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400edo: Difference between revisions

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→Subsets and supersets: Added 1600edo and 2000edo as notable 400edo supersets
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m Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"
 
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! rowspan="2" | [[Comma list]]
! rowspan="2" | [[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
|-
|-
Line 93: Line 93:
|-
|-
| 2.3.5
| 2.3.5
| {{monzo| -7 22 -12 }}, {{monzo| 47 -15 -10 }}
| {{Monzo| -7 22 -12 }}, {{monzo| 47 -15 -10 }}
| {{mapping| 400 634 929 }}
| {{Mapping| 400 634 929 }}
| &minus;0.1080
| −0.1080
| 0.1331
| 0.1331
| 4.44
| 4.44
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| 2.3.5.7
| 2.3.5.7
| 2401/2400, 1959552/1953125, 14348907/14336000
| 2401/2400, 1959552/1953125, 14348907/14336000
| {{mapping| 400 634 929 1123 }}
| {{Mapping| 400 634 929 1123 }}
| &minus;0.0965
| −0.0965
| 0.1170
| 0.1170
| 3.90
| 3.90
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| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 5632/5625, 9801/9800, 46656/46585
| 2401/2400, 5632/5625, 9801/9800, 46656/46585
| {{mapping| 400 634 929 1123 1384 }}
| {{Mapping| 400 634 929 1123 1384 }}
| &minus;0.1166
| −0.1166
| 0.1121
| 0.1121
| 3.74
| 3.74
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| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 676/675, 1001/1000, 1716/1715, 4096/4095, 39366/39325
| 676/675, 1001/1000, 1716/1715, 4096/4095, 39366/39325
| {{mapping| 400 634 929 1123 1384 1480 }}
| {{Mapping| 400 634 929 1123 1384 1480 }}
| &minus;0.0734
| −0.0734
| 0.1407
| 0.1407
| 4.69
| 4.69
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| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 4096/4095
| 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 4096/4095
| {{mapping| 400 634 929 1123 1384 1480 1635 }}
| {{Mapping| 400 634 929 1123 1384 1480 1635 }}
| &minus;0.0645
| −0.0645
| 0.1321
| 0.1321
| 4.40
| 4.40
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| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 676/675, 936/935, 969/968, 1001/1000, 1156/1155, 1216/1215, 1716/1715
| 676/675, 936/935, 969/968, 1001/1000, 1156/1155, 1216/1215, 1716/1715
| {{mapping| 400 634 929 1123 1384 1480 1635 1699 }}
| {{Mapping| 400 634 929 1123 1384 1480 1635 1699 }}
| &minus;0.0413
| −0.0413
| 0.1380
| 0.1380
| 4.60
| 4.60
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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 />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperament
! Temperament
|-
|-
Line 149: Line 149:
| 83\400
| 83\400
| 249.00
| 249.00
| {{monzo| -26 18 -1 }}
| {{Monzo| -26 18 -1 }}
| [[Monzismic]]
| [[Monzismic]]
|-
|-
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| 25/21
| 25/21
| [[Quinmite]]
| [[Quinmite]]
|-
| 1
| 131\400
| 393.00
| 2744/2187
| [[Emmthird]] (7-limit)
|-
|-
| 1
| 1
Line 183: Line 189:
|-
|-
| 5
| 5
| 123\400<br />(37\400)
| 123\400<br>(37\400)
| 369.00<br />(111.00)
| 369.00<br>(111.00)
| 1024/891<br />(16/15)
| 1024/891<br>(16/15)
| [[Quintosec]]
| [[Quintosec]]
|-
|-
| 10
| 10
| 83\400<br />(3\400)
| 83\400<br>(3\400)
| 249.00<br />(9.00)
| 249.00<br>(9.00)
| 15/13<br />(176/175)
| 15/13<br>(176/175)
| [[Decoid]]
| [[Decoid]]
|-
|-
| 80
| 80
| 166\400<br />(1\400)
| 166\400<br>(1\400)
| 498.00<br />(3.00)
| 498.00<br>(3.00)
| 4/3<br />(245/243)
| 4/3<br>(245/243)
| [[Octogintic]]
| [[Octogintic]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct


== Scales ==
== Scales ==
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