1-3-7-9 hexany

The simplest no-5's Hexany. This creates a scale of 1 9/8 7/6 21/16 3/2 7/4 2/1, with steps of 9/8 28/27 9/8 8/7 7/6 8/7. This is particularly interesting, because it can be viewed as a detemper of the basic archy diatonic scale in the same way that the 1-3-5-9 hexany detempers meantone. Like those, the septimal pentatonic scale is more even, but has a smaller diatonic semitone once extended to a hexatonic scale. Similarly, major chords are simpler in the 5-limit, while minor ones are simpler in the 7-limit, making the notes with minor chords above them the more obvious roots. Since the notes are fairly evenly spaced and none are more than 33 cents away from 12edo, it maps unambiguously to a standard keyboard layout.

! 1-3-7-9_Hexany.scl
!
1 3 7 9 2-combination Hexany
6
!
9/8
7/6
21/16
3/2
7/4
2/1

Suggested keyboard mapping: Start on A, using all white notes except the F.

Music

• Sevish: Murmurations (3rd part). Hexdeep