Hexany: Difference between revisions

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~~The~~ Wikipedia ~~article on it~~ is:

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]].

[~~http~~://~~en.wikipedia.org~~/~~wiki~~/~~Hexany Hexany~~] [[Category:~~hexany~~]]

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

[[~~Category~~:~~scale~~]]

[[Category:~~theory~~]]

== Example ==

[[Category:~~todo:add_definition~~]]

Here is a step-by-step construction of the canonical 1-3-5-7 hexany (i.e. using [[1/1]], [[3/1]], [[5/1]], and [[7/1]] with the smallest product as the root):

# Multiply together each pair of intervals (to find the combinations): {1 × 3, 1 × 5, 1 × 7, 3 × 5, 3 × 7, 5 × 7} = {3, 5, 7, 15, 21, 35};

# Divide each product by the smallest element of the previous set (to base the scale on 1/1): {3/3, 5/3, 7/3, 15/3, 21/3, 35/3} = {1/1, 5/3, 7/3, 5/1, 7/1, 35/3};

# [[Octave reduction|Octave-reduce]] each element: {1/1, 5/3, 7/6, 5/4, 7/4, 35/24};

# Sort the elements in ascending order: {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: {7/6, 5/4, 35/24, 5/3, 7/4, 2/1}.

== Pages for individual hexanies ==

''See [[:Category:Hexanies]].''

== External links ==

* [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.

* [[Paul Erlich]]. [https://sethares.engr.wisc.edu/paperspdf/Erlich-Forms.pdf The Forms of Tonality].

[[Category:Hexanies| ]]

[[Category:6-tone scales]]

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-The Wikipedia article on it is:
+{{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]].
-[http://en.wikipedia.org/wiki/Hexany Hexany]      [[Category:hexany]]
+A '''stellated hexany''' is a 14-tone scale and is also called a '''dekatesserany'''.
-[[Category:scale]]
-[[Category:theory]]
+== Example ==
-[[Category:todo:add_definition]]
+Here is a step-by-step construction of the canonical 1-3-5-7 hexany (i.e. using [[1/1]], [[3/1]], [[5/1]], and [[7/1]] with the smallest product as the root):
+# Multiply together each pair of intervals (to find the combinations):<br>{1 × 3, 1 × 5, 1 × 7, 3 × 5, 3 × 7, 5 × 7}<br> = {3, 5, 7, 15, 21, 35};
+# Divide each product by the smallest element of the previous set (to base the scale on 1/1):<br>{3/3, 5/3, 7/3, 15/3, 21/3, 35/3}<br>= {1/1, 5/3, 7/3, 5/1, 7/1, 35/3};
+# [[Octave reduction|Octave-reduce]] each element:<br>{1/1, 5/3, 7/6, 5/4, 7/4, 35/24};
+# 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}.
+== Pages for individual hexanies ==
+''See [[:Category:Hexanies]].''
+== External links ==
+* [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.
+* [[Paul Erlich]]. [https://sethares.engr.wisc.edu/paperspdf/Erlich-Forms.pdf The Forms of Tonality].
+{{todo|add examples|add illustration|expand}}
+[[Category:Hexanies| ]] <!-- main article -->
+[[Category:6-tone scales]]