistent to the 15-odd-limit. The equal temperament tempers out 2401/2400, 1959552/1953125 and [-29 23 -2 -1⟩ in the 7-limit; 5632/5625, 2401/2400, 137781/137500 and 43923/43904 in the 11-limit; 1001/1000, 1716/1715, 4096/4095, 39366/39325 and 6656/6655 in the 13-limit. 701edo supports zisa and quinmite.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.101 | +0.562 | +0.076 | -0.105 | -0.014 | -0.533 | +0.347 | -0.029 | -0.761 | +0.186 |
| Relative (%) | +0.0 | -5.9 | +32.8 | +4.4 | -6.2 | -0.8 | -31.1 | +20.3 | -1.7 | -44.5 | +10.8 | |
| Steps (reduced) |
701 (0) |
1111 (410) |
1628 (226) |
1968 (566) |
2425 (322) |
2594 (491) |
2865 (61) |
2978 (174) |
3171 (367) |
3405 (601) |
3473 (669) | |
Subsets and supersets
701edo is the 126th prime EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1111 701⟩ | [⟨701 1111]] | +0.0317 | 0.0317 | 1.85 |
| 2.3.5 | [-22 30 -11⟩, [55 -1 -23⟩ | [⟨701 1111 1628]] | −0.0596 | 0.1316 | 7.69 |
| 2.3.5.7 | 2401/2400, 1959552/1953125, [-29 23 -2 -1⟩ | [⟨701 1111 1628 1968]] | −0.0514 | 0.1149 | 6.71 |
| 2.3.5.7.11 | 5632/5625, 2401/2400, 137781/137500, 43923/43904 | [⟨701 1111 1628 1968 2425]] | −0.0350 | 0.1078 | 6.30 |
| 2.3.5.7.11.13 | 1001/1000, 1716/1715, 4096/4095, 39366/39325, 6656/6655 | [⟨701 1111 1628 1968 2425 2594]] | −0.0286 | 0.0995 | 5.81 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 177\701 | 302.996 | 25/21 | Quinmite |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct