Mavila: Difference between revisions

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== Inverted major and minor intervals: the antidiatonic scale ==

In mavila, the comma 135/128 vanishes, 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 ~~anti-diatonic~~ scale.)

In mavila, the comma 135/128 vanishes, 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.

This has some very strange implications for music. The mavila ~~diatonic~~ 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.

As an example, the anti-Ionian scale has steps of ssLsssL, which looks like the regular Ionian scale except the "L" intervals are now "s" and vice versa.

Because of the structure of this unique tuning, it is true that every existing piece of common practice music has a "shadow" version in mavila temperament. That is, when Beethoven wrote Fur Elise, he actually wrote two compositions – the one that you know, and the antidiatonic equivalent in mavila temperament. It's only that the antidiatonic versions have never been heard before. Examples of this are provided below.

The mavila antidiatonic scale is also similar to the [[pelog]] scale used in Javanese and Balinese gamelan music, although the pelog's scale tuning is subject to regional variation. In particular, the antidiatonic scale supposes exactly two interval sizes, whereas pelog usually has unequal intervals throughout the scale.

== Modal harmony ==

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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.

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. If the mavila fifth is flatter than that of 16edo (675 cents), it will instead generate an mos at 25 notes. This is similar to how if the meantone fifth is tuned sharper than 12edo, it will instead generate a 17-tone mos rather than a 19-tone one.

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. If the mavila fifth is flatter than that of 16edo (675 cents), it will instead generate an mos at 25 notes. This is similar to how if the meantone fifth is tuned sharper than 12edo, it will instead generate a 17-tone mos rather than a 19-tone one.

== Music ==

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 == Inverted major and minor intervals: the antidiatonic scale ==
-In mavila, the comma 135/128 vanishes, 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 anti-diatonic scale.)
+In mavila, the comma 135/128 vanishes, 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.
-This has some very strange implications for music. The mavila diatonic 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.
 As an example, the anti-Ionian scale has steps of ssLsssL, which looks like the regular Ionian scale except the "L" intervals are now "s" and vice versa.
 Because of the structure of this unique tuning, it is true that every existing piece of common practice music has a "shadow" version in mavila temperament. That is, when Beethoven wrote Fur Elise, he actually wrote two compositions – the one that you know, and the antidiatonic equivalent in mavila temperament. It's only that the antidiatonic versions have never been heard before. Examples of this are provided below.
+The mavila antidiatonic scale is also similar to the [[pelog]] scale used in Javanese and Balinese gamelan music, although the pelog's scale tuning is subject to regional variation. In particular, the antidiatonic scale supposes exactly two interval sizes, whereas pelog usually has unequal intervals throughout the scale.
 == Modal harmony ==
@@ Line 40: / Line 42: @@
 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. If the mavila fifth is flatter than that of 16edo (675 cents), it will instead generate an mos at 25 notes. This is similar to how if the meantone fifth is tuned sharper than 12edo, it will instead generate a 17-tone mos rather than a 19-tone one.
+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. If the mavila fifth is flatter than that of 16edo (675 cents), it will instead generate an mos at 25 notes. This is similar to how if the meantone fifth is tuned sharper than 12edo, it will instead generate a 17-tone mos rather than a 19-tone one.
 == Music ==