351edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
351 factors into | 351 factors into {{factorisation|351}} with subset edos {{EDOs| 3, 9, 13, 27, 39, and 117 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 15: | Line 15: | ||
|- | |- | ||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br />8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
| Line 26: | Line 26: | ||
| {{monzo| -556 351 }} | | {{monzo| -556 351 }} | ||
| {{mapping| 351 556 }} | | {{mapping| 351 556 }} | ||
| 0.3471 | | +0.3471 | ||
| 0.3472 | | 0.3472 | ||
| 10.16 | | 10.16 | ||
| Line 33: | Line 33: | ||
| {{monzo| -36 11 8 }}, {{monzo| -11 26 -13 }} | | {{monzo| -36 11 8 }}, {{monzo| -11 26 -13 }} | ||
| {{mapping| 351 556 815 }} | | {{mapping| 351 556 815 }} | ||
| 0.2298 | | +0.2298 | ||
| 0.3284 | | 0.3284 | ||
| 9.61 | | 9.61 | ||
| Line 40: | Line 40: | ||
| 19683/19600, 65625/65536, 235298/234375 | | 19683/19600, 65625/65536, 235298/234375 | ||
| {{mapping| 351 556 815 985 }} | | {{mapping| 351 556 815 985 }} | ||
| 0.2885 | | +0.2885 | ||
| 0.3021 | | 0.3021 | ||
| 8.84 | | 8.84 | ||
| Line 47: | Line 47: | ||
| 441/440, 19683/19600, 35937/35840, 65625/65536 | | 441/440, 19683/19600, 35937/35840, 65625/65536 | ||
| {{mapping| 351 556 815 985 1214 }} | | {{mapping| 351 556 815 985 1214 }} | ||
| 0.2823 | | +0.2823 | ||
| 0.2705 | | 0.2705 | ||
| 7.91 | | 7.91 | ||
| Line 59: | Line 59: | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br /> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 68: | Line 68: | ||
| [[Squarschmidt]] | | [[Squarschmidt]] | ||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||