1193edo
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 supports the gross temperament.
Prime harmonics
| 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 | 4.40 |
| 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
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 91\1193 | 91.533948 | [144 -22 -47⟩ | Gross |