Rothenberg propriety: Difference between revisions
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It's easy to see the concept in action at the 7-step diatonic scale (<code>L-L-s-L-L-L-s</code>) as rendered in three different EDOs: | It's easy to see the concept in action at the 7-step diatonic scale (<code>L-L-s-L-L-L-s</code>) as rendered in three different EDOs: | ||
* [[12edo]] (<code>2-2-1-2-2-2-1</code>) is ''proper'' but not strictly proper because of the ambiguities of d5 (1+2+2+1=6) and A4 (2+2+2=6) in three-step and | * [[12edo|12EDO]] (<code>2-2-1-2-2-2-1</code>) is ''proper'' but not strictly proper because of the ambiguities of d5 (1+2+2+1=6) and A4 (2+2+2=6) in three-step and four-step intervals. | ||
* [[17edo]] (<code>3-3-1-3-3-3-1</code>) is ''improper'' because of the contradiction in d5 (1+3+3+1=8) being smaller than A4 (3+3+3=9). | * [[17edo|17EDO]] (<code>3-3-1-3-3-3-1</code>) is ''improper'' because of the contradiction in d5 (1+3+3+1=8) being smaller than A4 (3+3+3=9). | ||
* [[19edo]] (<code>3-3-2-3-3-3-2</code>) is ''strictly proper''. | * [[19edo|19EDO]] (<code>3-3-2-3-3-3-2</code>) is ''strictly proper''. | ||
== See also == | == See also == | ||
* [[Wikipedia: Rothenberg propriety]] | * [[Wikipedia: Rothenberg propriety]] | ||
* [[MOS scale]] | * [[MOS scale]] | ||
Revision as of 00:45, 21 March 2021
Rothenberg propriety is a concept in the theory of musical scales. It classifies scales as proper, strictly proper, and improper.
“Rothenberg calls a scale 'strictly proper' if it possesses a generic ordering, 'proper' if it admits ambiguities but no contradictions, and 'improper' if it admits contradictions.”[1]
Examples
It's easy to see the concept in action at the 7-step diatonic scale (L-L-s-L-L-L-s) as rendered in three different EDOs:
- 12EDO (
2-2-1-2-2-2-1) is proper but not strictly proper because of the ambiguities of d5 (1+2+2+1=6) and A4 (2+2+2=6) in three-step and four-step intervals. - 17EDO (
3-3-1-3-3-3-1) is improper because of the contradiction in d5 (1+3+3+1=8) being smaller than A4 (3+3+3=9). - 19EDO (
3-3-2-3-3-3-2) is strictly proper.
See also
References
- ↑ Carey, Norman (1998). Distribution Modulo One and Musical Scales, p.103, n.19. University of Rochester. Ph.D. dissertation.