739edo

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739edo

740edo →

Prime factorization	739 (prime)
Step size	1.62382 ¢
Fifth	432\739 (701.488 ¢)
Semitones (A1:m2)	68:57 (110.4 ¢ : 92.56 ¢)
Consistency limit	5
Distinct consistency limit	5

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 2^1/739, 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

Approximation of odd harmonics in 739edo

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

Table of rank-2 temperaments by generator

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 distinct

Music

Francium

• "Keep Bamboozling" from I Want To (2025) – Spotify | Bandcamp | YouTube – in Luna, 739edo tuning