Combination product set - Revision history

Inthar: /* Types of CPSes */

2026-02-24T04:01:46Z

Types of CPSes

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	Common sizes for CPSes have specific names:		Common sizes for CPSes have specific names:
	# '''Hexany''': Choose 2 out of a list of 4 intervals		# '''Hexany''': Choose 2 out of a list of 4 intervals
	#* '''Stellated hexany''': A hexany combined with combinations of 1 and combinations of 3		#* '''Stellated hexany''': A hexany combined with combinations of 1 and combinations of 3, totaling 14 notes
	#* '''Bihexany''': Superimposition of two offset hexanies		#* '''Bihexany''': Superimposition of two offset hexanies
	# '''Dekany''': Choose 2 (or 3) out of a list of 5 intervals		# '''Dekany''': Choose 2 (or 3) out of a list of 5 intervals

2026-01-31T11:39:07Z

music

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	== Music ==		== Music ==
	* [https://youtu.be/62FggGa9bMg~~?si=fC72fRe9f8Zk8OcA~~ Eikosany Study - Daniel Corral (1 3 5 7 9 11 eikosany)]		* [https://youtu.be/62FggGa9bMg Eikosany Study - Daniel Corral (1 3 5 7 9 11 eikosany)]
	* [https://youtu.be/AWeFIOwGBh8~~?si=w1ddUi3LjNLTAsHk~~ Nodial - Outward Once (an eikosany)]		* [https://youtu.be/AWeFIOwGBh8 Nodial - Outward Once (an eikosany)]
			* [https://youtu.be/0n1AqB_SY7c Sevish - Murmurations (1 3 5 7 9 dekany)]
			* [https://youtu.be/5IyRbPr9QV0 dotuXil - waterpad (1 3 5 7 9 dekany)]
	{{Cat\|Scale construction}}		{{Cat\|Scale construction}}

2026-01-30T01:35:33Z

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	CPSes are notable as ''every'' note of a CPS has a different JI chord on it.		CPSes are notable as ''every'' note of a CPS has a different JI chord on it.

	A CPS is a subset of an iterated [[cross-set]] of a chord with itself. Specifically, a CPS of chord X is the subset of all elements of cross-set(X, cross-set(X, cross-set(...))) that do not stack any ratio of X more than once. CPSes were developed by Erv Wilson.		A CPS is a subset of an iterated [[cross-set]] of a chord with itself. Specifically, a CPS of chord X is the subset of all elements of cross-set(X, cross-set(X, cross-set(..., cross-set(X, X)...))) that do not stack any ratio of X more than once. CPSes were developed by Erv Wilson.
	== Example (1, 3, 5, 7 hexany) ==		== Example (1, 3, 5, 7 hexany) ==
	# In this example we choose four odd harmonics: 1, 3, 5, 7.		# In this example we choose four odd harmonics: 1, 3, 5, 7.

2026-01-30T00:26:19Z

← Older revision		Revision as of 00:26, 30 January 2026
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	CPSes are notable as ''every'' note of a CPS has a different JI chord on it.		CPSes are notable as ''every'' note of a CPS has a different JI chord on it.

	A CPS is a subset of an iterated [[cross-set]] of a chord with itself. CPSes were developed by Erv Wilson.		A CPS is a subset of an iterated [[cross-set]] of a chord with itself. Specifically, a CPS of chord X is the subset of all elements of cross-set(X, cross-set(X, cross-set(...))) that do not stack any ratio of X more than once. CPSes were developed by Erv Wilson.
	== Example (1, 3, 5, 7 hexany) ==		== Example (1, 3, 5, 7 hexany) ==
	# In this example we choose four odd harmonics: 1, 3, 5, 7.		# In this example we choose four odd harmonics: 1, 3, 5, 7.

2026-01-29T08:16:12Z

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	# This results in a list of notes. One note is chosen as the tonic.		# This results in a list of notes. One note is chosen as the tonic.
	# The resulting intervals relative to the tonic are octave-reduced.		# The resulting intervals relative to the tonic are octave-reduced.

