1-3-7-21 hexany

A 7-limit Hexany. This creates a scale of 1 7/6 21/16 49/32 7/4 2/1, with steps of 7/6 9/8 7/6 8/7 8/7. This is particularly notable because it is the second simplest hexany that results in a pentatonic scale, with 7/4 appearing twice as the reduced product of 1x21 and 3x7. This means any dekanies built using it will also wind up with 9 or fewer notes. Unlike the smallest pentatonic dekany, the notes are quite evenly spaced, with a ratio of less than 4:3 between the largest and smallest steps. The most consonant mode is the symmetrical one, which makes the steps 1/1 8/7 4/3 3/2 7/4 2/1, revealing this to be a detemper of semaphore temperament. As such, songs composed in that temperament can also be played using this scale while remaining recognisable.

! 1-3-7-21_Hexany.scl
!
1 3 5 15 2-combination Hexany
5
!
7/6
21/16
49/32
7/4
2/1

Suggested keyboard mapping: E G A C D E