475edo: Difference between revisions
Review |
→Regular temperament properties: + ragitritonic/garitritonic |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 475 factors into | Since 475 factors into {{factorisation|475}}, 475edo has subset edos {{EDOs| 5, 19, 25, and 95 }}. [[950edo]], which doubles it, gives a good correction to the harmonic 7. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! 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]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 753 -475 }} | ||
| {{ | | {{Mapping| 475 753 }} | ||
| | | −0.1138 | ||
| 0.1138 | | 0.1138 | ||
| 4.50 | | 4.50 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| -14 -19 19 }}, {{monzo| 47 -15 -10 }} | ||
| {{ | | {{Mapping| 475 753 1103 }} | ||
| | | −0.1064 | ||
| 0.0935 | | 0.0935 | ||
| 3.70 | | 3.70 | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 53: | Line 55: | ||
| 98304/78125 | | 98304/78125 | ||
| [[Squarschmidt]] | | [[Squarschmidt]] | ||
|- | |||
| 1 | |||
| 233\475 | |||
| 588.63 | |||
| 351/250 | |||
| [[Ragitritonic]] (475d) / [[garitritonic]] (475e) | |||
|- | |- | ||
| 5 | | 5 | ||
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| [[Enneadecal]] (475d) | | [[Enneadecal]] (475d) | ||
|} | |} | ||
<nowiki>* | <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 | ||