99edo: Difference between revisions

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 === Subsets and supersets ===
 Since 99 factors into primes as {{nowrap| 3<sup>2</sup> × 11 }}, 99edo has subset edos {{EDOs| 3, 9, 11, and 33 }}. Splitting 99edo's step in half yields [[198edo]], correcting prime 11, slightly improving prime 13, and aligning both 11 and 13 with the sharp tunings of the lower odd primes. Because of this, 198edo can be seen as a complex yet notable true full 13-limit tuning.
+=== 7-prime-limited odd-limit analysis ===
+Unlike all previous edos, 99edo is ''distinctly'' [[consistent]] and monotone (i.e. when tempered using the patent val, the relative sizes of any two intervals are never conflated ''or'' reversed) up to the 7-prime-limited 45-odd-limit:
+{{Databox
+|collapse=true
+|title=The 7-prime-limited 45-odd-limit, by 99edo mapping (SW3 format)
+|text=
+<pre>
+(*
+-PL 45-OL odds:
+3 5 7 9 15 21 25 27 35 45
+Mapping   Ratio     Error  *)
+(* 4\99*) 36/35 (* -0.286c *)
+(* 5\99*) 28/27 (* -2.355c *)
+(* 6\99*) 25/24 (* +2.055c *)
+(* 7\99*) 21/20 (* +0.381c *)
+(* 9\99*) 16/15 (* -2.640c *)
+(*10\99*) 15/14 (* +1.769c *)
+(*11\99*) 27/25 (* +0.096c *)
+(*13\99*) 35/32 (* +2.436c *)
+(*15\99*) 10/9  (* -0.586c *)
+(*16\99*) 28/25 (* -2.259c *)
+(*17\99*) 9/8   (* +2.151c *)
+(*19\99*) 8/7   (* -0.871c *)
+(*22\99*) 7/6   (* -0.204c *)
+(*24\99*) 32/27 (* -3.226c *)
+(*25\99*) 25/21 (* +1.184c *)
+(*26\99*) 6/5   (* -0.490c *)
+(*31\99*) 56/45 (* -2.845c *)
+(*32\99*) 5/4   (* +1.565c *)
+(*35\99*) 32/25 (* -3.130c *)
+(*36\99*) 9/7   (* +1.280c *)
+(*37\99*) 35/27 (* -0.790c *)
+(*39\99*) 21/16 (* +1.946c *)
+(*41\99*) 4/3   (* -1.075c *)
+(*43\99*) 27/20 (* +1.661c *)
+(*45\99*) 48/35 (* -1.361c *)
+(*47\99*) 25/18 (* +0.980c *)
+(*48\99*) 7/5   (* -0.694c *)
+(*49\99*) 45/32 (* +3.716c *)
+(*50\99*) 64/45
+(*51\99*) 10/7
+(*52\99*) 36/25
+(*54\99*) 35/24
+(*56\99*) 40/27
+(*58\99*) 3/2
+(*60\99*) 32/21
+(*62\99*) 54/35
+(*63\99*) 14/9
+(*64\99*) 25/16
+(*67\99*) 8/5
+(*68\99*) 45/28
+(*73\99*) 5/3
+(*74\99*) 42/25
+(*75\99*) 27/16
+(*77\99*) 12/7
+(*80\99*) 7/4
+(*82\99*) 16/9
+(*83\99*) 25/14
+(*84\99*) 9/5
+(*86\99*) 64/35
+(*88\99*) 50/27
+(*89\99*) 28/15
+(*90\99*) 15/8
+(*92\99*) 40/21
+(*93\99*) 48/25
+(*94\99*) 27/14
+(*95\99*) 35/18
+(*99\99*) 2/1
+</pre>
+}}
+The 7-prime-limited 49-odd-limit is where non-distinctness first shows up: namely, T49/48 = T50/49 (this is characteristic of all Ennealimmal tunings). However, 99edo remains monotone and consistent up to the 7-prime-limited 567-odd-limit (the next 7-limit odd 625 is inconsistent):
+{{Databox
+|collapse=true
+|title=The 7-prime-limited 567-odd-limit, by 99edo mapping (SW3 format)
+|text=
