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475edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|475}} == Theory == 475et is only consistent to the 5-odd-limit. It can be considered for the 2.3.5.11.13.19.23 subgroup, tempering out 23..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|475}}
{{ED intro}}


== Theory ==
== Theory ==
475et is only consistent to the [[5-odd-limit]]. It can be considered for the 2.3.5.11.13.19.23 [[subgroup]], tempering out [[2376/2375]], 11132/11115, [[3250/3249]], 42757/42750, 11979/11960 and 14300/14283. It [[support]]s [[will]], [[countritonic]] and [[cotoneum]].
475edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| -14 -19 19 }} ([[enneadeca]]) and {{monzo| 47 -15 -10 }} (quintosec comma) in the 5-limit. In the 7-limit, the 475d [[val]] [[support]]s [[enneadecal]] and the [[patent val]] supports [[cotoneum]].
 
It can be considered for the 2.3.5.11.13.19.23 [[subgroup]], tempering out [[2376/2375]], [[3250/3249]], 11132/11115, 11979/11960, 14300/14283 and 42757/42750.  


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
475 factors into 5<sup>2</sup> × 19, with 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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|753 -475}}
! rowspan="2" | [[Comma list]]
|{{mapping|475 753}}
! rowspan="2" | [[Mapping]]
| -0.1138
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 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}}
| {{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
|-
|-
|1
| 1
|157\475
| 157\475
|396.63
| 396.63
|98304/78125
| 98304/78125
|[[Squarschmidt]]
| [[Squarschmidt]]
|-
|-
|5
| 1
|329\475<br>(44\475)
| 233\475
|831.16<br>(111.16)
| 588.63
|80/49<br>(15/14)
| 351/250
|[[Qintosec]]
| [[Ragitritonic]] (475d) / [[garitritonic]] (475e)
|-
|-
|19
| 5
|197\475<br>(3\475)
| 329\475<br>(44\475)
|497.68<br>(7.58)
| 831.16<br>(111.16)
|4/3<br>(225/224)
| 160/99<br>(16/15)
|[[Enneadecal]]
| [[Quintosec]]
|-
| 19
| 197\475<br>(3\475)
| 497.68<br>(7.58)
| 4/3<br>(225/224)
| [[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
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
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