398edo: 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" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 398 factors into | Since 398 factors into {{factorisation|398}}, 398edo has [[2edo]] and [[199edo]] as its subsets. | ||
== 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| 631 -398 }} | | {{monzo| 631 -398 }} | ||
| {{mapping| 398 631 }} | | {{mapping| 398 631 }} | ||
| | | −0.1759 | ||
| 0.1759 | | 0.1759 | ||
| 5.83 | | 5.83 | ||
| Line 24: | Line 33: | ||
| 390625000/387420489, {{monzo| -53 10 16 }} | | 390625000/387420489, {{monzo| -53 10 16 }} | ||
| {{mapping| 398 631 924 }} | | {{mapping| 398 631 924 }} | ||
| | | −0.0622 | ||
| 0.2157 | | 0.2157 | ||
| 7.15 | | 7.15 | ||
| Line 45: | Line 54: | ||
| 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935 | | 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935 | ||
| {{mapping| 398 631 924 1117 1377 1473 }} | | {{mapping| 398 631 924 1117 1377 1473 }} | ||
| | | −0.0243 | ||
| 0.2313 | | 0.2313 | ||
| 7.67 | | 7.67 | ||
|} | |||
=== 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 70: | Line 86: | ||
| 11/10 | | 11/10 | ||
| [[Bisupermajor]] | | [[Bisupermajor]] | ||
|} | |||
<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 | |||