443edo: 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 22: | Line 31: | ||
| 0.1183 | | 0.1183 | ||
| 4.37 | | 4.37 | ||
|} | |||
=== 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 32: | Line 48: | ||
| 15/13 | | 15/13 | ||
| [[Hemischis]] (443) | | [[Hemischis]] (443) | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Scales == | == Scales == | ||
Revision as of 13:15, 16 November 2024
| ← 442edo | 443edo | 444edo → |
Theory
443edo is inconsistent to the 5-odd-limit and the error of harmonic 5 is quite large. To start with, the patent val ⟨443 702 1029 1244 1533] as well as the 443cde val ⟨443 702 1028 1243 1532] are worth considering.
Using the patent val, the equal temperament tempers out 6144/6125, 32805/32768, and 67108864/66976875 in the 7-limit; 540/539, 5632/5625, 8019/8000, and 131072/130977 in the 11-limit. It supports hemischis, the 130 & 313 temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.37 | +1.05 | +0.93 | +1.28 | -0.80 | +0.69 | +0.46 | +0.17 | -0.23 | +0.79 |
| Relative (%) | +0.0 | -13.8 | +38.6 | +34.2 | +47.2 | -29.5 | +25.4 | +16.8 | +6.2 | -8.6 | +29.1 | |
| Steps (reduced) |
443 (0) |
702 (259) |
1029 (143) |
1244 (358) |
1533 (204) |
1639 (310) |
1811 (39) |
1882 (110) |
2004 (232) |
2152 (380) |
2195 (423) | |
Subsets and supersets
443edo is the 86th prime edo. 886edo, which doubles it, gives a good correction until the 11-limit.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-702 443⟩ | [⟨443 702]] | 0.1183 | 0.1183 | 4.37 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 92\443 | 249.21 | 15/13 | Hemischis (443) |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct