457edo

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457edo

458edo →

Prime factorization	457 (prime)
Step size	2.62582 ¢
Fifth	267\457 (701.094 ¢)
Semitones (A1:m2)	41:36 (107.7 ¢ : 94.53 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

457et tempers out 283115520/282475249, 1220703125/1219784832, 26873856/26796875, 65625/65536 and 200120949/200000000 in the 7-limit; 95703125/95664294, 100663296/100656875, 161280/161051, 29296875/29218112, 166698/166375, 1953125/1951488, 151263/151250, 2359296/2358125, 540/539, 5767168/5764801, 825000/823543, 8019/8000, 160083/160000, 16808715/16777216, 539055/537824, 244515348/244140625, 67110351/67108864 and 43923/43904 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 457edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.86	-0.32	+0.10	+0.90	+0.10	-0.27	-1.18	+0.08	-0.80	-0.76	-0.70
	Relative (%)	-32.8	-12.1	+3.9	+34.4	+4.0	-10.1	-44.9	+2.9	-30.3	-28.9	-26.8
Steps (reduced)		724 (267)	1061 (147)	1283 (369)	1449 (78)	1581 (210)	1691 (320)	1785 (414)	1868 (40)	1941 (113)	2007 (179)	2067 (239)

Subsets and supersets

457edo is the 88th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-724 457⟩	⟨457 724]	0.2716	0.2716	10.34
2.3.5	[-36 11 8⟩, [-5 31 -19⟩	⟨457 724 1061]	0.2267	0.2307	8.79
2.3.5.7	19683/19600, 65625/65536, 7381125/7340032	⟨457 724 1061 1283]	0.1609	0.2300	8.76
2.3.5.7.11	540/539, 8019/8000, 19683/19600, 43923/43904	⟨457 724 1061 1283 1581]	0.1227	0.2194	8.36
2.3.5.7.11.13	540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923	⟨457 724 1061 1283 1581 1691]	0.1142	0.2012	7.66
2.3.5.7.11.13.17	936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224	⟨457 724 1061 1283 1581 1691 1868]	0.0952	0.1920	7.31

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	10\457	26.258	49/48	Sfourth
1	136\457	357.11	49/40	Dodifo
1	213\457	559.30	864/625	Tritriple