Mavila: Difference between revisions

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'''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. Like [[meantone]], mavila is based on the [[chain of fifths]], but as a result of tempering out 135/128 rather than [[81/80]], the fifths are supposedly 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 [[2L 5s|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 the fifth, third, etc. steps in the antidiatonic scale.

This has some very strange implications for music. The mavila antidiatonic scale is similar to the normal [[5L 2s|diatonic]] scale, except interval classes are flipped. Wherever there was a major third, you will 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 [[5L 2s|diatonic]] scale, except interval classes are flipped. Wherever there was a major third, you will 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 – 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, every existing piece of common practice music has, effectively, a shadow version in mavila temperament. That is, ~~when~~ Beethoven ~~wrote~~ Für Elise, he actually ~~wrote~~ two ~~compositions—the~~ one that you know, and the antidiatonic equivalent in mavila temperament~~. It is only~~ that ~~the antidiatonic versions have~~ never been heard before until now. Examples of this are provided ~~below~~.

Because of the structure of this unique tuning, every existing piece of common practice music has, effectively, a shadow version in mavila temperament. That is, with {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Für Elise}}, there are actually two compositions – the one that you know, and the antidiatonic equivalent in mavila temperament that has never been heard before until now. Examples of this are provided in the [[#Music]] section.

Mavila's antidiatonic scale is similar to [[Pelog]] scales used in Indonesian gamelan music. While Pelog's exact tuning is subject to significant regional variation and usually has unequal intervals throughout the scale (as opposed to having exactly two interval sizes), it can be well approximated by the antidiatonic scales of [[9edo]] and [[16edo]].

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 '''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. Like [[meantone]], mavila is based on the [[chain of fifths]], but as a result of tempering out 135/128 rather than [[81/80]], the fifths are supposedly 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 [[2L 5s|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 the fifth, third, etc. steps in the antidiatonic scale.
-This has some very strange implications for music. The mavila antidiatonic scale is similar to the normal [[5L 2s|diatonic]] scale, except interval classes are flipped. Wherever there was a major third, you will 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 [[5L 2s|diatonic]] scale, except interval classes are flipped. Wherever there was a major third, you will 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 – 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, every existing piece of common practice music has, effectively, a shadow version in mavila temperament. That is, when Beethoven wrote Für Elise, he actually wrote two compositions—the one that you know, and the antidiatonic equivalent in mavila temperament. It is only that the antidiatonic versions have never been heard before until now. Examples of this are provided below.
+Because of the structure of this unique tuning, every existing piece of common practice music has, effectively, a shadow version in mavila temperament. That is, with {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Für Elise}}, there are actually two compositions – the one that you know, and the antidiatonic equivalent in mavila temperament that has never been heard before until now. Examples of this are provided in the [[#Music]] section.
 Mavila's antidiatonic scale is similar to [[Pelog]] scales used in Indonesian gamelan music. While Pelog's exact tuning is subject to significant regional variation and usually has unequal intervals throughout the scale (as opposed to having exactly two interval sizes), it can be well approximated by the antidiatonic scales of [[9edo]] and [[16edo]].