337edo

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337edo

338edo →

Prime factorization	337 (prime)
Step size	3.56083 ¢
Fifth	197\337 (701.484 ¢)
Semitones (A1:m2)	31:26 (110.4 ¢ : 92.58 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

337et tempers out 16875/16807, 1280000000/1275989841, 14348907/14336000, 5250987/5242880, 420175/419904 and 201768035/201326592 in the 7-limit. It provides the optimal patent val for the kleirtismic temperament.

Odd harmonics

Approximation of odd harmonics in 337edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.47	-1.74	-0.28	-0.94	+0.61	-0.17	+1.35	-1.69	+1.60	-0.75	-1.57
	Relative (%)	-13.2	-49.0	-7.9	-26.5	+17.2	-4.8	+37.8	-47.5	+44.8	-21.1	-44.0
Steps (reduced)		534 (197)	782 (108)	946 (272)	1068 (57)	1166 (155)	1247 (236)	1317 (306)	1377 (29)	1432 (84)	1480 (132)	1524 (176)

Subsets and supersets

337edo is the 68th prime EDO.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-534 337⟩	⟨337 534]	0.1487	0.1487	4.18
2.3.5	15625/15552, [-88 57 -1⟩	⟨337 534 782]	0.3495	0.3089	8.67
2.3.5.7	15625/15552, 16875/16807, 7381125/7340032	⟨337 534 782 946]	0.2870	0.2886	8.10

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	67\337	238.58	147/128	Tokko
1	89\337	316.91	6/5	Hanson