1-3-5-7-15 dekany

The simplest 15-odd-limit dekany. This creates a scale of 1 35/32 7/6 5/4 35/24 25/16 5/3 7/4 15/8, with steps of 35/32 16/15 15/14 7/6 15/14 16/15 21/20 15/14 16/15. This is notable because it is the simplest dekany that winds up with fewer than 10 notes, with 5/4 appearing twice as the reduced product of 1x15 and 3x5. This does not have a perfect fifth above the root, but does have four other ones, plus two additional fifths that are flat by a marvel comma and still entirely usable as a regular fifth. Although it does not contain a diatonic scale, it still has many other simple consonances, making it a highly accessible introduction to xenharmony that contains several notes almost exactly 50 cents out from 12edo, but does not provide so many options as to be overwhelming.

Circle diagram.

Circle diagram (rotated).

! 1-3-5-7-15_Dekany.scl
!
1 3 5 7 15 2-combination Dekany
9
!
155.139
266.871
386.313
653.184
772.627
884.358
968.825
1088.268
1200

Suggested keyboard mapping: Start on C, skipping the C#, E & G notes.