Rothenberg propriety: Difference between revisions

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'''Rothenberg propriety''' is a concept in the theory of musical [[scale]]s developed by David Rothenberg. It classifies scales as '''proper''', '''strictly proper''', and '''improper'''.

A scale is "strictly proper" if every "second" is smaller than every "third," every "third" smaller than every "fourth," etc. The terms "third" and "fourth," in Rothenberg's paper, refer to "generic interval classes" within the scale rather than the familiar diatonic interval categories. The diatonic scale in 31-EDO is strictly proper; the double harmonic scale (C Db E F G Ab B C) in 26-EDO is strictly proper (and is a very interesting listen!) as the B-Db "third" is now ~~smaller~~ than the Db-E "second" (unlike in 12, 31, etc).

A scale is "strictly proper" if every "second" is smaller than every "third," every "third" smaller than every "fourth," etc. The terms "third" and "fourth," in Rothenberg's paper, refer to "generic interval classes" within the scale rather than the familiar diatonic interval categories. The diatonic scale in 31-EDO is strictly proper; the double harmonic scale (C Db E F G Ab B C) in 26-EDO is strictly proper (and is a very interesting listen!) as the B-Db "third" is now larger than the Db-E "second" (unlike in 12, 31, etc).

A scale is "proper" if there is some interval class (e.g. "fourth") which is the *same* size as the next-larger one (e.g. a "fifth"), but nothing which is strictly larger. The diatonic scale in 12-EDO is proper, since the augmented fourth is the same size as the diminished fifth; the double harmonic scale in 19-EDO is proper.

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 '''Rothenberg propriety''' is a concept in the theory of musical [[scale]]s developed by David Rothenberg. It classifies scales as '''proper''', '''strictly proper''', and '''improper'''.
-A scale is "strictly proper" if every "second" is smaller than every "third," every "third" smaller than every "fourth," etc. The terms "third" and "fourth," in Rothenberg's paper, refer to "generic interval classes" within the scale rather than the familiar diatonic interval categories. The diatonic scale in 31-EDO is strictly proper; the double harmonic scale (C Db E F G Ab B C) in 26-EDO is strictly proper (and is a very interesting listen!) as the B-Db "third" is now smaller than the Db-E "second" (unlike in 12, 31, etc).
+A scale is "strictly proper" if every "second" is smaller than every "third," every "third" smaller than every "fourth," etc. The terms "third" and "fourth," in Rothenberg's paper, refer to "generic interval classes" within the scale rather than the familiar diatonic interval categories. The diatonic scale in 31-EDO is strictly proper; the double harmonic scale (C Db E F G Ab B C) in 26-EDO is strictly proper (and is a very interesting listen!) as the B-Db "third" is now larger than the Db-E "second" (unlike in 12, 31, etc).
 A scale is "proper" if there is some interval class (e.g. "fourth") which is the *same* size as the next-larger one (e.g. a "fifth"), but nothing which is strictly larger. The diatonic scale in 12-EDO is proper, since the augmented fourth is the same size as the diminished fifth; the double harmonic scale in 19-EDO is proper.

Rothenberg propriety: Difference between revisions

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