733edo: Difference between revisions
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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|Comma List]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning Error | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning Error | |||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|1162 -733}} | | {{monzo|1162 -733}} | ||
| {{mapping|733 1162}} | | {{mapping|733 1162}} | ||
| | | −0.1149 | ||
| 0.1149 | | 0.1149 | ||
| 7.02 | | 7.02 | ||
| Line 32: | Line 33: | ||
| {{monzo|38 -2 -15}}, {{monzo|42 -47 14}} | | {{monzo|38 -2 -15}}, {{monzo|42 -47 14}} | ||
| {{mapping|733 1162 1702}} | | {{mapping|733 1162 1702}} | ||
| | | −0.0829 | ||
| 0.1042 | | 0.1042 | ||
| 6.36 | | 6.36 | ||
| Line 39: | Line 40: | ||
| 420175/419904, 67108864/66976875, 48828125/48771072 | | 420175/419904, 67108864/66976875, 48828125/48771072 | ||
| {{mapping|733 1162 1702 2058}} | | {{mapping|733 1162 1702 2058}} | ||
| | | −0.0926 | ||
| 0.0918 | | 0.0918 | ||
| 5.61 | | 5.61 | ||
| Line 46: | Line 47: | ||
| 3025/3024, 19712/19683, 180224/180075, 1953125/1951488 | | 3025/3024, 19712/19683, 180224/180075, 1953125/1951488 | ||
| {{mapping|733 1162 1702 2058 2536}} | | {{mapping|733 1162 1702 2058 2536}} | ||
| | | −0.0965 | ||
| 0.0824 | | 0.0824 | ||
| 5.03 | | 5.03 | ||
| 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 67: | Line 69: | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
[[Category:Luna]] | [[Category:Luna]] | ||
Revision as of 16:17, 15 January 2025
| ← 732edo | 733edo | 734edo → |
Theory
733edo is consistent to the 11-odd-limit, tempering out 3025/3024, 19712/19683, 180224/180075 and 1953125/1951488. It supports hemiluna and French decimal.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.364 | +0.044 | +0.342 | +0.387 | -0.691 | -0.181 | +0.441 | +0.375 | +0.164 | -0.697 |
| Relative (%) | +0.0 | +22.2 | +2.7 | +20.9 | +23.7 | -42.2 | -11.0 | +26.9 | +22.9 | +10.0 | -42.6 | |
| Steps (reduced) |
733 (0) |
1162 (429) |
1702 (236) |
2058 (592) |
2536 (337) |
2712 (513) |
2996 (64) |
3114 (182) |
3316 (384) |
3561 (629) |
3631 (699) | |
Subsets and supersets
733edo is the 130th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1162 -733⟩ | [⟨733 1162]] | −0.1149 | 0.1149 | 7.02 |
| 2.3.5 | [38 -2 -15⟩, [42 -47 14⟩ | [⟨733 1162 1702]] | −0.0829 | 0.1042 | 6.36 |
| 2.3.5.7 | 420175/419904, 67108864/66976875, 48828125/48771072 | [⟨733 1162 1702 2058]] | −0.0926 | 0.0918 | 5.61 |
| 2.3.5.7.11 | 3025/3024, 19712/19683, 180224/180075, 1953125/1951488 | [⟨733 1162 1702 2058 2536]] | −0.0965 | 0.0824 | 5.03 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 118\733 | 193.179 | 262144/234375 | Luna |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct