373edo

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373edo

374edo →

Prime factorization	373 (prime)
Step size	3.21716 ¢
Fifth	218\373 (701.34 ¢)
Semitones (A1:m2)	34:29 (109.4 ¢ : 93.3 ¢)
Consistency limit	15
Distinct consistency limit	15

The 373 equal divisions of the octave (373edo), or the 373(-tone) equal temperament (373tet, 373et) when viewed from a regular temperament perspective, is the equal division of the octave into 373 parts of about 3.22 cents each.

Theory

373edo is consistent to the 15-odd-limit, with harmonics 3 through 13 all tuned flat. It tempers out [8 14 -13⟩ (parakleisma) and [-51 19 9⟩ (untriton comma) in the 5-limit; 2401/2400 (breedsma), 65625/65536 (horwell), and 43046721/42875000 in the 7-limit; 3025/3024, 8019/8000, 24057/24010, and 496125/495616 in the 11-limit; 729/728, 1001/1000, 1716/1715, 4225/4224, and 10648/10647 in the 13-limit, enabling squbemic chords and sinbadmic chords. It supports the hemitert temperament.

373edo is the 74th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-591 373⟩	[⟨373 591]]	+0.1939	0.1939	6.03
2.3.5	[8 14 -13⟩, [-51 19 9⟩	[⟨373 591 866]]	+0.1658	0.1632	5.07
2.3.5.7	2401/2400, 65625/65536, 43046721/42875000	[⟨373 591 866 1047]]	+0.1654	0.1413	4.39
2.3.5.7.11	2401/2400, 3025/3024, 8019/8000, 65625/65536	[⟨373 591 866 1047 1290]]	+0.2008	0.1449	4.50
2.3.5.7.11.13	729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224	[⟨373 591 866 1047 1290 1380]]	+0.2056	0.1327	4.12

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	12\373	38.61	45/44	Hemitert
1	24\373	77.21	256/245	Tertiaseptal
1	98\373	315.28	6/5	Parakleismic (5-limit)
1	111\373	357.10	768/625	Dodifo (5-limit)
1	162\373	521.18	875/648	Maviloid
1	183\373	588.74	45/32	Untriton (5-limit)