351edo: Difference between revisions
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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 |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== 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 == | ||
{ | {| 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 | ||
| {{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 24: | 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 31: | 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 38: | 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 | ||
|} | |||
=== 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 | ||
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| 98304/78125 | | 98304/78125 | ||
| [[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 | |||