Mavila: Difference between revisions
That paper was nice addition; unfortunately it's a bit hard to read so I'm putting it in an "external link" section. Great to find the year when this temp was discovered |
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{{About|the regular temperament|the scale structure sometimes associated with it|7L 2s}} | {{About|the regular temperament|the scale structure sometimes associated with it|7L 2s}} | ||
'''Mavila''' is a [[temperament]] first discovered by [[Erv Wilson]], possibly in 1989<ref>A ''Linear Tuning of 4-"5"-"6" Artihmetic Mean (−3=5)'' paper from 1989 was referenced in Erv Wilson's ''Meta Meantone & Meta Mavila'' paper.</ref>, after studying the tuning of the timbila music of the Chopi tribe in Mozambique. | |||
'''Mavila''' is | |||
See [[Pelogic family #Mavila]] for more technical data. | See [[Pelogic family #Mavila]] for more technical data. | ||
== Inverted major and minor intervals: the antidiatonic scale == | == Inverted major and minor intervals: the antidiatonic scale == | ||
In mavila, the major chroma ([[135/128]]) is tempered out, rather than 81/80. As a result, the fifths are very flat (~675-680 cents or so), flatter than even 7edo. As a result, stacking 7 of these fifths gives you an "antidiatonic" mos scale, where in a certain sense, major and minor intervals get "reversed". For example, stacking four fifths and octave-reducing now gets you a 6/5 ''minor'' third, whereas stacking three fourths and octave-reducing now gets you a 5/4 ''major'' third. Note that since we have a heptatonic scale, terms like "fifths", "thirds", etc. make perfect sense and really are five, three, etc. steps in the antidiatonic scale. | |||
In mavila, the | |||
This has some very strange implications for music. The mavila antidiatonic scale is similar to the normal diatonic scale – except interval classes are flipped. Wherever there was a major third, you'll find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major – you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad. | This has some very strange implications for music. The mavila antidiatonic scale is similar to the normal diatonic scale – except interval classes are flipped. Wherever there was a major third, you'll find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major – you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad. | ||
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== Tunings == | == Tunings == | ||
The fifths of mavila are very flat – 16edo (675.0 cents) and 23edo (678.3 cents) are typical tunings, and the optimal 5-limit tuning is 679.8 cents. As a result, mavila is best played with specialized timbres: either timbres with high rolloff (such as sine waves, marimba, and ocarina) | The fifths of mavila are very flat – 16edo (675.0 cents) and 23edo (678.3 cents) are typical tunings, and the optimal 5-limit tuning is 679.8 cents. As a result, mavila is best played with specialized timbres: either timbres with high rolloff (such as sine waves, marimba, and ocarina) or high inharmonicity (detuned partials, such as Gamelans, bells, or Timbila instruments). [[Stretched and compressed tuning|Octave stretching]] may also help. | ||
As with meantone, mavila has its own tuning spectrum. 7edo, with its 685.714 cent 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. | |||
Much like meantone, mavila is [[support|supported]] by several low-numbered edos, which will basically be the same size as the mosses listed above. | Much like meantone, mavila is [[support|supported]] by several low-numbered edos, which will basically be the same size as the mosses listed above. | ||
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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 9edo, which 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 | The next edo supporting mavila is [[9edo]], which has a fifth of 666.67 cents 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 mavila[23]. | 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]. | ||
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| 685.714 | | 685.714 | ||
| Upper bound of 5-odd-limit diamond monotone<br>5-limit 9-odd-limit diamond monotone (singleton) | | Upper bound of 5-odd-limit diamond monotone<br>5-limit 9-odd-limit diamond monotone (singleton) | ||
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