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]].  
'''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


See [[Magic family #Muggles]] for more technical data.  
See [[Magic family #Muggles]] for more technical data.  


== Tuning spectra ==
== Tuning spectra ==
 
=== Muggles ===
Gencom: [2 5/4; 45/44 65/64 78/77 126/125]
Gencom: [2 5/4; 45/44 65/64 78/77 126/125]


Gencom mapping: [{{map| 1 0 2 5 0 4 }}, {{map| 0 5 1 -7 11 -1 }}]
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"
Line 16: Line 19:
! Comments
! Comments
|-
|-
|
|  
| 11/9
| 11/9
| 347.408
| 347.408
|
|  
|-
|-
|
|  
| 16/13
| 16/13
| 359.472
| 359.472
|
|  
|-
|-
|
|  
| 15/11
| 15/11
| 372.610
| 372.610
|
|  
|-
|-
|
|  
| 13/10
| 13/10
| 372.893
| 372.893
|
|  
|-
|-
|
|  
| 12/11
| 12/11
| 374.894
| 374.894
|
|
|-
| 5\16
|
| 375.000
|  
|-
|-
|
|  
| 8/7
| 8/7
| 375.882
| 375.882
|
|  
|-
|-
|
|  
| 13/11
| 13/11
| 375.899
| 375.899
|
|  
|-
|-
|
|  
| 11/10
| 11/10
| 376.500
| 376.500
|
|  
|-
|-
|
|  
| 14/11
| 14/11
| 376.805
| 376.805
|
|  
|-
|-
|
|  
| 13/12
| 13/12
| 376.905
| 376.905
|
|
|-
| 11\35
|
| 377.143
|  
|-
|-
|
|  
| 7/5
| 7/5
| 377.186
| 377.186
|
|  
|-
|-
|
|  
| 11/8
| 11/8
| 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 }}
| <span style="font-size:0.75em">{{monzo| 0 113 -12 -68 58 -26 }}</span>
| 377.630
| 377.630
| 13-odd-limit least squares
| 13-odd-limit least squares
|-
|-
|
|  
| {{monzo| 0 -21 -5 27 }}
| {{monzo| 0 -21 -5 27 }}
| 377.640
| 377.640
| 7-odd-limit least squares
| 7-odd-limit least squares
|-
|-
|
|  
| {{monzo| 0 134 9 -81 63 -33 }}
| <span style="font-size:0.75em">{{monzo| 0 134 9 -81 63 -33 }}</span>
| 377.718
| 377.718
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|
|
| {{monzo| 0 85 -14 -62 46 }}
| <span style="font-size:0.9em">{{monzo| 0 85 -14 -62 46 }}</span>
| 377.758
| 377.758
| 11-odd-limit least squares
| 11-odd-limit least squares
|-
|-
|
|  
| 7/6
| 7/6
| 377.761
| 377.761
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
|
|  
| 15/13
| 15/13
| 378.249
| 378.249
|
|  
|-
|-
|
|  
| 15/14
| 15/14
| 378.419
| 378.419
|
|  
|-
|-
|
|  
| 18/13
| 18/13
| 378.489
| 378.489
|
|  
|-
|-
|
|  
| 9/7
| 9/7
| 378.534
| 378.534
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
|
|  
| {{monzo| 0 93 -4 -44 }}
| {{monzo| 0 93 -4 -44 }}
| 378.554
| 378.554
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
|-
|
|  
| 14/13
| 14/13
| 378.617
| 378.617
|
|  
|-
|-
|
|  
| 6/5
| 6/5
| 378.910
| 378.910
|
|  
|-
|-
| 6\19
| 6\19
|
|  
| 378.947
| 378.947
|
|  
|-
|-
|
|  
| 10/9
| 10/9
| 379.733
| 379.733
|
|  
|-
|-
|
|  
| 27/20
| 27/20
| 379.968
| 379.968
| 5-odd-limit least squares
| 5-odd-limit least squares
|-
| 19\60
|
| 380.000
|
|-
| 32\101
|
| 380.198
|
|-
|-
|
|
Line 166: Line 169:
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| 13\41
|  
|
| 16/15
| 380.488
| 381.378
|
|
|-
| 7\22
|
| 381.818
|
|-
|
| 5/4
| 386.314
|
|}
 
=== 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"
|-
! ET<br>Generator
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged Interval)]]
! Generator<br>(¢)
! Comments
|-
|
| 16/13
| 359.472
|
|-
|
| 11/8
| 369.736
|
|-
|
| 13/11
| 372.302
|
|-
|
| 11/10
| 372.499
|
|-
|
| 13/10
| 372.893
|
|-
| 5\16
|
| 375.000
|
|-
|
| 12/11
| 375.064
|
|-
|
| 8/7
| 375.882
|
|-
|
| 15/11
| 376.086
|
|-
|
| 11/9
| 376.839
|
|-
|
| 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
|
|-
|
| 18/13
| 378.489
|
|-
|
| 9/7
| 378.534
| 9-odd-limit minimax
|-
|
| 14/13
| 378.617
|
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|  
| 378.947
|  
|-
|-
| 33\104
|  
|
| 10/9
| 380.769
| 379.733
|
|  
|-
|-
| 20\63
|
| 380.952
|
|
| 4/3
| 380.391
| 5-odd-limit minimax
|-
|-
|
|  
| 16/15
| 16/15
| 381.378
| 381.378
|
|  
|-
|-
| 7\22
| 7\22
|
|  
| 381.818
| 381.818
|
|  
|-
|-
|
|  
| 5/4
| 5/4
| 386.314
| 386.314
|
|
|-
|
| 14/11
| 391.246
|  
|}
|}


Revision as of 01:09, 9 January 2022

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

See Magic family #Muggles for more technical data.

Tuning spectra

Muggles

Gencom: [2 5/4; 45/44 65/64 78/77 126/125]

Gencom mapping: [⟨1 0 2 5 0 4], ⟨0 5 1 -7 11 -1]]

ET
Generator 		Eigenmonzo
(Unchanged Interval) 		Generator
(¢) 		Comments
11/9 347.408
16/13 359.472
15/11 372.610
13/10 372.893
12/11 374.894
5\16 375.000
8/7 375.882
13/11 375.899
11/10 376.500
14/11 376.805
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
18/13 378.489
9/7 378.534 9-odd-limit minimax
[0 93 -4 -44⟩ 378.554 9-odd-limit least squares
14/13 378.617
6/5 378.910
6\19 378.947
10/9 379.733
27/20 379.968 5-odd-limit least squares
4/3 380.391 5-odd-limit minimax
16/15 381.378
7\22 381.818
5/4 386.314

Muggloid

Gencom: [2 5/4; 33/32 65/64 105/104 126/125]

Gencom mapping: [⟨1 0 2 5 5 4], ⟨0 5 1 -7 -5 -1]]

ET
Generator 		Eigenmonzo
(Unchanged Interval) 		Generator
(¢) 		Comments
16/13 359.472
11/8 369.736
13/11 372.302
11/10 372.499
13/10 372.893
5\16 375.000
12/11 375.064
8/7 375.882
15/11 376.086
11/9 376.839
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
18/13 378.489
9/7 378.534 9-odd-limit minimax
14/13 378.617
6/5 378.910
6\19 378.947
10/9 379.733
4/3 380.391 5-odd-limit minimax
16/15 381.378
7\22 381.818
5/4 386.314
14/11 391.246

Template:IoT

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