Muggles: Difference between revisions
Jump to navigation
Jump to search
Cleanup |
+interval chain |
||
| Line 7: | Line 7: | ||
See [[Magic family #Muggles]] for more technical data. | See [[Magic family #Muggles]] for more technical data. | ||
== Interval chain == | |||
Odd harmonics 1–13 and their inverses are in '''bold'''. | |||
{| class="wikitable center-1 right-2" | |||
|- | |||
! # | |||
! 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 | |||
|- | |||
| 7 | |||
| 249.4 | |||
| '''8/7''' | |||
|- | |||
| 8 | |||
| 627.9 | |||
| 10/7 | |||
|- | |||
| 9 | |||
| 1006.3 | |||
| 9/5 | |||
|- | |||
| 10 | |||
| 184.8 | |||
| '''9/8''' | |||
|- | |||
| 11 | |||
| 563.3 | |||
| 45/32, 48/35 | |||
|- | |||
| 12 | |||
| 941.8 | |||
| 12/7 | |||
|- | |||
| 13 | |||
| 120.3 | |||
| 15/14 | |||
|} | |||
<nowiki/>* In 2.3.5.7.13 CWE tuning | |||
== Tuning spectra == | == Tuning spectra == | ||
Revision as of 04:58, 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.
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 |
| 7 | 249.4 | 8/7 |
| 8 | 627.9 | 10/7 |
| 9 | 1006.3 | 9/5 |
| 10 | 184.8 | 9/8 |
| 11 | 563.3 | 45/32, 48/35 |
| 12 | 941.8 | 12/7 |
| 13 | 120.3 | 15/14 |
* In 2.3.5.7.13 CWE tuning
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 |