Mavila: Difference between revisions
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== Inverted major and minor intervals: the antidiatonic scale == | == Inverted major and minor intervals: the antidiatonic scale == | ||
As a result of tempering out 135/128 rather than 81/80, the fifths are very flat ({{nowrap|~{{dash| | As a result of tempering out 135/128 rather than 81/80, the fifths are very flat ({{nowrap|~{{dash|670, 680}}}}{{c}} or so), flatter than even that of [[7edo]] (4\7). Consequently, 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. | ||
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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Mavila generates a 16-tone "chromatic" mos. In a certain sense, much of mavila makes sense if viewed within the lens of a 16-tone chromatic gamut, similarly to how much of meantone is thought of in the setting of a 12-tone chromatic gamut. | Mavila generates a 16-tone "chromatic" mos. In a certain sense, much of mavila makes sense if viewed within the lens of a 16-tone chromatic gamut, similarly to how much of meantone is thought of in the setting of a 12-tone chromatic gamut. | ||
After the 16-tone "chromatic" scale is the 23-tone "enharmonic" mos, which can be thought of as an "extended mavila" analogous to the "extended meantone" 19-tone enharmonic scale. | After the 16-tone "chromatic" scale is the 23-tone or 25-tone "enharmonic" mos (depending on the tuning of the fifth), which can be thought of as an "extended mavila" analogous to the "extended meantone" 19-tone enharmonic scale. The two alternative enharmonic scales are similar to how if the fifth is tuned sharper than 12edo, it will generate a 17-tone mos rather than a 19-tone one. | ||
== Tunings == | == Tunings == | ||
The fifths of mavila are very flat—16edo (675.0{{c}}) and 23edo (678.3{{c}}) are typical tunings | 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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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]. | ||
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 678{{c}}, and | 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. | 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. | ||
=== Tuning spectrum === | === Tuning spectrum === | ||
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|- | |- | ||
! Edo<br />Generator | ! Edo<br />Generator | ||
! [[Eigenmonzo|Eigenmonzo<br />(Unchanged | ! [[Eigenmonzo|Eigenmonzo<br />(Unchanged interval)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||