Rothenberg propriety - Revision history

Sintel: fix quotation mark abuse

2024-05-17T18:17:28Z

fix quotation mark abuse

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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'''.		'''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 larger 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.		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.

	A scale is "improper" if it isn't strictly proper or proper; e.g. there is some interval class (e.g. 'fourth') that is larger than the next-larger class (e.g. 'fifth'). The diatonic scale in 17-EDO is improper as the augmented fourth is now larger than the diminished fifth. The double harmonic scale is improper in 12-EDO and 31-EDO.		A scale is ''improper'' if it isn't strictly proper or proper; e.g. there is some interval class (e.g. fourth) that is larger than the next-larger class (e.g. fifth). The diatonic scale in 17-EDO is improper as the augmented fourth is now larger than the diminished fifth. The double harmonic scale is improper in 12-EDO and 31-EDO.

	If there are two generic interval classes which share some specific interval (such as the 12-EDO diatonic scale with the 600 cent interval), ~~e.g. the scale is "proper,"~~ the resulting intervals are called ''ambiguous.'' In an improper scale, the interval classes that are ~~"mis-ordered"~~ relative to one another are called ''contradictions.''		If there are two generic interval classes which share some specific interval (such as the 12-EDO diatonic scale with the 600 cent interval), the resulting intervals are called ''ambiguous''. In an improper scale, the interval classes that are misordered relative to one another are called ''contradictions''.

	This metric has been extended several ways - see also:		This metric has been extended several ways - see also:

	# [[Lumma stability]] and impropriety factor		# [[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 Rothenberg efficiency] on [[Tonalsoft encyclopedia]]
	# [http://www.tonalsoft.com/enc/r/rothenberg-redundancy.aspx "Rothenberg redundancy"] on [[Tonalsoft encyclopedia]]		# [http://www.tonalsoft.com/enc/r/rothenberg-redundancy.aspx Rothenberg redundancy] on [[Tonalsoft encyclopedia]]
	# [http://www.tonalsoft.com/enc/r/rothenberg-stability.aspx "Rothenberg stability"] on [[Tonalsoft encyclopedia]]		# [http://www.tonalsoft.com/enc/r/rothenberg-stability.aspx Rothenberg stability] on [[Tonalsoft encyclopedia]]

	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>

Bcmills: “have constant structure” → “are constant structures”

2024-05-06T13:37:44Z

“have constant structure” → “are constant structures”

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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>		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>

	Strictly proper scales ~~have~~ [[constant structure]], and proper but not strictly proper scales do not. Improper scales usually do, but see the 22edo example below for a counter-example.		Strictly proper scales are [[constant structure\|constant structures]], and proper but not strictly proper scales are not. Improper scales usually do, but see the 22edo example below for a counter-example.

	== Examples ==		== Examples ==

Bcmills: /* See also */: added link to Constant structure

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See also: : added link to Constant structure

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	== See also ==		== See also ==
	* [[MOS scale]]		* [[MOS scale]]
			* [[Constant structure]]

	== References ==		== References ==

Inthar at 02:23, 1 February 2023

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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>		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>

	Strictly proper scales have [[constant structure]], and proper scales do not. Improper scales usually do, but see the 22edo example below for a counter-example.		Strictly proper scales have [[constant structure]], and proper but not strictly proper scales do not. Improper scales usually do, but see the 22edo example below for a counter-example.

	== Examples ==		== Examples ==

TallKite at 02:18, 1 February 2023

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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>		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>

	Strictly proper scales have [[constant structure]], and proper scales do not.		Strictly proper scales have [[constant structure]], and proper scales do not. Improper scales usually do, but see the 22edo example below for a counter-example.

	== Examples ==		== Examples ==

TallKite: clarification of improper = CS

2023-02-01T02:16:52Z

clarification of improper = CS

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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>		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 ==		== 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).		* [[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''.		* [[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 ==		== See also ==

TallKite: related this page to constant structure

2023-02-01T01:26:31Z

related this page to constant structure

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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>		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.

	== Examples ==		== Examples ==

TallKite: fixed a mistake

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fixed a mistake

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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'''.		'''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.		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.

Fredg999 category edits: Moving from Category:Scale theory to Category:Scale using Cat-a-lot

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Moving from Category:Scale theory to Category:Scale using Cat-a-lot

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	* [http://lumma.org/music/theory/RothenbergExcerpts.txt Lumma, Carl. (2011?). ''A Quick Tour of Rothenberg's Musical Pattern Recognition Model''.]		* [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]]

	{{Todo\|expand}}		{{Todo\|expand}}

Fredg999: Added Wikipedia box, created external links section with new link and detailed descriptions

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Added Wikipedia box, created external links section with new link and detailed descriptions

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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:

	# ~~http://www.tonalsoft.com/enc/l/lumma-~~stability~~.aspx~~		# [[Lumma stability]] and impropriety factor
	~~# http://www.tonalsoft.com/enc/l/lumma-~~impropriety~~.aspx~~		# [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 ==
	* [[Wikipedia: Rothenberg propriety]]
	* [[MOS scale]]		* [[MOS scale]]

	== References ==		== References ==
	* http://lumma.org/tuning/rothenberg/AModelForPatternPerception.pdf
	<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}}