Muggles: Difference between revisions
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| en = Muggles | | en = Muggles | ||
| de = Magische Temperaturen #Muggel | | de = Magische Temperaturen #Muggel | ||
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{{Infobox regtemp | |||
| Title = Muggles | |||
| Subgroups = 2.3.5.7, 2.3.5.7.13 | |||
| 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) | |||
| Edo join 1 = 16 | Edo join 2 = 19 | |||
| Mapping = 1; 5 1 -7 11 -1 | |||
| Generators = 5/4 | |||
| Generators tuning = 377.7 | |||
| Optimization method = CWE | |||
| MOS scales = [[3L 7s]], [[3L 10s]], [[3L 13s]], [[16L 3s]] | |||
| Odd limit 1 = 9 | Mistuning 1 = 18.6 | Complexity 1 = 19 | |||
| Odd limit 2 = 13 | Mistuning 2 = 29.0 | Complexity 2 = 19 | |||
}} | }} | ||
'''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]] and can be described as the 16 & 19 temperament; [[16edo]], [[35edo]], and [[54edo]] with the flat-fifth bd [[val]] all are muggles tunings. As a tuning noted for having both very flat [[3/2|3rd]] and [[5/4|5th]] harmonics, and supported by [[19edo]], it is very analogous to [[flattone]]. Similarly to flattone, muggles can extend to the [[13-limit]] by equating [[5/4]] to both [[11/9]] and [[16/13]], thereby tempering out [[45/44]] and [[65/64]]. | '''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]] and can be described as the 16 & 19 temperament; [[16edo]], [[35edo]], and [[54edo]] with the flat-fifth bd [[val]] all are muggles tunings. As a tuning noted for having both very flat [[3/2|3rd]] and [[5/4|5th]] harmonics, and supported by [[19edo]], it is very analogous to [[flattone]]. Similarly to flattone, muggles can extend to the [[13-limit]] by equating [[5/4]] to both [[11/9]] and [[16/13]], thereby tempering out [[45/44]] and [[65/64]]. | ||
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== Interval chain == | == Interval chain == | ||
Odd harmonics 1–13 and their inverses are in '''bold'''. | Odd harmonics 1–13 and their inverses are in '''bold'''. | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
Revision as of 09:45, 8 April 2026
| Muggles |
45/44, 126/125, 385/384 (11-limit);
45/44, 65/64, 78/77, 126/125
(13-limit)
13-odd-limit: 29.0 ¢
13-odd-limit: 19 notes
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 and can be described as the 16 & 19 temperament; 16edo, 35edo, and 54edo with the flat-fifth bd val all are muggles tunings. As a tuning noted for having both very flat 3rd and 5th harmonics, and supported by 19edo, it is very analogous to flattone. Similarly to flattone, muggles can extend to the 13-limit by equating 5/4 to both 11/9 and 16/13, thereby tempering out 45/44 and 65/64.
This temperament was named by Gene Ward Smith in 2003[1].
See Magic family #Muggles for more technical data.
Interval chain
Odd harmonics 1–13 and their inverses are in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.00 | 1/1 |
| 1 | 378.5 | 5/4, 16/13, 26/21 |
| 2 | 757.0 | 20/13, 32/21 |
| 3 | 1135.4 | 25/13 |
| 4 | 313.9 | 6/5 |
| 5 | 692.4 | 3/2 |
| 6 | 1070.9 | 13/7, 15/8, 24/13 |
| 7 | 249.4 | 8/7, 15/13 |
| 8 | 627.9 | 10/7 |
| 9 | 1006.3 | 9/5 |
| 10 | 184.8 | 9/8 |
| 11 | 563.3 | 18/13 |
| 12 | 941.8 | 12/7 |
| 13 | 120.3 | 15/14 |
* In 2.3.5.7.13 CWE tuning
Tuning spectra
Muggles
| Edo generator |
Unchanged interval (eigenmonzo) |
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 |