1553edo

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1553edo

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Prime factorization	1553 (prime)
Step size	0.772698 ¢
Fifth	908\1553 (701.61 ¢)
Semitones (A1:m2)	144:119 (111.3 ¢ : 91.95 ¢)
Dual sharp fifth	909\1553 (702.382 ¢)
Dual flat fifth	908\1553 (701.61 ¢)
Dual major 2nd	264\1553 (203.992 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

1553edo is only consistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. Assume the patent val, 1553et tempers out 200120949/200000000 in the 7-limit; 102487/102400, 759375/758912, 2359296/2358125, and 369140625/369098752 in the 11-limit; 1716/1715, 40656/40625, 59535/59488, 105644/105625, 196625/196608, 200000/199927, 823875/823543, 8859375/8859136, 34034175/34027136, and 75000000/74942413, in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 1553edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.345	+0.035	+0.137	+0.082	-0.384	+0.168	-0.310	+0.132	-0.024	-0.208	-0.071
	Relative (%)	-44.7	+4.6	+17.8	+10.6	-49.7	+21.7	-40.1	+17.0	-3.1	-26.9	-9.2
Steps (reduced)		2461 (908)	3606 (500)	4360 (1254)	4923 (264)	5372 (713)	5747 (1088)	6067 (1408)	6348 (136)	6597 (385)	6821 (609)	7025 (813)

Subsets and supersets

1553edo is the 245th prime edo. 3106edo, which doubles it, provides a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-2461 1553⟩	⟨1553 2461]	0.1089	0.1089	14.09
2.3.5	1224440064/1220703125, [-201 99 19⟩	⟨1553 2461 3606]	0.0675	0.1064	13.77
2.3.5.7	200120949/200000000, 2579890176/2573571875, 23066015625/23018340352	⟨1553 2461 3606 4360]	0.0384	0.1051	13.60
2.3.5.7.11	24057/24010, 759375/758912, 2359296/2358125, 992436543/991232000	⟨1553 2461 3606 4360 5372]	0.0529	0.0984	12.73
2.3.5.7.11.13	729/728, 1716/1715, 40656/40625, 196625/196608, 14085981/14080000	⟨1553 2461 3606 4360 5372 5747]	0.0366	0.0970	12.55
2.3.5.7.11.13.17	729/728, 1716/1715, 1089/1088, 14400/14399, 27648/27625, 14085981/14080000	⟨1553 2461 3606 4360 5372 5747 6348]	0.0267	0.0930	12.04
2.3.5.7.11.13.17.19	729/728, 1716/1715, 1089/1088, 5985/5984, 4200/4199, 21888/21875, 287469/287375	⟨1553 2461 3606 4360 5372 5747 6348 6597]	0.0241	0.0872	11.29