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

1193 equal divisions of the octave (abbreviated 1193edo), or 1193-tone equal temperament (1193tet), 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 of 1193edo 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 +14 -6 -17 -10 +38 -34 +22 +39 +43 -36
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

Music

Francium