Hexany - Revision history

Yourmusic Productions: /* Stellated Hexanies */ add link to related type of scale.

2026-05-06T17:00:29Z

Stellated Hexanies: add link to related type of scale.

← Older revision		Revision as of 17:00, 6 May 2026
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	Divided by the smallest element, octave reduced and sorted by order, this is: <br>{1/1, 35/32, 9/8, 7/6, 5/4, 21/16, 45/32, 35/24, 3/2, 105/64, 5/3, 7/4, 15/8, 63/32}.		Divided by the smallest element, octave reduced and sorted by order, this is: <br>{1/1, 35/32, 9/8, 7/6, 5/4, 21/16, 45/32, 35/24, 3/2, 105/64, 5/3, 7/4, 15/8, 63/32}.

			If you include the combinations of 0 out of 4 and 4 out of 4 as well, you get a 16 note scale known as a [[The_block_and_the_tesseract\|tesseract]] which is always solidly rooted with all the other notes otonal to the 1.

	== Bihexany ==		== Bihexany ==

BudjarnLambeth: /* Bihexany */

2025-10-05T09:17:46Z

Bihexany

← Older revision		Revision as of 09:17, 5 October 2025
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	== Bihexany ==		== Bihexany ==
	Another way of expanding out a hexany is by taking two copies of the same hexany and offsetting them by some other interval. This is particularly useful because the resulting 12 note scale can be mapped onto a standard keyboard with no missed or repeated notes, giving you as many harmonic options as possible without having to buy a custom instrument to play the scale properly. For example, two 1-3-5-9 hexanies separated by a 7/5 would produce a scale of: <br>{1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 5/3 7/4 15/8 2/1}		Another way of expanding out a hexany is by taking two copies of the ''same'' hexany and offsetting them by some other interval. This is particularly useful because the resulting 12 note scale can be mapped onto a standard keyboard with no missed or repeated notes, giving you as many harmonic options as possible without having to buy a custom instrument to play the scale properly. For example, two 1-3-5-9 hexanies separated by a 7/5 would produce a scale of: <br>{1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 5/3 7/4 15/8 2/1}

	== Duohexany ==		== Duohexany ==

BudjarnLambeth: Add duohexany section

2025-10-05T09:16:29Z

Add duohexany section

← Older revision		Revision as of 09:16, 5 October 2025
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	== Bihexany ==		== Bihexany ==
	Another way of expanding out a hexany is by taking two copies of the same hexany and offsetting them by some other interval. This is particularly useful because the resulting 12 note scale can be mapped onto a standard keyboard with no missed or repeated notes, giving you as many harmonic options as possible without having to buy a custom instrument to play the scale properly. For example, two 1-3-5-9 hexanies separated by a 7/5 would produce a scale of: <br>{1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 5/3 7/4 15/8 2/1}		Another way of expanding out a hexany is by taking two copies of the same hexany and offsetting them by some other interval. This is particularly useful because the resulting 12 note scale can be mapped onto a standard keyboard with no missed or repeated notes, giving you as many harmonic options as possible without having to buy a custom instrument to play the scale properly. For example, two 1-3-5-9 hexanies separated by a 7/5 would produce a scale of: <br>{1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 5/3 7/4 15/8 2/1}

			== Duohexany ==
			Two ''different'' hexanies together is a duohexany. If the hexanies have no intervals in common, this will result in a 12 note scale mappable to a standard keyboard. If they share intervals, the notes per octave will be less than 12.

	== Pages for individual hexanies ==		== Pages for individual hexanies ==

BudjarnLambeth: /* Pages for individual hexanies */

2025-09-27T01:23:23Z

Pages for individual hexanies

← Older revision		Revision as of 01:23, 27 September 2025
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	== Pages for individual hexanies ==		== Pages for individual hexanies ==
	''See [[:Category:Hexanies]] and [[Gallery of combination product sets~~#Hexanies (6-tone)~~]]''		''See [[:Category:Hexanies]] and [[Gallery of combination product sets]]''

	== External links ==		== External links ==

BudjarnLambeth: /* Pages for individual hexanies */

2025-09-27T01:20:18Z

Pages for individual hexanies

← Older revision		Revision as of 01:20, 27 September 2025
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	== Pages for individual hexanies ==		== Pages for individual hexanies ==
	''See [[:Category:Hexanies]].''		''See [[:Category:Hexanies]] and [[Gallery of combination product sets#Hexanies (6-tone)]]''

	== External links ==		== External links ==

Yourmusic Productions: Fix math error.

2025-09-05T12:35:13Z

Fix math error.

← Older revision		Revision as of 12:35, 5 September 2025
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	== Bihexany ==		== Bihexany ==
	Another way of expanding out a hexany is by taking two copies of the same hexany and offsetting them by some other interval. This is particularly useful because the resulting 12 note scale can be mapped onto a standard keyboard with no missed or repeated notes, giving you as many harmonic options as possible without having to buy a custom instrument to play the scale properly. For example, two 1-3-5-9 hexanies separated by a 7/5 would produce a scale of: <br>{1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 7/4 15/8 2/1}		Another way of expanding out a hexany is by taking two copies of the same hexany and offsetting them by some other interval. This is particularly useful because the resulting 12 note scale can be mapped onto a standard keyboard with no missed or repeated notes, giving you as many harmonic options as possible without having to buy a custom instrument to play the scale properly. For example, two 1-3-5-9 hexanies separated by a 7/5 would produce a scale of: <br>{1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 5/3 7/4 15/8 2/1}

	== Pages for individual hexanies ==		== Pages for individual hexanies ==

Yourmusic Productions: Add description of bihexanies too.

