319edo

← 318edo

319edo

320edo →

Prime factorization	11 × 29
Step size	3.76176 ¢
Fifth	187\319 (703.448 ¢) (→ 17\29)
Semitones (A1:m2)	33:22 (124.1 ¢ : 82.76 ¢)
Dual sharp fifth	187\319 (703.448 ¢) (→ 17\29)
Dual flat fifth	186\319 (699.687 ¢)
Dual major 2nd	54\319 (203.135 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

319et is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. Using the patent val, it tempers out 156250000/155649627, 1220703125/1219784832, 6144/6125, 10976/10935 and 420175/419904 in the 7-limit; 95703125/95664294, 161280/161051, 35156250/35153041, 4000/3993, 117649/117612, 1296000/1294139, 6250/6237, 107495424/107421875, 4302592/4296875, 825000/823543, 422576/421875, 15488/15435, 3025/3024, 59290/59049, 766656/765625, 456533/455625, 202397184/201768035, 3294225/3294172, 585640/583443 and 644204/643125 in the 11-limit. It supports mystery in the 5-limit and protolangwidge.

Odd harmonics

Approximation of odd harmonics in 319edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+1.49	+1.15	+1.71	-0.78	+1.66	-1.66	-1.12	+0.37	-0.33	-0.56	-0.06
	Relative (%)	+39.7	+30.5	+45.4	-20.6	+44.1	-44.0	-29.8	+9.9	-8.9	-14.9	-1.6
Steps (reduced)		506 (187)	741 (103)	896 (258)	1011 (54)	1104 (147)	1180 (223)	1246 (289)	1304 (28)	1355 (79)	1401 (125)	1443 (167)

Subsets and supersets

319 factors into 11 × 29, with 11edo and 29edo as its subset edos. 638edo, 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	[-1011 319⟩	[⟨319 1011]]	+0.1223	0.1223	3.25
2.9.5	32805/32768, [54 35 -71⟩	[⟨319 1011 741]]	-0.0832	0.3072	8.17