Hexany: Difference between revisions

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

== Example ==

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# 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}.

== 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 ==

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 {{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 '''stellated hexany''' is a 14-tone scale and is also called a '''dekatesserany'''.
 == Example ==
@@ Line 11: / Line 9: @@
 # 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}.
+== 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 ==