1193edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 55: | Line 64: | ||
| 0.0664 | | 0.0664 | ||
| 6.60 | | 6.60 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 77: | Line 93: | ||
| 768/625 | | 768/625 | ||
| [[Dodifo]] | | [[Dodifo]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == | ||
Revision as of 12:55, 16 November 2024
| ← 1192edo | 1193edo | 1194edo → |
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
| 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
| 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