403edo

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403edo

404edo →

Prime factorization	13 × 31
Step size	2.97767 ¢
Fifth	236\403 (702.73 ¢)
Semitones (A1:m2)	40:29 (119.1 ¢ : 86.35 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

403et tempers out 134217728/133984375, 78125000/78121827 and 2100875/2097152 in the 7-limit; 100663296/100656875, 806736/805255, 2097152/2096325, 12005/11979, 7168000/7144929, 131072/130977, 107495424/107421875, 42875/42768, 1684375/1679616, 3025/3024, 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit.

Approximation of odd harmonics in 403edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.77	+0.78	-1.08	-1.43	-0.45	-0.83	-1.42	-0.74	+0.25	-0.31	+0.01
	Relative (%)	+26.0	+26.3	-36.4	-48.0	-15.1	-27.7	-47.7	-24.8	+8.5	-10.4	+0.5
Steps (reduced)		639 (236)	936 (130)	1131 (325)	1277 (68)	1394 (185)	1491 (282)	1574 (365)	1647 (35)	1712 (100)	1770 (158)	1823 (211)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[639 -403⟩	⟨403 639]	-0.2443	0.2443	8.20
2.3.5	[9 -13 5⟩, [81 -13 -26⟩	⟨403 639 936]	-0.2753	0.2042	6.86
2.3.5.7	3136/3125, 1600000/1594323, 2100875/2097152	⟨403 639 936 1131]	-0.3751	0.2473	8.31
2.3.5.7.11	3025/3024, 3388/3375, 42875/42768, 131072/130977	⟨403 639 936 1131 1394]	-0.0621	0.3160	10.61
2.3.5.7.11.13	2080/2079, 3025/3024, 3388/3375, 4096/4095, 42875/42768	⟨403 639 936 1131 1394 1491]	-0.0146	0.3074	10.32
2.3.5.7.11.13.17	2080/2079, 595/594, 1225/1224, 3025/3024, 4096/4095, 3388/3375	⟨403 639 936 1131 1394 1491 1647]	+0.0133	0.2927	9.83

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	106\403	315.63	6/5	Egads
1	53\403	157.82	36756909/33554432	Hemiegads