3776edo

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3776edo

3777edo →

Prime factorization	26 × 59
Step size	0.317797 ¢
Fifth	2209\3776 (702.013 ¢)
Semitones (A1:m2)	359:283 (114.1 ¢ : 89.94 ¢)
Consistency limit	13
Distinct consistency limit	13

Theory

3776edo is a good 2.3.11.13.19. system. It does not tune the 15-odd-limit consistently, though a reasonable represenation exists through the 19-limit patent val, where it is a tuning for the oganesson temperament in the 19-limit, which sets 1/118th of the octave to an interval that represents 169/168, 170/169, and 171/170 tempered together.

It tempers out the quartisma in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.

Odd harmonics

Approximation of odd harmonics in 3776edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.058	+0.127	+0.136	+0.115	+0.059	+0.044	-0.133	-0.083	-0.055	-0.124	+0.010
	Relative (%)	+18.2	+40.0	+42.8	+36.3	+18.6	+14.0	-41.9	-26.0	-17.4	-39.1	+3.0
Steps (reduced)		5985 (2209)	8768 (1216)	10601 (3049)	11970 (642)	13063 (1735)	13973 (2645)	14752 (3424)	15434 (330)	16040 (936)	16585 (1481)	17081 (1977)

Regular temperament properties

Rank-2 temperaments

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
118	1781\3776 (21\3776)	565.995 (6.67)	165/119 (?)	Oganesson