475edo: Difference between revisions

Review
Regular temperament properties: + ragitritonic/garitritonic
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|475}}
{{ED intro}}


== Theory ==
== Theory ==
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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 475 factors into 5<sup>2</sup> × 19, 475edo has subset edos {{EDOs| 5, 19, 25, and 95 }}. [[950edo]], which doubles it, gives a good correction to the harmonic 7.
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|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning Error
! 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 }}
| {{Monzo| 753 -475 }}
| {{mapping| 475 753 }}
| {{Mapping| 475 753 }}
| -0.1138
| −0.1138
| 0.1138
| 0.1138
| 4.50
| 4.50
|-
|-
| 2.3.5
| 2.3.5
| {{monzo| -14 -19 19 }}, {{monzo| 47 -15 -10 }}
| {{Monzo| -14 -19 19 }}, {{monzo| 47 -15 -10 }}
| {{mapping| 475 753 1103 }}
| {{Mapping| 475 753 1103 }}
| -0.1064
| −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>Ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
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| 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 lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<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