1-3-5-7-9-11-13-15 evdomindasany
The simplest possible evdomindasany, comprised of four-combination sum products of the first 8 odd numbers. This creates a scale of: 1 65/64 143/140 33/32 117/112 15/14 13/12 11/10 495/448 143/128 9/8 1287/1120 65/56 33/28 143/120 135/112 39/32 99/80 5/4 143/112 9/7 13/10 585/448 297/224 429/320 11/8 39/28 45/32 99/70 1287/896 117/80 165/112 143/96 3/2 429/280 99/64 351/224 11/7 715/448 45/28 13/8 33/20 117/70 27/16 143/84 55/32 195/112 99/56 143/80 9/5 117/64 11/6 13/7 15/8 429/224 27/14 39/20 55/28 2/1, with steps of 65/64 176/175 105/104 78/77 40/39 91/90 66/65 225/224 91/90 144/143 143/140 100/99 66/65 91/90 2025/2002 91/90 66/65 100/99 143/140 144/143 91/90 225/224 66/65 91/90 40/39 78/77 105/104 176/175 65/64 56/55 275/273 91/90 144/143 143/140 105/104 78/77 352/351 65/64 144/143 91/90 66/65 78/77 105/104 572/567 105/104 78/77 66/65 91/90 144/143 65/64 352/351 78/77 105/104 143/140 144/143 91/90 275/273 56/55. (12 notes are duplicated, reducing it from a 70 note scale to a 58 note one.)
Despite having even more notes than hexapenindasanies, these do have the merit of being slightly easier to calculate, as like hexanies, eikosanies and other combination product sets that use exactly half the overall number of factors for any one note, they are symmetrical, which means you can doublecheck whether you got all your calculations correct by seeing if you can find the points of symmetry in your steps. (in this case, they reflect around 2025/2002 and 572/567) Even with that assisting factor, a scale this size is still a significant effort to calculate and an even greater one to represent in a clear form or actually play, with the scalecircle generator having overlapping text at even the most extreme settings. With no note larger than a quartertone and 36 perfect fifths all around the scale, plus many more imperfect but still diatonic ones produced by the numerous comma steps, there is a wealth of harmonies both simple and complex to be found here, and someone could spend a lifetime exploring just this tuning system if they had instruments capable of playing it.
! 1-3-5-7-9-11-13-15_Evdomindasany.scl ! 1 3 5 7 9 11 13 15 4-combination Evdomindasany 58 ! 26.841 53.272 72.402 84.467 138.572 155.139 165.004 191.845 203.910 223.039 266.871 303.576 320.143 342.482 368.914 386.313 431.875 454.213 470.781 507.486 551.317 582.512 590.223 609.353 635.785 658.123 689.890 701.955 721.084 755.227 786.422 818.188 840.527 866.959 905.865 924.994 937.631 968.825 1005.531 1017.596 1044.437 1049.362 1088.268 1107.398 1133.830 1156.168 1172.736 1200