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

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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 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.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_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 ==

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.

* [[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]]

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 ==

; [[Daniel Corral]]

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; [[Elkay & Cee]]

* ''[https://soundcloud.com/elkayandcee/hexany-1357 Hexany1357]''

; [[Inhibitd]]

* ''[https://soundcloud.com/inhibitd/the-sphere-7-limit-hexany The Sphere]''

; [[Kalleaho]]

* ''[https://soundcloud.com/kalleaho/nocturne Nocturne]''

; [[Paul Maaswinkel]]

* ''[https://soundcloud.com/paulmaaswinkel/dungeon-brunch Dungeon Brunch]''

; [[Node Audio]]

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-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 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.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_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 ==
+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.
+* [[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]]
+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 ==
 ; [[Daniel Corral]]
@@ Line 25: / Line 65: @@
 ; [[Elkay & Cee]]
 * ''[https://soundcloud.com/elkayandcee/hexany-1357 Hexany1357]''
+; [[Inhibitd]]
+* ''[https://soundcloud.com/inhibitd/the-sphere-7-limit-hexany The Sphere]''
+; [[Kalleaho]]
+* ''[https://soundcloud.com/kalleaho/nocturne Nocturne]''
+; [[Paul Maaswinkel]]
+* ''[https://soundcloud.com/paulmaaswinkel/dungeon-brunch Dungeon Brunch]''
 ; [[Node Audio]]