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

337edo is consistent to the 9-odd-limit, but the error of harmonic 5 is quite large. If the harmonic is used at all, it tends very flat. The equal temperament tempers out 16875/16807, 420175/419904, and 5250987/5242880 in the 7-limit. It supports 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*	Cents*	Associated Ratio*	Temperaments
1	67\337	238.58	147/128	Tokko
1	89\337	316.91	6/5	Hanson

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

Francium

• "The End Of A Good Day" from Mysteries (2023) Spotify | Bandcamp | YouTube