1-3-5-7 hexany: Difference between revisions

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== Expansions ==

As it has 1 as a factor, turning this from a standard hexany into a stellated hexany only adds two notes to your options rather than a full 14 due to the large number of repeated notes, which still leaves plenty of gaps on a standard keyboard.

* [[1-3-5-7 stellated hexany]]

There are 6 ways of expanding this out to a bihexany that will put a 3/2 above the root, expanding your options in a way that gives you a stable 5-limit chord to centre your scale upon and plenty of other consonant chords. 3 of them produce a full 12 note scale.

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* [[1-3-5-7 by 6/5 bihexany]]

* [[1-3-5-7 by 12/7 bihexany]]

Other bihexanies derived from this that produce a 10 note scale are: (using the rotation that produces the more consonant mode overall where possible)

* [[1-3-5-7 by 8/7 bihexany]]

* [[1-3-5-7 by 8/5 bihexany]]

* [[1-3-5-7 by 10/7 bihexany]]

Other bihexanies derived from this that produce a 11 note scale are:

* [[1-3-5-7 by 15/14 bihexany]]

* [[1-3-5-7 by 40/21 bihexany]]

* [[1-3-5-7 by 48/35 bihexany]]

All other offset intervals will produce a 12 note scale with at least 4 perfect fifths, although they may not be positioned in a way that provides familiar chord sequences. Ones that have five or more perfect fifths include:

* [[1-3-5-7 by 9/8 bihexany]]

* [[1-3-5-7 by 21/16 bihexany]]

* [[1-3-5-7 by 16/15 bihexany]]

* [[1-3-5-7 by 56/45 bihexany]]

* [[1-3-5-7 by 64/35 bihexany]]

* [[1-3-5-7 by 80/63 bihexany]]

== Music ==

@@ Line 19: / Line 19: @@
 == Expansions ==
+As it has 1 as a factor, turning this from a standard hexany into a stellated hexany only adds two notes to your options rather than a full 14 due to the large number of repeated notes, which still leaves plenty of gaps on a standard keyboard.
+* [[1-3-5-7 stellated hexany]]
 There are 6 ways of expanding this out to a bihexany that will put a 3/2 above the root, expanding your options in a way that gives you a stable 5-limit chord to centre your scale upon and plenty of other consonant chords. 3 of them produce a full 12 note scale.
@@ Line 31: / Line 34: @@
 * [[1-3-5-7 by 6/5 bihexany]]
 * [[1-3-5-7 by 12/7 bihexany]]
+Other bihexanies derived from this that produce a 10 note scale are: (using the rotation that produces the more consonant mode overall where possible)
+* [[1-3-5-7 by 8/7 bihexany]]
+* [[1-3-5-7 by 8/5 bihexany]]
+* [[1-3-5-7 by 10/7 bihexany]]
+Other bihexanies derived from this that produce a 11 note scale are:
+* [[1-3-5-7 by 15/14 bihexany]]
+* [[1-3-5-7 by 40/21 bihexany]]
+* [[1-3-5-7 by 48/35 bihexany]]
+All other offset intervals will produce a 12 note scale with at least 4 perfect fifths, although they may not be positioned in a way that provides familiar chord sequences. Ones that have five or more perfect fifths include:
+* [[1-3-5-7 by 9/8 bihexany]]
+* [[1-3-5-7 by 21/16 bihexany]]
+* [[1-3-5-7 by 16/15 bihexany]]
+* [[1-3-5-7 by 56/45 bihexany]]
+* [[1-3-5-7 by 64/35 bihexany]]
+* [[1-3-5-7 by 80/63 bihexany]]
 == Music ==