1-3-5-7-9-11-15 enaeikosany

The second simplest possible enaeikosany. This creates a scale of 1 33/32 35/32 9/8 55/48 7/6 5/4 21/16 11/8 45/32 35/24 3/2 25/16 77/48 5/3 55/32 7/4 11/6 15/8 2/1, with steps of 33/32 35/33 36/35 55/54 56/55 15/14 21/20 22/21 45/44 28/27 36/35 25/24 77/75 80/77 33/32 56/55 22/21 45/44 16/15. As usual, the introduction of factors of 15 results in some duplicated notes, reducing this to a 19 note scale. However, as all the notes that remain are now easily distinct, the resulting scale is actually more melodically effective and easier to work with than the simplest enaeikosany. 11 of the notes have perfect fifths above them and all of them have multiple usable thirds, making composition relatively convenient for a larger just intonation scale.

Circle diagram.

! 1-3-5-7-9-11-15_Enaeikosany.scl
!
1 3 5 7 9 11 15 2-combination Enaeikosany
19
!
53.272
138.572
203.910
235.676
266.871
342.482
386.313
470.781
524.886
551.317
653.184
689.890
701.955
818.188
840.527
884.358
968.825
1049.362
1088.268
1107.398
1200