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Muggles: Difference between revisions

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{{Infobox regtemp
{{Infobox regtemp
| Title = Muggles
| Title = Muggles
| Subgroups = 2.3.5.7, 2.3.5.7.13
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
| Comma basis = [[126/125]], [[525/512]] (7-limit);<br>[[45/44]], [[126/125]], [[385/384]] (11-limit);<br>[[45/44]], [[65/64]], [[78/77]], [[126/125]]<br>(13-limit)
| Comma basis = [[126/125]], [[525/512]] (7-limit);<br>[[45/44]], [[126/125]], [[385/384]] (11-limit);<br>[[45/44]], [[65/64]], [[78/77]], [[126/125]]<br>(13-limit)
| Edo join 1 = 16 | Edo join 2 = 19
| Edo join 1 = 16 | Edo join 2 = 19
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<nowiki/>* In 2.3.5.7.13 CWE tuning
<nowiki/>* In 2.3.5.7.13 CWE tuning


== Tuning spectra ==
== Tunings ==
=== Muggles ===
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~5/4 = 378.7441{{c}}
| CWE: ~5/4 = 378.5328{{c}}
| POTE: ~5/4 = 378.4794{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~5/4 = 377.1761{{c}}
| CWE: ~5/4 = 377.7336{{c}}
| POTE: ~5/4 = 377.6530{{c}}
|}
 
=== Target tunings ===
{| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Target tunings
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 7-odd-limit
| ~5/4 = 377.761{{c}}
| 7/6
| ~5/4 = 377.640{{c}}
| {{Monzo| 0 -21 -5 27 }}
|-
| 9-odd-limit
| ~5/4 = 378.534{{c}}
| 9/7
| ~5/4 = 378.554{{c}}
| {{Monzo| 0 93 -4 -44 }}
|-
| 11-odd-limit
| ~5/4 = 377.393{{c}}
| 11/8
| ~5/4 = 377.758{{c}}
| {{Monzo| 0 85 -14 -62 46 }}
|-
| 13-odd-limit
| ~5/4 = 377.393{{c}}
| 11/8
| ~5/4 = 377.630{{c}}
| {{Monzo| 0 113 -12 -68 58 -26 }}
|-
| 15-odd-limit
| ~5/4 = 377.393{{c}}
| 11/8
| ~5/4 = 377.718{{c}}
| {{Monzo| 0 134 9 -81 63 -33 }}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
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|  
|  
| 375.000
| 375.000
|  
| Lower bound of 7-odd-limit diamond monotone
|-
|-
|  
|  
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| 377.393
| 377.393
| 11-, 13- and 15-odd-limit minimax
| 11-, 13- and 15-odd-limit minimax
|-
|
| {{monzo| 0 113 -12 -68 58 -26 }}
| 377.630
| 13-odd-limit least squares
|-
|
| {{monzo| 0 -21 -5 27 }}
| 377.640
| 7-odd-limit least squares
|-
|
| {{monzo| 0 134 9 -81 63 -33 }}
| 377.718
| 15-odd-limit least squares
|-
|
| {{monzo| 0 85 -14 -62 46 }}
| 377.758
| 11-odd-limit least squares
|-
|-
|  
|  
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| 378.534
| 378.534
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|
| {{monzo| 0 93 -4 -44 }}
| 378.554
| 9-odd-limit least squares
|-
|-
|  
|  
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|  
|  
| 378.947
| 378.947
|  
| Upper bound of 7-odd-limit diamond monotone; <br>9-, 11-, and 13-odd-limit diamond monotone (singleton)
|-
|-
|  
|  
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| 379.733
| 379.733
|  
|  
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|-
|
|
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|  
|  
| 381.818
| 381.818
|  
| 22d… val
|-
|-
|  
|  
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|  
|  
|}
|}
<nowiki/>* Besides the octave


== Notes ==
== References ==


[[Category:Muggles| ]] <!-- main article -->
[[Category:Muggles| ]] <!-- main article -->
Retrieved from "https://en.xen.wiki/w/Muggles"