Mavila: Difference between revisions

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: ''This page is about the regular temperament. For the scale structures sometimes associated with it, see [[7L 2s]] and [[2L 5s]].''

'''Mavila''' is a [[regular temperament|temperament]] where the [[135/128~~|major chroma (135/128)~~]] is tempered out. It 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.

'''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. It 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.

~~See [[Mavila family #Mavila]] for more technical data.~~

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 [[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.

~~== 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|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 [[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.

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's 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, 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.

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]].

See [[Mavila family #Mavila]] for more technical data.

== Modal harmony ==

@@ Line 1: / Line 1: @@
 : ''This page is about the regular temperament. For the scale structures sometimes associated with it, see [[7L&nbsp;2s]] and [[2L&nbsp;5s]].''
-'''Mavila''' is a [[regular temperament|temperament]] where the [[135/128|major chroma (135/128)]] is tempered out. It 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.
+'''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. It 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.
-See [[Mavila family #Mavila]] for more technical data.
+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 [[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.
-== 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|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 [[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.
 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's 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, 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.
 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]].
+See [[Mavila family #Mavila]] for more technical data.
 == Modal harmony ==

Mavila: Difference between revisions

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