1-3-5-7-9-11-13 pentatriandekany
The simplest possible pentatriandekany, comprised of three-combination sum products of the first 7 odd numbers. This creates a scale of 1 33/32 1001/960 21/20 13/12 11/10 9/8 91/80 7/6 143/120 39/32 99/80 77/60 13/10 21/16 429/320 11/8 7/5 231/160 117/80 143/96 3/2 91/60 63/40 77/48 13/8 33/20 273/160 7/4 143/80 9/5 11/6 91/48 77/40 39/20 2/1, with steps of 33/32 91/90 144/143 65/63 66/65 45/44 91/90 40/39 143/140 45/44 66/65 28/27 78/77 105/104 143/140 40/39 56/55 33/32 78/77 55/54 144/143 91/90 27/26 55/54 78/77 66/65 91/88 40/39 143/140 144/143 55/54 91/88 66/65 78/77 40/39. This has the same smallest step size as the corresponding enaeikosany, but reduces the size of the largest step to a third-tone, for a ratio of approximately 5.5 between them. It has plenty of perfect fifths, but since it only has factors of 5 in the denominator it does not have a simple major third above the root and 5-limit chords are few in general. At this density of notes it is still possible to construct all kinds of chords both consonant and dissonant all around the scale, even if the precise ratio you want is not always available.
! 1-3-5-7-9-11-13_Pentatriandekany.scl ! 1 3 5 7 9 11 13 3-combination Pentatriandekany 35 ! 53.272 72.402 84.467 138.572 165.004 203.910 223.039 266.871 303.576 342.482 368.914 431.875 454.213 470.781 507.486 551.317 582.512 635.785 658.123 689.890 701.955 721.084 786.422 818.188 840.527 866.959 924.994 968.825 1005.531 1017.596 1049.362 1107.398 1133.830 1156.168 1200