Rothenberg propriety: Difference between revisions

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== Examples ==
== Examples ==


The 7-step diatonic scale of [[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 five-step intervals.
It's easy to see the concept in action at the 7-step diatonic scale (5L 2s) as rendered in three different EDOs:


The 7-step diatonic scale of [[19edo]] (3-3-2-3-3-3-2) is ''strictly proper''.
* [[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 five-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).
The 7-step diatonic scale of [[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 ==
== See also ==

Revision as of 23:48, 1 January 2021

Rothenberg propriety is a concept in the theory of musical scales.

“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 (5L 2s) 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 five-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

  1. Carey, Norman (1998). Distribution Modulo One and Musical Scales, p.103, n.19. University of Rochester. Ph.D. dissertation.