# 701edo

 ← 700edo 701edo 702edo →
Prime factorization 701 (prime)
Step size 1.71184¢
Fifth 410\701 (701.854¢)
Semitones (A1:m2) 66:53 (113¢ : 90.73¢)
Consistency limit 15
Distinct consistency limit 15

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

Approximation of prime harmonics in 701edo
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

Table of rank-2 temperaments by generator
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