			CPSes are notable as ''every'' note of a CPS has a different JI chord on it.

	A CPS is a subset of an iterated [[cross-set]] of a chord with itself. CPSes were developed by Erv Wilson.		A CPS is a subset of an iterated [[cross-set]] of a chord with itself. CPSes were developed by Erv Wilson.

2026-01-29T08:08:44Z

Examples

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	# Select "Combination product set"		# Select "Combination product set"

	== ~~Examples~~ ==		== Music ==
	* [https://youtu.be/62FggGa9bMg?si=fC72fRe9f8Zk8OcA Eikosany Study - Daniel Corral (1 3 5 7 9 11 eikosany)]		* [https://youtu.be/62FggGa9bMg?si=fC72fRe9f8Zk8OcA Eikosany Study - Daniel Corral (1 3 5 7 9 11 eikosany)]
	* [https://youtu.be/AWeFIOwGBh8?si=w1ddUi3LjNLTAsHk Nodial - Outward Once (an eikosany)]		* [https://youtu.be/AWeFIOwGBh8?si=w1ddUi3LjNLTAsHk Nodial - Outward Once (an eikosany)]
	{{Cat\|Scale construction}}		{{Cat\|Scale construction}}

2026-01-29T08:08:29Z

Playing with CPSes

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	# Select "Combination product set"		# Select "Combination product set"

			== Examples ==
			* [https://youtu.be/62FggGa9bMg?si=fC72fRe9f8Zk8OcA Eikosany Study - Daniel Corral (1 3 5 7 9 11 eikosany)]
			* [https://youtu.be/AWeFIOwGBh8?si=w1ddUi3LjNLTAsHk Nodial - Outward Once (an eikosany)]
	{{Cat\|Scale construction}}		{{Cat\|Scale construction}}

2026-01-29T05:47:46Z

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	{{Problematic}}		{{Problematic}}
	{{Expert}}		{{Expert}}
	A '''combination product set''' (CPS) is a scale (usually [[Just ~~Intonation~~\|JI]]) generated by the following procedure:		A '''combination product set''' (CPS) is a scale (usually [[Just intonation\|JI]]) generated by the following procedure:

	# A list of chosen intervals (usually odd harmonics) is the starting point.		# A list of chosen intervals (usually odd harmonics) is the starting point.

2025-12-27T15:30:49Z

Types of CPSes

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	# '''Dekany''': Choose 2 (or 3) out of a list of 5 intervals		# '''Dekany''': Choose 2 (or 3) out of a list of 5 intervals
	# '''Pentadekany''': Choose 2 (or 4) out of a list of 6 intervals		# '''Pentadekany''': Choose 2 (or 4) out of a list of 6 intervals
	# '''Eikosany''': Choose 3 out of a list of 6 intervals		# '''Eikosany''': Choose 3 out of a list of 6 intervals, creating a 20-note scale

	== Playing with CPSes ==		== Playing with CPSes ==

2025-12-27T15:27:11Z

Types of CPSes

← Older revision		Revision as of 15:27, 27 December 2025
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	# '''Hexany''': Choose 2 out of a list of 4 intervals		# '''Hexany''': Choose 2 out of a list of 4 intervals
	#* '''Stellated hexany''': A hexany combined with combinations of 1 and combinations of 3		#* '''Stellated hexany''': A hexany combined with combinations of 1 and combinations of 3
	#* '''Bihexany''': ~~Two~~ offset hexanies		#* '''Bihexany''': Superimposition of two offset hexanies
	# '''Dekany''': Choose 2 (or 3) out of a list of 5 intervals		# '''Dekany''': Choose 2 (or 3) out of a list of 5 intervals
	# '''Pentadekany''': Choose 2 (or 4) out of a list of 6 intervals		# '''Pentadekany''': Choose 2 (or 4) out of a list of 6 intervals