Muggles: Difference between revisions

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'''Muggles''' is the rank-2 temperament [[tempering out]] [[126/125]], the starling comma, and [[525/512]], Avicenna's enharmonic diesis. It is an alternative 7-limit extension to [[magic]]. 11-limit extension of the muggles include:  
'''Muggles''' is the rank-2 [[regular temperament|temperament]] [[tempering out]] [[126/125]], the starling comma, and [[525/512]], Avicenna's enharmonic diesis. It is an alternative 7-limit extension to [[magic]]. 11-limit extension of the muggles include:  


* Muggles (3e&16 or 16&19) - tempering out 45/44 and 385/384
* Muggles (3e & 16 or 16 & 19) – tempering out 45/44 and 385/384
* Muggloid (3&16 or 16&19e) - tempering out 33/32 and 176/175
* Muggloid (3 & 16 or 16 & 19e) – tempering out 33/32 and 176/175


This temperament was named by [[Gene Ward Smith]] in 2003<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5279.html#5299 Yahoo! Tuning Group | ''Poptimal generators'']</ref>.
This temperament was named by [[Gene Ward Smith]] in 2003<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5279.html#5299 Yahoo! Tuning Group | ''Poptimal generators'']</ref>.
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== Tuning spectra ==
== Tuning spectra ==
=== Muggles ===
=== Muggles ===
Gencom: [2 5/4; 45/44 65/64 78/77 126/125]
Gencom mapping: [{{val| 1 0 2 5 0 4 }}, {{val| 0 5 1 -7 11 -1 }}]
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! ET<br>generator
! Edo<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! Generator (¢)
! comments
! Comments
|-
|-
|  
|  
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|-
|-
|  
|  
| 16/13
| 13/8
| 359.472
| 359.472
|  
|  
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|-
|-
|  
|  
| 12/11
| 11/6
| 374.894
| 374.894
|  
|  
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|-
|-
|  
|  
| 8/7
| 7/4
| 375.882
| 375.882
|  
|  
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|-
|-
|  
|  
| 14/11
| 11/7
| 376.805
| 376.805
|  
|  
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|-
|-
|  
|  
| <span style="font-size:0.75em">{{monzo| 0 113 -12 -68 58 -26 }}</span>
| {{monzo| 0 113 -12 -68 58 -26 }}
| 377.630
| 377.630
| 13-odd-limit least squares
| 13-odd-limit least squares
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|-
|-
|  
|  
| <span style="font-size:0.75em">{{monzo| 0 134 9 -81 63 -33 }}</span>
| {{monzo| 0 134 9 -81 63 -33 }}
| 377.718
| 377.718
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|
|
| <span style="font-size:0.9em">{{monzo| 0 85 -14 -62 46 }}</span>
| {{monzo| 0 85 -14 -62 46 }}
| 377.758
| 377.758
| 11-odd-limit least squares
| 11-odd-limit least squares
Line 127: Line 123:
|-
|-
|  
|  
| 18/13
| 13/9
| 378.489
| 378.489
|  
|  
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|-
|-
|  
|  
| 14/13
| 13/7
| 378.617
| 378.617
|  
|  
|-
|-
|  
|  
| 6/5
| 5/3
| 378.910
| 378.910
|  
|  
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|-
|-
|  
|  
| 10/9
| 9/5
| 379.733
| 379.733
|  
|  
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|-
|-
|
|
| 4/3
| 3/2
| 380.391
| 380.391
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|  
|  
| 16/15
| 15/8
| 381.378
| 381.378
|  
|  
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=== Muggloid ===
=== Muggloid ===
Gencom: [2 5/4; 33/32 65/64 105/104 126/125]
Gencom mapping: [{{val| 1 0 2 5 5 4 }}, {{val| 0 5 1 -7 -5 -1 }}]
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! ET<br>generator
! Edo<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! Generator (¢)
! comments
! Comments
|-
|-
|  
|  
| 16/13
| 13/8
| 359.472
| 359.472
|  
|  
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|-
|-
|  
|  
| 12/11
| 11/6
| 375.064
| 375.064
|  
|  
|-
|-
|  
|  
| 8/7
| 7/4
| 375.882
| 375.882
|  
|  
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|-
|-
|  
|  
| 18/13
| 13/9
| 378.489
| 378.489
|  
|  
Line 290: Line 282:
|-
|-
|  
|  
| 14/13
| 13/7
| 378.617
| 378.617
|  
|  
|-
|-
|  
|  
| 6/5
| 5/3
| 378.910
| 378.910
|  
|  
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|-
|-
|  
|  
| 10/9
| 9/5
| 379.733
| 379.733
|  
|  
|-
|-
|
|
| 4/3
| 3/2
| 380.391
| 380.391
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|  
|  
| 16/15
| 15/8
| 381.378
| 381.378
|  
|  
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|-
|-
|  
|  
| 14/11
| 11/7
| 391.246
| 391.246
|  
|  

Revision as of 04:44, 30 December 2024

Muggles is the rank-2 temperament tempering out 126/125, the starling comma, and 525/512, Avicenna's enharmonic diesis. It is an alternative 7-limit extension to magic. 11-limit extension of the muggles include:

  • Muggles (3e & 16 or 16 & 19) – tempering out 45/44 and 385/384
  • Muggloid (3 & 16 or 16 & 19e) – tempering out 33/32 and 176/175

This temperament was named by Gene Ward Smith in 2003[1].

See Magic family #Muggles for more technical data.

Tuning spectra

Muggles

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
11/9 347.408
13/8 359.472
15/11 372.610
13/10 372.893
11/6 374.894
5\16 375.000
7/4 375.882
13/11 375.899
11/10 376.500
11/7 376.805
13/12 376.905
11\35 377.143
7/5 377.186
11/8 377.393 11-, 13- and 15-odd-limit minimax
[0 113 -12 -68 58 -26⟩ 377.630 13-odd-limit least squares
[0 -21 -5 27⟩ 377.640 7-odd-limit least squares
[0 134 9 -81 63 -33⟩ 377.718 15-odd-limit least squares
[0 85 -14 -62 46⟩ 377.758 11-odd-limit least squares
7/6 377.761 7-odd-limit minimax
15/13 378.249
15/14 378.419
13/9 378.489
9/7 378.534 9-odd-limit minimax
[0 93 -4 -44⟩ 378.554 9-odd-limit least squares
13/7 378.617
5/3 378.910
6\19 378.947
9/5 379.733
27/20 379.968 5-odd-limit least squares
3/2 380.391 5-odd-limit minimax
15/8 381.378
7\22 381.818
5/4 386.314

Muggloid

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
13/8 359.472
11/8 369.736
13/11 372.302
11/10 372.499
13/10 372.893
5\16 375.000
11/6 375.064
7/4 375.882
15/11 376.086
11/9 376.839 11-, 13- and 15-odd-limit minimax
13/12 376.905
11\35 377.143
7/5 377.186
7/6 377.761 7-odd-limit minimax
15/13 378.249
15/14 378.419
13/9 378.489
9/7 378.534 9-odd-limit minimax
13/7 378.617
5/3 378.910
6\19 378.947
9/5 379.733
3/2 380.391 5-odd-limit minimax
15/8 381.378
7\22 381.818
5/4 386.314
11/7 391.246

Notes

  1. ↑ Yahoo! Tuning Group | Poptimal generators
Retrieved from "https://en.xen.wiki/index.php?title=Muggles&oldid=173820"