1-3-5-11-13 dekany
A 13-odd-limit dekany. This creates a scale of 1 13/12 55/48 5/4 65/48 11/8 143/96 13/8 5/3 11/6 2/1, with steps of 13/12 55/52 12/11 13/12 66/65 13/12 12/11 40/39 11/10 12/11. This has three perfect fifths, but not one above the root note. (although it does have both an imperfect fourth and fifth above the root) As it has factors of both 11 and 13, there are many notes that fall between the cracks of the 12edo keyboard, but there are no clusters of multiple small notes in quick succession that would make it difficult to map.
! 1-3-5-9-13_Dekany.scl ! 1 3 5 9 13 2-combination Dekany 10 ! 138.572 235.676 386.313 524.886 551.317 689.890 840.527 884.358 1049.362 1200
Suggested keyboard mapping: Start on C, skipping the Eb and Bb notes. This ensures that the notes with perfect fifths above them are always 7 steps above their root, even if they are not always mapped to the closest key on the 12edo keyboard.