773edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|773}} == Theory == 773edo is consistent to the 7-odd-limit. Using the patent val, it tempers out 2401/2400, 328..." |
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | |- | ||
! rowspan="2" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-1225 773}} | | {{monzo|-1225 773}} | ||
| {{mapping|773 1225}} | | {{mapping|773 1225}} | ||
| 0.0862 | | +0.0862 | ||
| 0.0862 | | 0.0862 | ||
| 5.55 | | 5.55 | ||
| Line 32: | Line 33: | ||
| 32805/32768, {{monzo|65 85 -86}} | | 32805/32768, {{monzo|65 85 -86}} | ||
| {{mapping|773 1225 1795}} | | {{mapping|773 1225 1795}} | ||
| 0.0241 | | +0.0241 | ||
| 0.1125 | | 0.1125 | ||
| 7.25 | | 7.25 | ||
| Line 39: | Line 40: | ||
| 2401/2400, 32805/32768, {{monzo|20 22 -20 -3}} | | 2401/2400, 32805/32768, {{monzo|20 22 -20 -3}} | ||
| {{mapping|773 1225 1795 2170}} | | {{mapping|773 1225 1795 2170}} | ||
| 0.0299 | | +0.0299 | ||
| 0.0979 | | 0.0979 | ||
| 6.31 | | 6.31 | ||
| Line 46: | Line 47: | ||
| 2401/2400, 32805/32768, 137781/137500, 766656/765625 | | 2401/2400, 32805/32768, 137781/137500, 766656/765625 | ||
| {{mapping|773 1225 1795 2170 2674}} | | {{mapping|773 1225 1795 2170 2674}} | ||
| 0.0365 | | +0.0365 | ||
| 0.0886 | | 0.0886 | ||
| 5.71 | | 5.71 | ||
| Line 53: | Line 54: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 72: | Line 74: | ||
| [[Helmholtz]] | | [[Helmholtz]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | |||
Revision as of 18:35, 7 February 2025
| ← 772edo | 773edo | 774edo → |
Theory
773edo is consistent to the 7-odd-limit. Using the patent val, it tempers out 2401/2400, 32805/32768, 137781/137500 and 766656/765625 in the 11-limit. It supports counterultrakleismic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.273 | +0.232 | -0.133 | -0.218 | -0.683 | +0.607 | +0.546 | +0.445 | -0.340 | +0.631 |
| Relative (%) | +0.0 | -17.6 | +15.0 | -8.5 | -14.1 | -44.0 | +39.1 | +35.2 | +28.7 | -21.9 | +40.6 | |
| Steps (reduced) |
773 (0) |
1225 (452) |
1795 (249) |
2170 (624) |
2674 (355) |
2860 (541) |
3160 (68) |
3284 (192) |
3497 (405) |
3755 (663) |
3830 (738) | |
Subsets and supersets
773edo is the 137th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1225 773⟩ | [⟨773 1225]] | +0.0862 | 0.0862 | 5.55 |
| 2.3.5 | 32805/32768, [65 85 -86⟩ | [⟨773 1225 1795]] | +0.0241 | 0.1125 | 7.25 |
| 2.3.5.7 | 2401/2400, 32805/32768, [20 22 -20 -3⟩ | [⟨773 1225 1795 2170]] | +0.0299 | 0.0979 | 6.31 |
| 2.3.5.7.11 | 2401/2400, 32805/32768, 137781/137500, 766656/765625 | [⟨773 1225 1795 2170 2674]] | +0.0365 | 0.0886 | 5.71 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 113\773 | 175.420 | 448/405 | Sesquiquartififths |
| 1 | 321\773 | 498.318 | 4/3 | Helmholtz |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct