------------------------------------------------------ Lattice for Pegasus-16 (Pegasus-15 plus 16/9) With 531/512 appearing twice ------------------------------------------------------ A subset of the 20-note genus musicum of 3^9 59^1 ------------------------------------------------------ Horizontal = 3:2 Diagonal = ~7:6 (4779:4096) Vertical = 59:48 or ~16/13 Eb* Bb* F* C* G* [D*] (~128/117) (~64/39) (~16/13) (~24/13) (~112/81) (~28/27) 59/54 ------- 59/36 ------- 59/48 ------- 59/32 ------- 177/128 ------ 531/512 | D* | A* | E* | B* | F#* | | (~28/27) | (~14/9) | (~7/6) | (~7/4) | (~21/16) | | 531/512----|-1593/1024---|-4779/4096---|-14337/8192---|-43011/32768 | | / | / | / | / | / | | / | / | / | / | / | | / | / | / | / | / | | / | / | / | / | / | 16/9 --------- 4/3 --------- 1/1 --------- 3/2 ---------- 9/8 --------- 27/16 C G D A E B Ratios of 59 differ from corresponding ratios of 7 by 14337:14336 (0.121 cents) Ratios of 59 differ from corresponding ratios of 13 by 768:767 (2.256 cents) Margo Schulter 13 January 2011