1-3-5-9 hexany: Difference between revisions
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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 [[dekany|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. | [[File:Hexany 1 3 5 9.png|thumb|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 [[dekany|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. | ||
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Revision as of 03:04, 5 October 2025
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 ! 9/8 5/4 3/2 5/3 15/8 2/1
Suggested keyboard mapping: Start on C, using all white notes except the F.
Music
- Murmurations (1st and 6th parts)