Mavila: Difference between revisions
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== Tunings == | == Tunings == | ||
The fifths of mavila are very | The fifths of mavila are very flat – 16edo (675.0{{c}}) and 23edo (678.3{{c}}) are typical tunings. As a result, mavila is best played with [[stretched and compressed tuning|stretched octaves]] and/or specialized timbres: either timbres with high rolloff (e.g. sine waves, marimba, and ocarina) or high inharmonicity (i.e. detuned partials, such as Gamelans, bells, or Timbila instruments). | ||
As with meantone, mavila has its own tuning spectrum. 7edo, with its 685.714{{c}} fifth, is often thought of as an informal dividing line between meantone and mavila, in which case it forms the sharpmost endpoint on the mavila tuning spectrum and the flatmost endpoint of the meantone spectrum: if the fifth is flatter than this, it will generate anti-diatonic scales, and if it is sharper than this, it will generate diatonic scales. The fifth of 9edo is also often thought of as the other (flatmost) endpoint on the mavila spectrum. | As with meantone, mavila has its own tuning spectrum. 7edo, with its 685.714{{c}} fifth, is often thought of as an informal dividing line between meantone and mavila, in which case it forms the sharpmost endpoint on the mavila tuning spectrum and the flatmost endpoint of the meantone spectrum: if the fifth is flatter than this, it will generate anti-diatonic scales, and if it is sharper than this, it will generate diatonic scales. The fifth of 9edo is also often thought of as the other (flatmost) endpoint on the mavila spectrum. | ||
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7edo can be thought of as a primitive tuning, yielding a completely equal heptatonic scale that is equally diatonic and anti-diatonic. | 7edo can be thought of as a primitive tuning, yielding a completely equal heptatonic scale that is equally diatonic and anti-diatonic. | ||
The next edo supporting mavila is | The next edo supporting mavila is 9edo, which has a fifth of 666.67{{c}} and approximates the Pelog tuning commonly found in Indonesian gamelan music. 9edo can be thought of as the first mavila edo (and the first edo in general) differentiating between 4:5:6 major and 10:12:15 minor chords. This is fairly interesting, as there is no real equivalent in meantone terms. It is larger than the "diatonic" sized mos, but smaller than the 16-tone "chromatic" mos. It is best thought of as a "superdiatonic" scale. | ||
It is also supported by 16edo, which is probably the most common tuning for mavila temperament. This can be thought of as the first edo offering the potential for chromatic mavila harmony, similar to 12edo for meantone. This is also the usual setting for the aforementioned Armodue theory, although the Armodue theory can easily be extended to larger mavila scales such as | It is also supported by 16edo, which is probably the most common tuning for mavila temperament. This can be thought of as the first edo offering the potential for chromatic mavila harmony, similar to 12edo for meantone. This is also the usual setting for the aforementioned Armodue theory, although the Armodue theory can easily be extended to larger mavila scales such as Mavila[23]. | ||
The next edo supporting mavila is 23edo, which is the second-most common tuning for mavila temperament, used frequently by [[Igliashon Jones]] in his [[Cryptic Ruse]] albums. The fifth is in the sharper range for a mavila fifth at 678{{c}}, and is consequently closer to 3/2 than in 16edo, although still fairly inharmonic compared to meantone. The anti-diatonic scale is more "quasi-equal" in this tuning than in 16edo. | The next edo supporting mavila is 23edo, which is the second-most common tuning for mavila temperament, used frequently by [[Igliashon Jones]] in his [[Cryptic Ruse]] albums. The fifth is in the sharper range for a mavila fifth at 678{{c}}, and is consequently closer to 3/2 than in 16edo, although still fairly inharmonic compared to meantone. The anti-diatonic scale is more "quasi-equal" in this tuning than in 16edo. | ||
25edo also supports mavila. The tuning is 672{{c}} and hence very flat, even flatter than 16edo, but not as flat as 9edo. This is 25edo's second-best 3/2; the alternate fifth generates 5edo. | 25edo also supports mavila. The tuning is 672{{c}} and hence very flat, even flatter than 16edo, but not as flat as 9edo. This is 25edo's second-best 3/2; the alternate fifth generates 5edo. | ||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit prime-optimized tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 677.145{{c}} | |||
| CWE: ~3/2 = 679.111{{c}} | |||
| POTE: ~3/2 = 679.806{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.11-subgroup prime-optimized tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 676.039{{c}} | |||
| CWE: ~3/2 = 678.978{{c}} | |||
| POTE: ~3/2 = 679.788{{c}} | |||
|} | |||
=== Tuning spectrum === | === Tuning spectrum === | ||
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=== Other tunings === | === Other tunings === | ||
* [[DKW theory|DKW]] (2.3.5): ~2 = | * [[DKW theory|DKW]] (2.3.5): ~2 = 1200.000{{c}}, ~3/2 = 675.456{{c}} | ||
== Music == | == Music == | ||