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

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[[File:1-3-5-7_hexany.png|thumb|Circle diagram.]]

[[File:1-3-5-7_hexany_rotated.png|thumb|Circle diagram (rotated to most consonant mode).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9, the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.

[[File:1-3-5-7_hexany_rotated.png|thumb|Circle diagram (rotated to most consonant mode).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour [[1-3-5-9_hexany|1-3-5-9]], the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.

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Suggested keyboard mapping: C D# E G A Bb C

== Expansions ==

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.

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

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

* [[1-3-5-7 by 36/35 bihexany]]

Another 3 have overlapping notes and so only produce 10 note scales, but may still be useful nonetheless.

* [[1-3-5-7 by 3/2 bihexany]]

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

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

== Music ==

; [[Daniel Corral]]

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 [[File:1-3-5-7_hexany.png|thumb|Circle diagram.]]
-[[File:1-3-5-7_hexany_rotated.png|thumb|Circle diagram (rotated to most consonant mode).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9, the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.
+[[File:1-3-5-7_hexany_rotated.png|thumb|Circle diagram (rotated to most consonant mode).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour [[1-3-5-9_hexany|1-3-5-9]], the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.
 <pre>
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 Suggested keyboard mapping: C D# E G A Bb C
+== Expansions ==
+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.
+* [[1-3-5-7 by 9/5 bihexany]]
+* [[1-3-5-7 by 9/7 bihexany]]
+* [[1-3-5-7 by 36/35 bihexany]]
+Another 3 have overlapping notes and so only produce 10 note scales, but may still be useful nonetheless.
+* [[1-3-5-7 by 3/2 bihexany]]
+* [[1-3-5-7 by 6/5 bihexany]]
+* [[1-3-5-7 by 12/7 bihexany]]
 == Music ==
 ; [[Daniel Corral]]