465edo: Difference between revisions
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,..." |
Review |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
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 === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
465 factors into 3 × 5 × 31, | 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" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|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|-737 465}} | | {{monzo| -737 465 }} | ||
|{{mapping|465 737}} | | {{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 | ||
| Line 46: | Line 46: | ||
! 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>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is 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 | ||