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465edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|465}} == Theory == 465et is consistent to the 5-odd-limit. It can be considered for the 2.3.5.11.13.17 subgroup, tempering out 936/935,..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|465}}
{{ED intro}}


== Theory ==
== Theory ==
465et is consistent to the [[5-odd-limit]]. It can be considered for the 2.3.5.11.13.17 [[subgroup]], tempering out [[936/935]], 1377/1375, 71874/71825, 131648/131625 and 225000/224939. It [[support]]s [[birds]], [[counterschismic]] and [[belobog]].
465edo is only [[consistent]] to the [[5-odd-limit]], and the errors of [[harmonic]]s beyond [[3/1|3]] tend to be quite large. It can be considered for the 2.3.5.11.13.17 [[subgroup]], [[tempering out]] [[936/935]], 1377/1375, 71874/71825, 131648/131625 and 225000/224939. It [[support]]s [[counterschismic]] in the 5-limit, and [[birds]] and [[belobog]] in the 7-limit using the [[patent val]].


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
465 factors into 3 × 5 × 31, with subset edos {{EDOs|3, 5, 15, 31, 93, and 155}}. [[930edo]], which doubles it, gives a good correction to the harmonic 7.
Since 465 factors into 3 × 5 × 31, 465edo has subset edos {{EDOs| 3, 5, 15, 31, 93, and 155 }}. [[930edo]], 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|-737 465}}
! rowspan="2" | [[Comma list]]
|{{mapping|465 737}}
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -737 465 }}
| {{mapping| 465 737 }}
| +0.0062
| +0.0062
| 0.0062
| 0.0062
| 0.24
| 0.24
|-
|-
|2.3.5
| 2.3.5
|{{monzo|25 15 -21}}, {{monzo|-22 30 -11}}
| {{monzo| 25 15 -21 }}, {{monzo| -22 30 -11 }}
|{{mapping|465 737 1080}}
| {{mapping| 465 737 1080 }}
| -0.1083
| −0.1083
| 0.1619
| 0.1619
| 6.27
| 6.27
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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
|193\465
| 193\465
|498.06
| 498.06
|4/3
| 4/3
|[[Counterschismic]]
| [[Counterschismic]]
|-
|-
|5
| 5
|322\465<br>(43\465)
| 322\465<br />(43\465)
|830.97<br>(110.97)
| 830.97<br />(110.97)
|80/49<br>(15/14)
| 80/49<br />(15/14)
|[[Qintosec]]
| [[Qintosec]] (465)
|}
|}
 
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|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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