Constant structure: Difference between revisions

Line 3:

The term "constant structure" was coined by [[Erv Wilson]]. In academic music theory, constant structure is called the partitioning property, but Erv got there first.

In terms of [[Rothenberg propriety]], ~~both improper and~~ strictly proper scales have CS, and proper scales do not.

In terms of [[Rothenberg propriety]], strictly proper scales have CS, and proper scales do not. Improper scales generally do. However the [[22edo]] scale C D E vF# G ^Ab B C (<code>4-4-3-2-2-6-1</code>) has both ambiguity (C-vF# 4th equals vF#-C 5th) and contradiction (^Ab-B 2nd exceeds E-G 3rd). The contradiction makes it improper and the ambiguity makes it not CS.

To determine if a scale is CS, all possible intervals between scale steps must be evaluated. An easy way to do this is with an [[interval matrix]] ([[Scala]] can do this for you). A CS scale will never have the same interval appear in multiple columns of the matrix (columns correspond to generic interval classes).

Line 289:

|}

F# and Gb are the same pitch (600 cents) in 12edo, and this interval occurs as both an (augmented) fourth and a (diminished) fifth - so not constant structure. However, a meantone tuning of this scale, in which F# is narrower than Gb, would have constant structure. As would a pythagorean tuning or superpyth tuning, in which F# is wider than Gb.

F# and Gb are the same pitch (600 cents) in 12edo, and this interval occurs as both an (augmented) fourth and a (diminished) fifth - so not constant structure. However, a meantone tuning of this scale, in which F# is narrower than Gb, would have constant structure. As would a pythagorean tuning or superpyth tuning such as 22edo, in which F# is wider than Gb.

== Density of CS scales in EDOs ==

@@ Line 3: / Line 3: @@
 The term "constant structure" was coined by [[Erv Wilson]]. In academic music theory, constant structure is called the partitioning property, but Erv got there first.
-In terms of [[Rothenberg propriety]], both improper and strictly proper scales have CS, and proper scales do not.
+In terms of [[Rothenberg propriety]], strictly proper scales have CS, and proper scales do not. Improper scales generally do. However the [[22edo]] scale C D E vF# G ^Ab B C (<code>4-4-3-2-2-6-1</code>) has both ambiguity (C-vF# 4th equals vF#-C 5th) and contradiction (^Ab-B 2nd exceeds E-G 3rd). The contradiction makes it improper and the ambiguity makes it not CS.
 To determine if a scale is CS, all possible intervals between scale steps must be evaluated. An easy way to do this is with an [[interval matrix]] ([[Scala]] can do this for you). A CS scale will never have the same interval appear in multiple columns of the matrix (columns correspond to generic interval classes).
@@ Line 289: / Line 289: @@
 |}
-F# and Gb are the same pitch (600 cents) in 12edo, and this interval occurs as both an (augmented) fourth and a (diminished) fifth - so not constant structure. However, a meantone tuning of this scale, in which F# is narrower than Gb, would have constant structure. As would a pythagorean tuning or superpyth tuning, in which F# is wider than Gb.
+F# and Gb are the same pitch (600 cents) in 12edo, and this interval occurs as both an (augmented) fourth and a (diminished) fifth - so not constant structure. However, a meantone tuning of this scale, in which F# is narrower than Gb, would have constant structure. As would a pythagorean tuning or superpyth tuning such as 22edo, in which F# is wider than Gb.
 == Density of CS scales in EDOs ==