Constant structure: Difference between revisions
m Adding Erv Wilson category |
related CS to Rothenberg's property. Added an improper example. |
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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. | 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. | |||
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). | 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). | ||
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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. | 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. | ||
== Density of CS scales in EDOs == | == Density of CS scales in EDOs == | ||