1-3-5-9 hexany
The second simplest possible Hexany, comprised of two-combination sum products of the first four 5-limit odd numbers. This creates a scale of 1 9/8 5/4 3/2 5/3 15/8 2/1, with steps of 9/8 10/9 6/5 10/9 9/8 16/15. This is particularly notable because it maps unambiguously to 6 out of 7 notes of the standard diatonic scale, giving you justly tuned C, Em, G & Am chords, although the D has a wolf fifth above it and no third available. This makes it a solid base for building dekanies, as adding a single other number will give you a 10 note scale that can contrast familiar and xenharmonic chords in a compositionally effective way in many cases.
! 1-3-5-9_Hexany.scl ! 1 3 5 9 2-combination Hexany 6 ! 203.901 386.313 701.955 884.358 1088.268 1200
Suggested keyboard mapping: Start on C, using all white notes except the F.
Expansions
As this is comprised entirely of simple 5-limit intervals, using one of those as an offset interval to produce a bihexany will produce a scale with less than 12 notes. While still usable, these 7 scales will not give you the greatest possible variety of options.
- 1-3-5-9 by 4/3 bihexany
- 1-3-5-9 by 6/5 bihexany
- 1-3-5-9 by 8/5 bihexany
- 1-3-5-9 by 10/9 bihexany
- 1-3-5-9 by 16/9 bihexany
- 1-3-5-9 by 16/15 bihexany
- 1-3-5-9 by 27/20 bihexany
Instead, an interval that is either close to a tritone, or falls precisely between the cracks of the 12edo keyboard will give you the most harmonic and melodic utility.
- 1-3-5-9 by 7/5 bihexany
- 1-3-5-9 by 64/45 bihexany
- 1-3-5-9 by 17/12 bihexany
- 1-3-5-9 by 13/9 bihexany
- 1-3-5-9 by 11/9 bihexany
Dekanies follow a similar pattern, with the extra four notes always forming a 1 9/8 5/4 3/2 tetrad, but its position related to the other 6 notes and number of overlaps varies widely.
Music
- Murmurations (1st and 6th parts)