1553edo

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1553edo

1554edo →

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. It has a reasonable approximation of the 2.9.5.7.13 subgroup, where it notably tempers out 4096/4095 and 140625/140608.

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 (%)
2.9	[4923 -1553⟩	[⟨1553 4923]]	-0.0130	0.0130	1.68
2.9.5	[93 -33 5⟩, [-36 -26 51⟩	[⟨1553 4923 3606]]	-0.0137	0.0106	1.38
2.9.5.7	[-5 5 5 -8⟩, [2 -10 14 -1⟩, [37 1 -4 -11⟩	[⟨1553 4923 3606 4360]]	-0.0225	0.0178	2.31
2.9.5.7.13	4096/4095, 140625/140608, 28829034/28824005, [4 10 -9 0 -4⟩	[⟨1553 4923 3606 4360 5372]]	-0.0271	0.0184	2.38

Music

Francium

• Stumbling Over Mystery (2023)