2025-09-05T12:31:52Z

Add description of bihexanies too.

← Older revision		Revision as of 12:31, 5 September 2025
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	Divided by the smallest element, octave reduced and sorted by order, this is: <br>{1/1, 35/32, 9/8, 7/6, 5/4, 21/16, 45/32, 35/24, 3/2, 105/64, 5/3, 7/4, 15/8, 63/32}.		Divided by the smallest element, octave reduced and sorted by order, this is: <br>{1/1, 35/32, 9/8, 7/6, 5/4, 21/16, 45/32, 35/24, 3/2, 105/64, 5/3, 7/4, 15/8, 63/32}.

			== Bihexany ==
			Another way of expanding out a hexany is by taking two copies of the same hexany and offsetting them by some other interval. This is particularly useful because the resulting 12 note scale can be mapped onto a standard keyboard with no missed or repeated notes, giving you as many harmonic options as possible without having to buy a custom instrument to play the scale properly. For example, two 1-3-5-9 hexanies separated by a 7/5 would produce a scale of: <br>{1 21/20 9/8 7/6 5/4 21/16 7/5 3/2 63/40 7/4 15/8 2/1}

	== Pages for individual hexanies ==		== Pages for individual hexanies ==

Yourmusic Productions: Properly explain what a stellated hexany is.

2025-09-05T10:12:36Z

Properly explain what a stellated hexany is.

← Older revision		Revision as of 10:12, 5 September 2025
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	{{Wikipedia\|Hexany}}		{{Wikipedia\|Hexany}}
	A '''hexany''' is a 6-note [[scale]] built using all the possible combinations of 2 [[interval]]s from a given set of 4 intervals. It is the simplest non-trivial case of a [[combination product set]].		A '''hexany''' is a 6-note [[scale]] built using all the possible combinations of 2 [[interval]]s from a given set of 4 intervals. It is the simplest non-trivial case of a [[combination product set]].

	~~A '''stellated hexany''' is a 14-tone scale and is also called a '''dekatesserany'''.~~

	== Example ==		== Example ==
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	# Sort the elements in ascending order:<br>{1/1, 7/6, 5/4, 35/24, 5/3, 7/4};		# Sort the elements in ascending order:<br>{1/1, 7/6, 5/4, 35/24, 5/3, 7/4};
	# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{7/6, 5/4, 35/24, 5/3, 7/4, 2/1}.		# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{7/6, 5/4, 35/24, 5/3, 7/4, 2/1}.

			== Stellated Hexanies ==
			A '''stellated hexany''' is a 14-tone scale and is also called a '''dekatesserany'''. This is formed by adding the combinations of 1 out of 4 and 3 out of 4 intervals to the set. In the case of the example above, that would expand it to a {1/1, 35/32, 5/4, 21/16 3/2, 105/64, 7/4, 15/8} scale. Note that many of the notes are repeated in this case because 1 is one of the factors and 1x3 is identical to 3, etc. The simplest stellated hexany without any repeated notes is the 3-5-7-9 one, which produces a scale of:

			{3, 5, 7, 9} {3x5=15, 3x7=21, 3x9=27, 5x7=35, 5x9=45, 7x9=63} {3x5x7=105, 3x5x9=135, 3x7x9=189, 5x7x9=315}

			Divided by the smallest element, octave reduced and sorted by order, this is: <br>{1/1, 35/32, 9/8, 7/6, 5/4, 21/16, 45/32, 35/24, 3/2, 105/64, 5/3, 7/4, 15/8, 63/32}.

	== Pages for individual hexanies ==		== Pages for individual hexanies ==

Fredg999 category edits: /* External links */ Add 1 link

2025-08-17T20:56:52Z

External links: Add 1 link

← Older revision		Revision as of 20:56, 17 August 2025
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	* [http://anaphoria.com/grady1-1.pdf ''Ervin Wilson's Hexany''] by Kraig Grady		* [http://anaphoria.com/grady1-1.pdf ''Ervin Wilson's Hexany''] by Kraig Grady
	* [https://www.youtube.com/watch?v=-GeR8XbFxvI The Tonality Cube] Demonstration video by 12tone music.		* [https://www.youtube.com/watch?v=-GeR8XbFxvI The Tonality Cube] Demonstration video by 12tone music.
			* [[Paul Erlich]]. [https://sethares.engr.wisc.edu/paperspdf/Erlich-Forms.pdf The Forms of Tonality].
	{{todo\|add examples\|add illustration\|expand}}		{{todo\|add examples\|add illustration\|expand}}

	[[Category:Hexanies\| ]] <!-- main article -->		[[Category:Hexanies\| ]] <!-- main article -->
	[[Category:6-tone scales]]		[[Category:6-tone scales]]

Fredg999: Removed term "mandala" (seems to be the name for a specific one)

2025-08-17T20:40:24Z

Removed term "mandala" (seems to be the name for a specific one)

← Older revision		Revision as of 20:40, 17 August 2025
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	A '''hexany''' is a 6-note [[scale]] built using all the possible combinations of 2 [[interval]]s from a given set of 4 intervals. It is the simplest non-trivial case of a [[combination product set]].		A '''hexany''' is a 6-note [[scale]] built using all the possible combinations of 2 [[interval]]s from a given set of 4 intervals. It is the simplest non-trivial case of a [[combination product set]].

	A '''stellated hexany''' is a 14-tone scale and is called ~~both a '''mandala''' and~~ a '''dekatesserany'''.		A '''stellated hexany''' is a 14-tone scale and is also called a '''dekatesserany'''.

	== Example ==		== Example ==