Rothenberg propriety: Difference between revisions
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{{Wikipedia|Rothenberg propriety}} | |||
'''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'''. | '''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'''. | ||
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This metric has been extended several ways - see also: | This metric has been extended several ways - see also: | ||
# | # [[Lumma stability]] and impropriety factor | ||
# [http://www.tonalsoft.com/enc/r/rothenberg-efficiency.aspx "Rothenberg efficiency"] on [[Tonalsoft encyclopedia]] | |||
# http://www.tonalsoft.com/enc/r/rothenberg-efficiency.aspx | # [http://www.tonalsoft.com/enc/r/rothenberg-redundancy.aspx "Rothenberg redundancy"] on [[Tonalsoft encyclopedia]] | ||
# http://www.tonalsoft.com/enc/r/rothenberg-redundancy.aspx | # [http://www.tonalsoft.com/enc/r/rothenberg-stability.aspx "Rothenberg stability"] on [[Tonalsoft encyclopedia]] | ||
# http://www.tonalsoft.com/enc/r/rothenberg-stability.aspx | |||
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> | 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> | ||
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== See also == | == See also == | ||
* [[MOS scale]] | * [[MOS scale]] | ||
== References == | == References == | ||
<references/> | <references/> | ||
== External links == | |||
* [http://lumma.org/tuning/rothenberg/AModelForPatternPerception.pdf Rothenberg, David. (1978). "A Model for Pattern Perception with Musical Applications. Part I: Pitch structures as order-preserving maps; Part II: The Information Content of Pitch Structures; Part III: The Graph Embedding of Pitch Structures". ''Mathematical Systems Theory'' 11, pp. 199-234, 353-372; 12, pp. 73-101.] | |||
* [http://lumma.org/music/theory/RothenbergExcerpts.txt Lumma, Carl. (2011?). ''A Quick Tour of Rothenberg's Musical Pattern Recognition Model''.] | |||
[[Category:Scale theory]] | [[Category:Scale theory]] | ||
{{Todo|expand}} | {{Todo|expand}} | ||