450edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|450}} == Theory == 450et is consistent to the 7-odd-limit. It can be considered for the 2.3.5.7.13.17.29.31.37 subgroup, tempering out 651/..." |
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== 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. It [[support]]s [[decal]] and [[varuna]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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== 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|-713 450}} | | {{monzo| -713 450 }} | ||
|{{mapping|450 713}} | | {{mapping| 450 713 }} | ||
| 0.1961 | | +0.1961 | ||
| 0.1961 | | 0.1961 | ||
| 7.35 | | 7.35 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-28 25 -5}}, {{monzo|25 15 -21}} | | {{monzo| -28 25 -5 }}, {{monzo| 25 15 -21 }} | ||
|{{mapping|450 713 1045}} | | {{mapping| 450 713 1045 }} | ||
| 0.0800 | | +0.0800 | ||
| 0.2293 | | 0.2293 | ||
| 8.60 | | 8.60 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|321489/320000 | | 235298/234375, 321489/320000, 26873856/26796875 | ||
|{{mapping|450 713 1045 1263}} | | {{mapping| 450 713 1045 1263 }} | ||
| 0.1336 | | +0.1336 | ||
| 0.2192 | | 0.2192 | ||
| 8.22 | | 8.22 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|2 | | 2 | ||
|61\450 | | 61\450 | ||
|162.67 | | 162.67 | ||
|1125/1024 | | 1125/1024 | ||
|[[Kwazy]] | | [[Kwazy]] | ||
|- | |- | ||
|5 | | 5 | ||
|187\450<br>(7\450) | | 187\450<br>(7\450) | ||
|498.67<br>(18.67) | | 498.67<br>(18.67) | ||
|4/3<br>(81/80) | | 4/3<br>(81/80) | ||
|[[Pental]] | | [[Pental]] (5-limit) | ||
|} | |} | ||
<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 | ||