Dekany - Revision history

BudjarnLambeth: /* See also */

2025-09-27T01:21:23Z

Fredg999 category edits: Removing from Category:10-tone scales using Cat-a-lot

2025-08-17T20:41:31Z

Removing from Category:10-tone scales using Cat-a-lot

← Older revision		Revision as of 20:41, 17 August 2025
Line 25:		Line 25:

	[[Category:Dekanies\| ]] <!-- main article -->		[[Category:Dekanies\| ]] <!-- main article -->
	~~[[Category:10-tone scales]]~~

	{{todo\|expand\|add illustration\|improve synopsis}}		{{todo\|expand\|add illustration\|improve synopsis}}

Fredg999 category edits: Removing from Category:Combination product sets using Cat-a-lot

2025-08-17T20:33:06Z

Removing from Category:Combination product sets using Cat-a-lot

← Older revision		Revision as of 20:33, 17 August 2025
Line 25:		Line 25:

	[[Category:Dekanies\| ]] <!-- main article -->		[[Category:Dekanies\| ]] <!-- main article -->
	~~[[Category:Combination product sets]]~~
	[[Category:10-tone scales]]		[[Category:10-tone scales]]

	{{todo\|expand\|add illustration\|improve synopsis}}		{{todo\|expand\|add illustration\|improve synopsis}}

BudjarnLambeth: /* Pages about dekanies */ Avoided duplicate content

2025-03-29T00:25:28Z

Pages about dekanies: Avoided duplicate content

← Older revision		Revision as of 00:25, 29 March 2025
Line 21:		Line 21:
	# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.		# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.

	== ~~Pages about dekanies~~ ==		== See also ==
	* [[~~1-3-5-7-9 dekany~~]]		* [[Gallery of combination product sets#Dekanies]]

	[[Category:Dekanies\| ]] <!-- main article -->		[[Category:Dekanies\| ]] <!-- main article -->

BudjarnLambeth: Added link to orphaned page

2025-03-29T00:23:29Z

Added link to orphaned page

← Older revision		Revision as of 00:23, 29 March 2025
Line 3:		Line 3:
	In this article, ''2-combination dekany'' refers to a 2)5 CPS and ''3-combination dekany'' refers to a 3)5 CPS; Erv Wilson did not necessarily use these terms.		In this article, ''2-combination dekany'' refers to a 2)5 CPS and ''3-combination dekany'' refers to a 3)5 CPS; Erv Wilson did not necessarily use these terms.

	== ~~Examples~~ ==		== Construction ==

	=== 2-combination dekany ===		=== 2-combination dekany ===
Line 20:		Line 20:
	# Sort the elements in ascending order:<br>{1/1, 11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40};		# Sort the elements in ascending order:<br>{1/1, 11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40};
	# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.		# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.

			== Pages about dekanies ==
			* [[1-3-5-7-9 dekany]]

	[[Category:Dekanies\| ]] <!-- main article -->		[[Category:Dekanies\| ]] <!-- main article -->

BudjarnLambeth: Todo

2024-12-21T05:38:55Z

Todo

← Older revision		Revision as of 05:38, 21 December 2024
Line 24:		Line 24:
	[[Category:Combination product sets]]		[[Category:Combination product sets]]
	[[Category:10-tone scales]]		[[Category:10-tone scales]]
	~~[[Category:~~todo:expand]]
			{{todo\|expand\|add illustration\|improve synopsis}}

Fredg999: Fixed internal link

2021-12-22T18:10:51Z

Fixed internal link

← Older revision		Revision as of 18:10, 22 December 2021
Line 1:		Line 1:
	A '''dekany''' is a 10-note [[scale]] built using all the possible combinations of either 2 or 3 [[~~intervals~~]] (but not a mix of both) from a given set of 5 intervals. It is a particular case of a [[combination product set]] (CPS).		A '''dekany''' is a 10-note [[scale]] built using all the possible combinations of either 2 or 3 [[interval]]s (but not a mix of both) from a given set of 5 intervals. It is a particular case of a [[combination product set]] (CPS).

	In this article, ''2-combination dekany'' refers to a 2)5 CPS and ''3-combination dekany'' refers to a 3)5 CPS; Erv Wilson did not necessarily use these terms.		In this article, ''2-combination dekany'' refers to a 2)5 CPS and ''3-combination dekany'' refers to a 3)5 CPS; Erv Wilson did not necessarily use these terms.

Fredg999: Added internal link markup

2021-08-08T00:47:24Z

Added internal link markup

← Older revision		Revision as of 00:47, 8 August 2021
Line 1:		Line 1:
	A '''dekany''' is a 10-note scale built using all the possible combinations of either 2 or 3 intervals (but not a mix of both) from a given set of 5 intervals. It is a particular case of a [[combination product set]] (CPS).		A '''dekany''' is a 10-note [[scale]] built using all the possible combinations of either 2 or 3 [[intervals]] (but not a mix of both) from a given set of 5 intervals. It is a particular case of a [[combination product set]] (CPS).

	In this article, ''2-combination dekany'' refers to a 2)5 CPS and ''3-combination dekany'' refers to a 3)5 CPS; Erv Wilson did not necessarily use these terms.		In this article, ''2-combination dekany'' refers to a 2)5 CPS and ''3-combination dekany'' refers to a 3)5 CPS; Erv Wilson did not necessarily use these terms.

