10009edo

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10009edo

10010edo →

Prime factorization	10009 (prime)
Step size	0.119892 ¢
Fifth	5855\10009 (701.968 ¢)
Semitones (A1:m2)	949:752 (113.8 ¢ : 90.16 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

10009edo is consistent to the 9-odd-limit. It can be used in the 2.3.5.7.13.19.29.31.41.47 subgroup, tempering out 60025/60021, 138240/138229, 140625/140608, 482125/482112, 4751360/4750893, 739375/739328, 5137600/5137263, 19552/19551 and 103936/103935. Using the 2.3.7.13.23.31 subgroup, it tempers out 8464/8463.

Prime harmonics

Approximation of prime harmonics in 10009edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	+0.0132	-0.0214	+0.0221	-0.0541	+0.0358	-0.0498	+0.0592	-0.0398	+0.0561	+0.0538
	Relative (%)	+0.0	+11.0	-17.8	+18.5	-45.1	+29.9	-41.6	+49.4	-33.2	+46.8	+44.9
Steps (reduced)		10009 (0)	15864 (5855)	23240 (3222)	28099 (8081)	34625 (4598)	37038 (7011)	40911 (875)	42518 (2482)	45276 (5240)	48624 (8588)	49587 (9551)

Subsets and supersets

10009edo is the 1231st prime edo. 20018edo, which doubles it, gives a good correction to the harmonic 11.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[15864 -10009⟩	[⟨10009 15864]]	-0.0042	0.0042	3.50
2.3.5	[56 -91 38⟩, [-304 79 77⟩	[⟨10009 15864 23240]]	+0.0003	0.0072	6.01
2.3.5.7	[-2 -3 15 -10⟩, [-48 0 11 8⟩, [5 -44 17 9⟩	[⟨10009 15864 23240 28099]]	-0.0018	0.0071	5.92

Music

Francium

• "Talk About Mysterious Spores" from I Want To (2025) – Spotify | Bandcamp | YouTube