1-3-5-7 hexany: Difference between revisions
Give this one extra attention as it's the starting point for hexanies. |
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[[File:1-3-5-7_hexany.png|thumb|Circle diagram.]] | [[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 | 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 == | == Music == | ||
; [[Daniel Corral]] | ; [[Daniel Corral]] | ||
Latest revision as of 10:57, 17 January 2026
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.
! 1-3-5-7_Hexany.scl ! 1 3 5 7 2-combination Hexany 6 ! 7/6 5/4 35/24 5/3 7/4 2/1
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.
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.
Another 3 have overlapping notes and so only produce 10 note scales, but may still be useful nonetheless.
Other bihexanies derived from this that produce a 10 note scale are: (using the rotation that produces the more consonant mode overall where possible)
Other bihexanies derived from this that produce a 11 note scale are:
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
- Murmurations (5th part)