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.

Mavila tunings necessarily require detuning either 5/4 or 3/2 by a significant amount; it is thus reasonable to call it an [[exotemperament]], though it is certainly more accurate than the archetypal exotemperaments such as father.

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.

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Because of the structure of this unique tuning, every existing piece of common practice music has, effectively, a shadow version in antidiatonic. 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 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]].

Mavila tunings range from [[9edo]] to 7edo, with [[16edo]], [[23edo]], and [[25edo]] being typical. These tunings detune 5/4 and 3/2 by significant amounts; it is thus reasonable to call mavila an [[exotemperament]], though it is certainly more accurate than the archetypal exotemperaments such as [[father]].

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.

Mavila was 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.

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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.
-Mavila tunings necessarily require detuning either 5/4 or 3/2 by a significant amount; it is thus reasonable to call it an [[exotemperament]], though it is certainly more accurate than the archetypal exotemperaments such as father.
 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.
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 Because of the structure of this unique tuning, every existing piece of common practice music has, effectively, a shadow version in antidiatonic. 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 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]].
+Mavila tunings range from [[9edo]] to 7edo, with [[16edo]], [[23edo]], and [[25edo]] being typical. These tunings detune 5/4 and 3/2 by significant amounts; it is thus reasonable to call mavila an [[exotemperament]], though it is certainly more accurate than the archetypal exotemperaments such as [[father]].
+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.
 Mavila was 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.