Muggles
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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 (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
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 | 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 | ||
| 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 |