709edo

← 708edo

709edo

710edo →

Prime factorization	709 (prime)
Step size	1.69252 ¢
Fifth	415\709 (702.398 ¢)
Semitones (A1:m2)	69:52 (116.8 ¢ : 88.01 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

709edo is only consistent to the 3-odd-limit. It can be used in the 2.3.11.13.17.19 subgroup, tempering out 2432/2431, 34816/34749, 25289/25272, 709631/708588 and 974651392/972714177.

Odd harmonics

Approximation of odd harmonics in 709edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.443	-0.418	-0.702	-0.807	+0.445	+0.657	+0.025	-0.019	+0.371	-0.259	-0.348
	Relative (%)	+26.2	-24.7	-41.5	-47.7	+26.3	+38.8	+1.5	-1.1	+21.9	-15.3	-20.5
Steps (reduced)		1124 (415)	1646 (228)	1990 (572)	2247 (120)	2453 (326)	2624 (497)	2770 (643)	2898 (62)	3012 (176)	3114 (278)	3207 (371)

Subsets and supersets

709edo is the 127th prime EDO. 2127edo, which triples it, gives a good correction to the harmonics 5 and 7.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1124 -709⟩	[⟨709 1124]]	-0.1397	0.1397	8.25

Music

Francium

• "I Want To" from I Want To (2025) – Spotify | Bandcamp | YouTube