User:AthiTrydhen/Abstract pergens: Difference between revisions

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This is an extension of work with [[User:TallKite]] on [[pergen]]s.

This is an extension of work with [[User:TallKite]] on [[pergen]]s and [[ups and downs notation]].

Pergens do not have to be based on chains of diatonic-like fifths; they could be based on other, more abstract chains of generators. The underlying principle is the same.

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==Ups and downs notation, and families of neutralizations==

Ups and downs notation may be used in addition to diamond-mos notation for MOS extensions. When there's a pergen there is inevitably an enharmonic ~~interval~~ as well, but in musical practices based on extensions of an MOS, the rank doesn't have to be preserved when ups and downs are added. An example, based on the diatonic paradigm, is Maqam Rast, which would be notated C D vE F G A vB C in ups and downs notation. In maqam practices that use binary Rast (LSSLLSS), there is an additional enharmonic ~~interval~~ of vvA1 which results in a pergen of (P8, P5/2). But in practices that use ternary Rast (LMSLLMS), the ups and downs would be totally independent of the chain of fifths. In extant maqam traditions that do so, the ^1 is less than half of an A1, but it doesn't have to be the case -- if otherwise, I would suggest that the larger ^1 be rewritten as a vA1, to simplify the notation. The resulting mirror-Rast scale would then be written C D ^Eb F G A ^Bb C.

Ups and downs notation may be used in addition to diamond-mos notation for MOS extensions. When there's a pergen there is inevitably an enharmonic unison as well, but in musical practices based on extensions of an MOS, the rank doesn't have to be preserved when ups and downs are added. An example, based on the diatonic paradigm, is Maqam Rast, which would be notated C D vE F G A vB C in ups and downs notation. In maqam practices that use binary Rast (LSSLLSS), there is an additional enharmonic unison of vvA1 which results in a pergen of (P8, P5/2). But in practices that use ternary Rast (LMSLLMS), the ups and downs would be totally independent of the chain of fifths. In extant maqam traditions that do so, the ^1 is less than half of an A1, but it doesn't have to be the case -- if otherwise, I would suggest that the larger ^1 be rewritten as a vA1, to simplify the notation. The resulting mirror-Rast scale would then be written C D ^Eb F G A ^Bb C.

The neutralization of an MOS is part of a one parameter family or a continuum of generally ternary scales (by turning Ls into Mm with L > M >= m > s), and sometimes, it may be musically worthwhile to look at points in the continuum other than the boundary where M = m. I call this process "partial neutralization". Partial neutralization can either be used for greater melodic expressivity, or to incorporate simple harmonic intervals, or both.

For diatonic, this results in various forms of ternary Rast, including a permutation of Zarlino where L = 9/8, M = 10/9, and m = 16/15. For oneirotonic, where strict neutralization would produce a half-octave, a partial neutralization can render what would be a half-octave as 7/5 or 10/7.

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-This is an extension of work with [[User:TallKite]] on [[pergen]]s.
+This is an extension of work with [[User:TallKite]] on [[pergen]]s and [[ups and downs notation]].
 Pergens do not have to be based on chains of diatonic-like fifths; they could be based on other, more abstract chains of generators. The underlying principle is the same.
@@ Line 24: / Line 24: @@
 ==Ups and downs notation, and families of neutralizations==
-Ups and downs notation may be used in addition to diamond-mos notation for MOS extensions. When there's a pergen there is inevitably an enharmonic interval as well, but in musical practices based on extensions of an MOS, the rank doesn't have to be preserved when ups and downs are added. An example, based on the diatonic paradigm, is Maqam Rast, which would be notated C D vE F G A vB C in ups and downs notation. In maqam practices that use binary Rast (LSSLLSS), there is an additional enharmonic interval of vvA1 which results in a pergen of (P8, P5/2). But in practices that use ternary Rast (LMSLLMS), the ups and downs would be totally independent of the chain of fifths. In extant maqam traditions that do so, the ^1 is less than half of an A1, but it doesn't have to be the case -- if otherwise, I would suggest that the larger ^1 be rewritten as a vA1, to simplify the notation. The resulting mirror-Rast scale would then be written C D ^Eb F G A ^Bb C.
+Ups and downs notation may be used in addition to diamond-mos notation for MOS extensions. When there's a pergen there is inevitably an enharmonic unison as well, but in musical practices based on extensions of an MOS, the rank doesn't have to be preserved when ups and downs are added. An example, based on the diatonic paradigm, is Maqam Rast, which would be notated C D vE F G A vB C in ups and downs notation. In maqam practices that use binary Rast (LSSLLSS), there is an additional enharmonic unison of vvA1 which results in a pergen of (P8, P5/2). But in practices that use ternary Rast (LMSLLMS), the ups and downs would be totally independent of the chain of fifths. In extant maqam traditions that do so, the ^1 is less than half of an A1, but it doesn't have to be the case -- if otherwise, I would suggest that the larger ^1 be rewritten as a vA1, to simplify the notation. The resulting mirror-Rast scale would then be written C D ^Eb F G A ^Bb C.
 The neutralization of an MOS is part of a one parameter family or a continuum of generally ternary scales (by turning Ls into Mm with L > M >= m > s), and sometimes, it may be musically worthwhile to look at points in the continuum other than the boundary where M = m. I call this process "partial neutralization". Partial neutralization can either be used for greater melodic expressivity, or to incorporate simple harmonic intervals, or both.
 For diatonic, this results in various forms of ternary Rast, including a permutation of Zarlino where L = 9/8, M = 10/9, and m = 16/15. For oneirotonic, where strict neutralization would produce a half-octave, a partial neutralization can render what would be a half-octave as 7/5 or 10/7.