475edo: Difference between revisions
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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" | ||
|- | |||
! 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| 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 | ||
|} | |||
=== 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 39: | Line 55: | ||
| 98304/78125 | | 98304/78125 | ||
| [[Squarschmidt]] | | [[Squarschmidt]] | ||
|- | |||
| 1 | |||
| 233\475 | |||
| 588.63 | |||
| 351/250 | |||
| [[Ragitritonic]] (475d) / [[garitritonic]] (475e) | |||
|- | |- | ||
| 5 | | 5 | ||
| 329\475<br | | 329\475<br>(44\475) | ||
| 831.16<br | | 831.16<br>(111.16) | ||
| 160/99<br | | 160/99<br>(16/15) | ||
| [[Quintosec]] | | [[Quintosec]] | ||
|- | |- | ||
| 19 | | 19 | ||
| 197\475<br | | 197\475<br>(3\475) | ||
| 497.68<br | | 497.68<br>(7.58) | ||
| 4/3<br | | 4/3<br>(225/224) | ||
| [[Enneadecal]] (475d) | | [[Enneadecal]] (475d) | ||
|} | |||
<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 | |||