50edo: Difference between revisions
→Approximation to JI: stop the creep and revert to 15-odd-limit cuz we wanna be able to compare it across similar edos in this range |
m →Regular temperament properties: cleanup |
||
| Line 392: | Line 392: | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 435: | Line 435: | ||
=== Commas === | === Commas === | ||
50edo [[tempers out]] the following [[comma]]s. (Note: | 50edo [[tempers out]] the following [[comma]]s. (Note: this assumes the [[val]] {{val| 50 79 116 140 173 185 204 212 226 }}, comma values in cents rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2. | ||
{| class="commatable wikitable center-all left-3 right-4 left-5" | {| class="commatable wikitable center-all left-3 right-4 left-5" | ||
|- | |- | ||
! [[Harmonic limit|Prime<br | ! [[Harmonic limit|Prime<br>limit]] | ||
! [[Ratio]]<ref group="note">{{rd}}</ref> | ! [[Ratio]]<ref group="note">{{rd}}</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
| Line 503: | Line 503: | ||
| {{monzo| 6 0 -5 2 }} | | {{monzo| 6 0 -5 2 }} | ||
| 6.08 | | 6.08 | ||
| Hemimean | | Hemimean comma | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 509: | Line 509: | ||
| {{monzo| 11 -10 -10 10 }} | | {{monzo| 11 -10 -10 10 }} | ||
| 5.57 | | 5.57 | ||
| [[Linus]] | | [[Linus comma]] | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 527: | Line 527: | ||
| {{monzo| -1 0 1 2 -2 }} | | {{monzo| -1 0 1 2 -2 }} | ||
| 21.33 | | 21.33 | ||
| | | Frostma | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 545: | Line 545: | ||
| {{monzo| 5 -1 3 0 -3 }} | | {{monzo| 5 -1 3 0 -3 }} | ||
| 3.03 | | 3.03 | ||
| Wizardharry | | Wizardharry comma | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 575: | Line 575: | ||
| {{monzo| 2 3 0 -1 1 -2 }} | | {{monzo| 2 3 0 -1 1 -2 }} | ||
| 7.30 | | 7.30 | ||
| Kestrel | | Kestrel comma | ||
|- | |- | ||
| 13 | | 13 | ||
| Line 587: | Line 587: | ||
| {{monzo| 2 -1 0 1 -2 1 }} | | {{monzo| 2 -1 0 1 -2 1 }} | ||
| 4.76 | | 4.76 | ||
| | | Minor minthma | ||
|- | |- | ||
| 13 | | 13 | ||
| Line 684: | Line 684: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
| Line 798: | Line 798: | ||
| [[Decic]] | | [[Decic]] | ||
|} | |} | ||
<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 | ||
== Instruments == | == Instruments == | ||