307edo

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307edo

308edo →

Prime factorization	307 (prime)
Step size	3.90879 ¢
Fifth	180\307 (703.583 ¢)
Semitones (A1:m2)	32:21 (125.1 ¢ : 82.08 ¢)
Dual sharp fifth	180\307 (703.583 ¢)
Dual flat fifth	179\307 (699.674 ¢)
Dual major 2nd	52\307 (203.257 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

307et tempers out 1220703125/1219784832, 48828125/48771072, 95703125/95551488 and 2401/2400 in the 7-limit; 100663296/100656875, 939524096/935859375, 16384/16335, 226492416/226474325, 2359296/2358125, 6250/6237, 172032/171875, 42875/42768, 4302592/4296875, 15488/15435, 3388/3375, 766656/765625, 166375/165888, 391314/390625, 3294225/3294172, 43923/43904 and 102487/102400 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 307edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+1.63	+0.66	+0.56	-0.65	-0.18	-0.14	-1.62	+0.58	-0.44	-1.73	+1.04
	Relative (%)	+41.7	+16.8	+14.2	-16.7	-4.6	-3.5	-41.5	+14.9	-11.4	-44.1	+26.6
Steps (reduced)		487 (180)	713 (99)	862 (248)	973 (52)	1062 (141)	1136 (215)	1199 (278)	1255 (27)	1304 (76)	1348 (120)	1389 (161)

Subsets and supersets

307edo is the 63rd prime edo. 614edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-973 307⟩	⟨307 973]	+0.1029	0.1030	2.64
2.9.5	32805/32768, [2 47 -65⟩	⟨307 973 713]	-0.0257	0.2004	5.13
2.9.5.7	32805/32768, 118098/117649, 589824/588245	⟨307 973 713 862]	-0.0687	0.1889	4.87
2.9.5.7.11	5632/5625, 8019/8000, 32805/32768, 46656/46585	⟨307 973 713 862 1062]	-0.0447	0.1756	4.49
2.9.5.7.11.13	729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647	⟨307 973 713 862 1062 1136]	-0.0311	0.1632	4.18
2.9.5.7.11.13.17	729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735	⟨307 973 713 862 1062 1136 1255]	-0.0470	0.1560	3.99

Music

Francium

• "Broken Music From A Broken Mind" from Melancholie (2023) Spotify | Bandcamp | YouTube