639edo

← 638edo

639edo

640edo →

Prime factorization	32 × 71
Step size	1.87793 ¢
Fifth	374\639 (702.347 ¢)
Semitones (A1:m2)	62:47 (116.4 ¢ : 88.26 ¢)
Consistency limit	17
Distinct consistency limit	17

Theory

639edo is distinctly consistent in the 17-odd-limit. It has a sharp tendency, with harmonics of 3 to 17 all tuned sharp. The 639h val gives a reasonable approximation of harmonic 19, where it tempers out [1 27 -18⟩ (ennealimma) and [55 -1 -23⟩ (counterwürschmidt comma) in the 5-limit; 2401/2400 and 4375/4374 in the 7-limit; 5632/5625 and 19712/19683 in the 11-limit; 2080/2079 and 4459/4455 in the 13-limit; 1156/1155, 2058/2057, and 2601/2600 in the 17-limit; 1216/1215, 1445/1444, 1540/1539, 2376/2375, and 2926/2925 in the 19-limit. It supports 11-limit ennealimmal and its 13-limit extension ennealimmalis.

Prime harmonics

Approximation of prime harmonics in 639edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.392	+0.541	+0.188	+0.795	+0.787	+0.209	-0.799	+0.834	-0.469	+0.504
	Relative (%)	+0.0	+20.9	+28.8	+10.0	+42.3	+41.9	+11.1	-42.6	+44.4	-25.0	+26.9
Steps (reduced)		639 (0)	1013 (374)	1484 (206)	1794 (516)	2211 (294)	2365 (448)	2612 (56)	2714 (158)	2891 (335)	3104 (548)	3166 (610)

Subsets and supersets

Since 639 = 3² × 71, it has subset edos 3, 9, 71, and 213.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [1013 -639⟩ | [⟨639 1013]] | −0.1238 | 0.1238 | 6.59 |- | 2.3.5 | [1 -27 18⟩, [55 -1 -23⟩ | [⟨639 1013 1484]] | −0.1601 | 0.1134 | 6.04 |- | 2.3.5.7 | 2401/2400, 4375/4374, [58 -14 -13 -2⟩ | [⟨639 1013 1484 1794]] | −0.1369 | 0.1062 | 5.65 |- | 2.3.5.7.11 | 2401/2400, 4375/4374, 5632/5625, 161280/161051 | [⟨639 1013 1484 1794 2211]] | −0.1554 | 0.1020 | 5.43 |- | 2.3.5.7.11.13 | 2080/2079, 2401/2400, 4375/4374, 5632/5625, 20480/20449 | [⟨639 1013 1484 1794 2211 2365]] | −0.1650 | 0.0955 | 5.08 |- | 2.3.5.7.11.13.17 | 1156/1155, 2058/2057, 2080/2079, 2401/2400, 4375/4374, 5632/5625 | [⟨639 1013 1484 1794 2211 2365 2612]] | −0.1487 | 0.0970 | 5.16 |- | 2.3.5.7.11.13.17.19 | 1156/1155, 1216/1215, 1445/1444, 2058/2057, 2080/2079, 2376/2375, 2401/2400 | [⟨639 1013 1484 1794 2211 2365 2612, 2715]] (639h) | −0.1618 | 0.0971 | 5.17 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 53\639 | 99.53 | 18/17 | Quindro |- | 1 | 206\639 | 386.85 | 5/4 | Counterwürschmidt |- | 9 | 168\639
(26\639) | 315.49
(48.83) | 6/5
(36/35) | Ennealimmal / ennealimmalis Template:Rank-2 end Template:Orf