1-3-5-9 hexany

Circle diagram.

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 it has 1 as a factor, turning this into a stellated hexany only adds two notes to the scale, which does mildly increase your compositional options, but they remain completely unxenharmonic.

• 1-3-5-9 stellated hexany

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 25/18 bihexany
• 1-3-5-9 by 17/12 bihexany
• 1-3-5-9 by 13/10 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.

• 1-3-5-7-9 dekany
• 1-3-5-9-11 dekany
• 1-3-5-9-13 dekany
• 1-3-5-9-15 dekany
• 1-3-5-9-17 dekany
• 1-3-5-9-19 dekany
• 1-3-5-9-21 dekany
• 1-3-5-9-23 dekany
• 1-3-5-9-25 dekany
• 1-3-5-9-27 dekany
• 1-3-5-9-45 dekany
• 1-3-5-9-81 dekany

Music

Hildegard von Kilju

• Antique Relic

JJ Cephei

• Capsule Tracker

Phexioenesystems

• Conversant/Expansive

Sevish

• Murmurations (1st and 6th parts)

Tito Silversax

• sfarsitul iernii (tracks 2-4)

Wrave

• Plinky Hexany