Rothenberg propriety: Difference between revisions

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Carey 1998 writes, ''“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.”''<ref>Carey, Norman (1998). ''[https://books.google.com/books?id=Fgc5AQAAIAAJ&dq=improper+rothenberg+music&focus=searchwithinvolume&q=improper Distribution Modulo One and Musical Scales]'', p.103, n.19. University of Rochester. Ph.D. dissertation.</ref>

~~Both improper and strictly~~ proper scales have [[constant structure]], and proper scales do not.

Strictly proper scales have [[constant structure]], and proper scales do not.

== Examples ==

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* [[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|19EDO]] (<code>3-3-2-3-3-3-2</code>) is ''strictly proper''.

The [[22edo|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). Such a scale is classified as improper.

== See also ==

@@ Line 19: / Line 19: @@
 Carey 1998 writes, ''“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.”''<ref>Carey, Norman (1998). ''[https://books.google.com/books?id=Fgc5AQAAIAAJ&dq=improper+rothenberg+music&focus=searchwithinvolume&q=improper Distribution Modulo One and Musical Scales]'', p.103, n.19. University of Rochester. Ph.D. dissertation.</ref>
-Both improper and strictly proper scales have [[constant structure]], and proper scales do not.
+Strictly proper scales have [[constant structure]], and proper scales do not.
 == Examples ==
@@ Line 28: / Line 28: @@
 * [[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|19EDO]] (<code>3-3-2-3-3-3-2</code>) is ''strictly proper''.
+The [[22edo|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). Such a scale is classified as improper.
 == See also ==