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450edo: Difference between revisions

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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/..."
 
m →Regular temperament properties: quintile isn't defined beyond the 5-limit
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|450}}
{{ED intro}}


== Theory ==
== 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 651/650, 1666/1665, 1887/1885, 2016/2015, 2295/2294, 5916/5915, 4901/4900 and 14229/14210. It [[support]]s [[decal]] and [[varuna]].
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>, with subset edos {{EDOs|2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, and 225}}.
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 ==
{| 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|-713 450}}
! rowspan="2" | [[Comma list]]
|{{mapping|450 713}}
! rowspan="2" | [[Mapping]]
| 0.1961
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| -713 450 }}
| {{Mapping| 450 713 }}
| +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, 26873856/26796875
| 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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=== 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
|-
|-
|2
| 2
|61\450
| 61\450
|162.67
| 162.67
|1125/1024
| 1125/1024
|[[Kwazy]]
| [[Kwazy]]
|-
| 5
| 7\450
| 18.67
| 81/80
| [[Quintile]]
|-
|-
|5
| 10
|187\450<br>(7\450)
| 7\450
|498.67<br>(18.67)
| 18.67
|4/3<br>(81/80)
| 81/80
|[[Pental]]
| [[Decile]]
|}
|}
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]


<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
[[Category:Decile]]
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