701edo

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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

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

Music

Francium

• "Don't Fancy Cooking Jonathan?" from Questions (2024) – Spotify | Bandcamp | YouTube – zisa in 701edo tuning
• "Fluffy Spider Silk" from Naughty Girl Era (2024) – Spotify | Bandcamp | YouTube