Fredg999: Removed external links (that were copied from Hexany)

2021-08-07T21:38:43Z

Removed external links (that were copied from Hexany)

← Older revision		Revision as of 21:38, 7 August 2021
Line 20:		Line 20:
	# Sort the elements in ascending order:<br>{1/1, 11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40};		# Sort the elements in ascending order:<br>{1/1, 11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40};
	# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.		# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.

	~~== External links ==~~
	* [[Wikipedia: Hexany]]
	* [http://anaphoria.com/grady1-1.pdf ''Ervin Wilson's Hexany''] by Kraig Grady

	[[Category:Dekanies\| ]] <!-- main article -->		[[Category:Dekanies\| ]] <!-- main article -->

Fredg999: Created page with "A '''dekany''' is a 10-note scale built using all the possible combinations of either 2 or 3 intervals (but not a mix of both) from a given set of 5 intervals. It is a particu..."

2021-08-07T21:37:23Z

Created page with "A '''dekany''' is a 10-note scale built using all the possible combinations of either 2 or 3 intervals (but not a mix of both) from a given set of 5 intervals. It is a particu..."

New page

A '''dekany''' is a 10-note scale built using all the possible combinations of either 2 or 3 intervals (but not a mix of both) from a given set of 5 intervals. It is a particular case of a [[combination product set]] (CPS).

In this article, ''2-combination dekany'' refers to a 2)5 CPS and ''3-combination dekany'' refers to a 3)5 CPS; Erv Wilson did not necessarily use these terms.

== Examples ==

=== 2-combination dekany ===
Here is a step-by-step construction of the canonical 1-3-5-7-11 2-combination dekany (i.e. using 2-combinations of [[1/1]], [[3/1]], [[5/1]], [[7/1]], and [[11/1]] with the smallest product as the root):
# Multiply together each pair of intervals (to find the combinations): {1 × 3, 1 × 5, 1 × 7, 1 × 11, 3 × 5, 3 × 7, 3 × 11, 5 × 7, 5 × 11, 7 × 11} = {3, 5, 7, 11, 15, 21, 33, 35, 55, 77};
# Divide each product by the smallest element of the previous set (to base the scale on 1/1): {3/3, 5/3, 7/3, 11/3, 15/3, 21/3, 33/3, 35/3, 55/3, 77/3} = {1/1, 5/3, 7/3, 11/3, 5/1, 7/1, 11/1, 35/3, 55/3, 77/3};
# [[Octave reduction|Octave-reduce]] each element: {1/1, 5/3, 7/6, 11/6, 5/4, 7/4, 11/8, 35/24, 55/48, 77/48};
# Sort the elements in ascending order: {1/1, 55/48, 7/6, 5/4, 11/8, 35/24, 77/48, 5/3, 7/4, 11/6};
# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale: {55/48, 7/6, 5/4, 11/8, 35/24, 77/48, 5/3, 7/4, 11/6, 2/1}.

=== 3-combination dekany ===
Here is a step-by-step construction of the canonical 1-3-5-7-11 3-combination dekany (i.e. using 3-combinations of [[1/1]], [[3/1]], [[5/1]], [[7/1]], and [[11/1]] with the smallest product as the root):
# Multiply together each pair of intervals (to find the combinations): {1 × 3 × 5, 1 × 3 × 7, 1 × 3 × 11, 1 × 5 × 7, 1 × 5 × 11, 1 × 7 × 11, 3 × 5 × 7, 3 × 5 × 11, 3 × 7 × 11, 5 × 7 × 11} = {15, 21, 33, 35, 55, 77, 105, 165, 231, 385};
# Divide each product by the smallest element of the previous set (to base the scale on 1/1): {15/15, 21/15, 33/15, 35/15, 55/15, 77/15, 105/15, 165/15, 231/15, 385/15} = {1/1, 7/5, 11/5, 7/3, 11/3, 77/15, 7/1, 11/1, 77/5, 77/3};
# [[Octave reduction|Octave-reduce]] each element: {1/1, 7/5, 11/10, 7/6, 11/6, 77/60, 7/4, 11/8, 77/40, 77/48};
# Sort the elements in ascending order: {1/1, 11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40};
# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale: {11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.

== External links ==
* [[Wikipedia: Hexany]]
* [http://anaphoria.com/grady1-1.pdf ''Ervin Wilson's Hexany''] by Kraig Grady

[[Category:Dekanies| ]] 
[[Category:Combination product sets]]
[[Category:10-tone scales]]
[[Category:todo:expand]]

← Older revision		Revision as of 01:21, 27 September 2025
Line 21:		Line 21:
	# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.		# Replace the unison (1/1) by the octave ([[2/1]]) for a Scala-compatible octave-repeating scale:<br>{11/10, 7/6, 77/60, 11/8, 7/5, 77/48, 7/4, 11/6, 77/40, 2/1}.

	== ~~See also~~ ==		== Pages for individual dekanies ==
	* [[Gallery of combination product sets#Dekanies]]		''See [[:Category:Dekanies]] and [[Gallery of combination product sets#Dekanies (10-tone)]]''

	[[Category:Dekanies\| ]] <!-- main article -->		[[Category:Dekanies\| ]] <!-- main article -->
	{{todo\|expand\|add illustration\|improve synopsis}}		{{todo\|expand\|add illustration\|improve synopsis}}