701edo

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 2^1/701, 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
Error	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
Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	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

Music

Francium

"Don't Fancy Cooking Jonathan?" from Questions (2024) – Spotify | Bandcamp | YouTube – zisa in 701edo tuning