+<pre>
+(* 1*) 225/224; 126/125; 245/243;
+(* 2*) 81/80; 64/63;
+(* 3*) 50/49; 49/48; 128/125;
+(* 4*) 525/512; 36/35; 250/243;
+(* 5*) 405/392; 28/27;
+(* 6*) 25/24; 256/245; 392/375;
+(* 7*) 360/343; 21/20; 256/243;
+(* 8*) 135/128; 200/189; 343/324;
+(* 9*) 16/15;
+(*10*) 15/14; 343/320;
+(*11*) 27/25; 175/162;
+(*12*) 243/224; 160/147;
+(*13*) 375/343; 35/32; 192/175;
+(*14*) 54/49; 441/400; 448/405;
+(*15*) 567/512; 10/9;
+(*16*) 125/112; 384/343; 28/25;
+(*17*) 9/8; 640/567;
+(*18*) 500/441; 567/500; 245/216; 256/225;
+(*19*) 8/7; 343/300;
+(*20*) 225/196; 147/128; 280/243;
+(*21*) 125/108; 512/441;
+(*22*) 400/343; 7/6;
+(*23*) 75/64; 288/245; 147/125;
+(*24*) 405/343; 189/160; 32/27;
+(*25*) 25/21; 343/288; 448/375;
+(*26*) 6/5;
+(*27*) 135/112; 98/81;
+(*28*) 243/200; 175/144; 128/105;
+(*29*) 49/40;
+(*30*) 315/256; 216/175; 100/81;
+(*31*) 243/196; 56/45;
+(*32*) 5/4;
+(*33*) 432/343; 63/50; 512/405;
+(*34*) 81/64; 80/63; 343/270;
+(*35*) 245/192; 32/25;
+(*36*) 9/7;
+(*37*) 162/125; 35/27;
+(*38*) 125/96; 64/49; 98/75;
+(*39*) 450/343; 21/16;
+(*40*) 324/245; 250/189;
+(*41*) 4/3;
+(*42*) 75/56; 343/256; 168/125;
+(*43*) 27/20; 256/189;
+(*44*) 200/147; 49/36; 512/375;
+(*45*) 175/128; 48/35; 343/250;
+(*46*) 135/98; 441/320; 112/81;
+(*47*) 243/175; 25/18;
+(*48*) 480/343; 7/5;
+(*49*) 45/32; 800/567; 343/243;
+(*50*) 486/343; 567/400; 64/45;
+(*51*) 10/7; 343/240;
+(*52*) 36/25; 350/243;
+(*53*) 81/56; 640/441; 196/135;
+(*54*) 500/343; 35/24; 256/175;
+(*55*) 375/256; 72/49; 147/100;
+(*56*) 189/128; 40/27;
+(*57*) 125/84; 512/343; 112/75;
+(*58*) 3/2;
+(*59*) 189/125; 245/162;
+(*60*) 32/21; 343/225;
+(*61*) 75/49; 49/32; 192/125;
+(*62*) 54/35; 125/81;
+(*63*) 14/9;
+(*64*) 25/16; 384/245;
+(*65*) 540/343; 63/40; 128/81;
+(*66*) 405/256; 100/63; 343/216;
+(*67*) 8/5;
+(*68*) 45/28; 392/243;
+(*69*) 81/50; 175/108; 512/315;
+(*70*) 80/49;
+(*71*) 105/64; 288/175; 400/243;
+(*72*) 81/49; 224/135;
+(*73*) 5/3;
+(*74*) 375/224; 576/343; 42/25;
+(*75*) 27/16; 320/189; 686/405;
+(*76*) 250/147; 245/144; 128/75;
+(*77*) 12/7; 343/200;
+(*78*) 441/256; 216/125;
+(*79*) 243/140; 256/147; 392/225;
+(*80*) 600/343; 7/4;
+(*81*) 225/128; 432/245; 1000/567; 441/250;
+(*82*) 567/320; 16/9;
+(*83*) 25/14; 343/192; 224/125;
+(*84*) 9/5; 1024/567;
+(*85*) 405/224; 800/441; 49/27;
+(*86*) 175/96; 64/35; 686/375;
+(*87*) 147/80; 448/243;
+(*88*) 324/175; 50/27;
+(*89*) 640/343; 28/15;
+(*90*) 15/8;
+(*91*) 648/343; 189/100; 256/135;
+(*92*) 243/128; 40/21; 343/180;
+(*93*) 375/196; 245/128; 48/25;
+(*94*) 27/14; 784/405;
+(*95*) 243/125; 35/18; 1024/525;
+(*96*) 125/64; 96/49; 49/25;
+(*97*) 63/32; 160/81;
+(*98*) 486/245; 125/63; 448/225;
+(*99*) 2/1;
+</pre>
+}}
 == Intervals ==