1193edo

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1193edo

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Prime factorization	1193 (prime)
Step size	1.00587 ¢
Fifth	698\1193 (702.096 ¢)
Semitones (A1:m2)	114:89 (114.7 ¢ : 89.52 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

1193et tempers out 2401/2400 in the 7-limit; 117440512/117406179, 26214400/26198073, 151263/151250, 369140625/369098752, 537109375/536870912, 3025/3024, 41503/41472 and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the Gross temperament. 1193edo is the 196th prime edo.

Approximation of prime harmonics in 1193edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.141	-0.061	-0.175	-0.103	+0.378	-0.345	+0.224	+0.393	+0.431	-0.358
	Relative (%)	+0.0	+14.0	-6.0	-17.4	-10.2	+37.5	-34.3	+22.2	+39.1	+42.9	-35.6
Steps (reduced)		1193 (0)	1891 (698)	2770 (384)	3349 (963)	4127 (548)	4415 (836)	4876 (104)	5068 (296)	5397 (625)	5796 (1024)	5910 (1138)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1891 -1193⟩	⟨1193 1891]	-0.0443	0.0443	4.40
2.3.5	[10 -40 -23⟩, [77 -31 -12⟩	⟨1193 1891 2770]	-0.0209	0.0491	4.88
2.3.5.7	2401/2400, [-13 -12 15 -1⟩, [-18 -13 13 3⟩, [36 -16 -7 2⟩	⟨1193 1891 2770 3349]	-0.000028	0.0558	5.55
2.3.5.7.11	2401/2400, 3025/3024, 41503/41472, 151263/151250, 26214400/26198073	⟨1193 1891 2770 3349 4127]	+0.0059	0.0513	5.10
2.3.5.7.11.13	2401/2400, 3025/3024, 154880/154791, 1071875/1070784, 1960000/1957527, 5175625/5174928	⟨1193 1891 2770 3349 4127 4415]	-0.0121	0.0617	6.13
2.3.5.7.11.13.17	2401/2400, 2431/2430, 2601/2600, 3025/3024, 8624/8619, 12376/12375, 37180/37179, 42500/42471, 47432/47385, 122825/122694, 154880/154791	⟨1193 1891 2770 3349 4127 4415 4876]	+0.0017	0.0664	6.60

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	91\1193	91.533948	[144 -22 -47⟩	Gross