450edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
450edo is [[consistent]] to the [[7-odd-limit]]. It can be considered for the 2.3.5.7.13.17.29.31.37 [[subgroup]], where it [[tempering out|tempers out]] 651/650, 1666/1665, 1887/1885, 2016/2015, 2295/2294, 5916/5915, 4901/4900 and 14229/14210 | 450edo is [[consistent]] to the [[7-odd-limit]]. It tempers out the [[triwellisma]] and the [[varunisma]] in the [[7-limit]], [[support]]ing and providing the [[optimal patent val]] for 7-limit [[decile]]. It can be considered for the 2.3.5.7.13.17.29.31.37 [[subgroup]], where it [[tempering out|tempers out]] 651/650, 1666/1665, 1887/1885, 2016/2015, 2295/2294, 5916/5915, 4901/4900 and 14229/14210. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
450 factors into 2 × 3<sup>2</sup> × 5<sup>2</sup>, | Since 450 factors into {{nowrap| 2 × 3<sup>2</sup> × 5<sup>2</sup> }}, 450edo has subset edos {{EDOs| 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, and 225 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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|- | |- | ||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -713 450 }} | ||
| {{ | | {{Mapping| 450 713 }} | ||
| +0.1961 | | +0.1961 | ||
| 0.1961 | | 0.1961 | ||
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|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| -28 25 -5 }}, {{monzo| 25 15 -21 }} | ||
| {{ | | {{Mapping| 450 713 1045 }} | ||
| +0.0800 | | +0.0800 | ||
| 0.2293 | | 0.2293 | ||
| Line 39: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 235298/234375, 321489/320000, 26873856/26796875 | | 235298/234375, 321489/320000, 26873856/26796875 | ||
| {{ | | {{Mapping| 450 713 1045 1263 }} | ||
| +0.1336 | | +0.1336 | ||
| 0.2192 | | 0.2192 | ||
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 62: | Line 62: | ||
|- | |- | ||
| 5 | | 5 | ||
| | | 7\450 | ||
| | | 18.67 | ||
| | | 81/80 | ||
| [[ | | [[Quintile]] | ||
|- | |||
| 10 | |||
| 7\450 | |||
| 18.67 | |||
| 81/80 | |||
| [[Decile]] | |||
|} | |} | ||
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | |||
[[Category:Decile]] | |||