# 1193edo

 ← 1192edo 1193edo 1194edo →
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

1193 equal divisions of the octave (abbreviated 1193edo or 1193ed2), also called 1193-tone equal temperament (1193tet) or 1193 equal temperament (1193et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1193 equal parts of about 1.01 ¢ each. Each step represents a frequency ratio of 21/1193, or the 1193rd root of 2.

## Theory

1193edo is consistent to the 11-odd-limit. The equal temperament tempers out 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. It supports the gross temperament.

### 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 it is distinct

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