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

1193edo is consistent to the 11-odd-limit. As an equal temperament, it tempers out [144 -22 -47⟩ (gross comma) in the 5-limit; 2401/2400 in the 7-limit; 3025/3024, 41503/41472, 151263/151250, 17561600/17537553, 26214400/26198073, 95703125/95664294, and 117440512/117406179 in the 11-limit.

Prime harmonics

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)

Subsets and supersets

1193edo is the 196th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[1891 -1193⟩	[⟨1193 1891]]	−0.0443	0.0443	4.41
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⟩, [41 -15 -5 -2⟩	[⟨1193 1891 2770 3349]]	−0.000028	0.0558	5.55
2.3.5.7.11	2401/2400, 3025/3024, 17561600/17537553, 95703125/95664294	[⟨1193 1891 2770 3349 4127]]	+0.0059	0.0513	5.10
2.3.5.7.11.13	2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244	[⟨1193 1891 2770 3349 4127 4415]]	−0.0121	0.0617	6.14
2.3.5.7.11.13.17	2401/2400, 2431/2430, 2601/2600, 3025/3024, 4096/4095, 42500/42471	[⟨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*	Cents*	Associated ratio*	Temperaments
1	91\1193	91.534	[144 -22 -47⟩	Gross
1	257\1193	258.508	125/108	Lafa
1	355\1193	357.083	768/625	Dodifo

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Music

Francium

• "I Made A Gross Mistake" from Gross Temperament EP (2023) Spotify | Bandcamp | YouTube – gross in 1193edo
• 1193 (2024) – Spotify | bandcamp | YouTube – 4-piece EP in 1193edo