433edo

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433edo

434edo →

Prime factorization	433 (prime)
Step size	2.77136 ¢
Fifth	253\433 (701.155 ¢)
Semitones (A1:m2)	39:34 (108.1 ¢ : 94.23 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

433et tempers out 4096000/4084101, 95703125/95551488 and 1640558367/1638400000 in the 7-limit; 161280/161051, 25165824/25109315, 1019215872/1019046875, 4000/3993, 2359296/2358125, 6250/6237, 180224/180075, 17537553/17500000, 3025/3024 and 1362944/1361367 in the 11-limit.

Subsets and supersets

433edo is the 84th prime edo.

Odd harmonics

Approximation of odd harmonics in 433edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.80	-1.09	+1.15	+1.17	+0.18	-0.80	+0.88	+0.36	-0.98	+0.35	+0.82
	Relative (%)	-28.9	-39.5	+41.5	+42.2	+6.6	-29.0	+31.6	+12.9	-35.3	+12.7	+29.8
Steps (reduced)		686 (253)	1005 (139)	1216 (350)	1373 (74)	1498 (199)	1602 (303)	1692 (393)	1770 (38)	1839 (107)	1902 (170)	1959 (227)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-686 433⟩	⟨433 686]	0.2525	0.2525	9.11
2.3.5	[-21 3 7⟩, [-29 52 -23⟩	⟨433 686 1005]	0.3254	0.2306	8.32
2.3.5.7	19683/19600, 4096000/4084101, 2109375/2097152	⟨433 686 1005 1216]	0.1414	0.3759	13.56
2.3.5.7.11	3025/3024, 6250/6237, 30375/30184, 180224/180075	⟨433 686 1005 1216 1498]	0.1026	0.3451	12.45
2.3.5.7.11.13	2080/2079, 625/624, 3025/3024, 18954/18865, 41472/41405	⟨433 686 1005 1216 1498 1602]	0.1217	0.3179	11.47
2.3.5.7.11.13.17	2080/2079, 375/374, 715/714, 936/935, 1377/1372, 76032/75803	⟨433 686 1005 1216 1498 1602 1770]	0.0919	0.3033	10.94

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	98\433	271.594	75/64	Orson

Music

• sleeping as we don't know by Francium