@@ Line 1: / Line 1: @@
-'''99edo''' is the [[EDO|equal division of the octave]] into 99 parts of 12.1212 [[cent|cents]] each.
+{{Infobox ET}}
+{{ED intro}} The step size of this system is close to [[144/143]], the grossma.
 == Theory ==
-edo is a very strong 7-limit (and 9 odd limit) temperament, but extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. It [[tempering_out|tempers out]] 393216/390625 ([[würschmidt comma]]) and 1600000/1594323 ([[amity comma]]) in the [[5-limit]]; 2401/2400 ([[2401/2400|breedsma]]), 3136/3125 ([[hemimean comma]]), and 4375/4374 ([[4375/4374|ragisma]]) in the [[7-limit]], supporting [[hemififths]], [[amity]], [[parakleismic]], [[hemiwürschmidt]] and [[ennealimmal]] temperaments, and is pretty well a perfect tuning for [[hendecatonic]] temperament. It has a sound defined by the slight sharpness (1.075, 1.565, 0.871 cents) of its 3, 5, and 7.
+edo is a very strong [[7-limit]] (and [[9-odd-limit]]) tuning, with a sound defined by the slight sharpness (1.1, 1.6, 0.9 cents) of its [[3/1|3]], [[5/1|5]], and [[7/1|7]]. As an equal temperament, it [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and 1600000/1594323 ([[amity comma]]) in the [[5-limit]]; 5120/5103 ([[5120/5103|argent comma]]), 2401/2400 ([[2401/2400|breedsma]]), 3136/3125 ([[hemimean comma]]), and 4375/4374 ([[4375/4374|ragisma]]) in the [[7-limit]], [[support]]ing [[hemififths]], [[amity]], [[parakleismic]], [[hemiwürschmidt]] and [[ennealimmal]] temperaments, and is pretty well a perfect tuning for [[hendecatonic (temperament)|hendecatonic]] temperament.
-Using the [[patent val]], 99edo is the [[optimal patent val]] for the rank four temperament tempering out [[121/120]]; zeus, the rank three temperament tempering out 121/120 and [[176/175]]; [[Würschmidt family #Hemiwur|hemiwür]], one of the rank two 11-limit extensions of hemiwürschmidt; and [[hitchcock]] (11-limit amity), the rank two temperament which also tempers out [[2200/2187]]. Using the {{val|99 157 230 278 343}} (99e) val, it tempers out [[896/891]], [[243/242]], [[441/440]] and [[540/539]], and is an excellent tuning for the 11-limit version of hemififths temperament. Hence 99 equal divisions, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.
+Extending it to the [[11-limit]] requires choosing which mapping one wants to use, as both are nearly equally far off the mark. Using the {{val| 99 157 230 278 '''343''' }} (99e) val, it tempers out [[243/242]], [[441/440]], [[540/539]] and [[896/891]], and is an excellent tuning for the 11-limit version of hemififths temperament. Using the [[patent val]], 99edo is the [[optimal patent val]] for the rank-4 temperament tempering out [[121/120]]; zeus, the rank-3 temperament tempering out 121/120 and [[176/175]]; [[hemiwür]], one of the rank-2 11-limit extensions of hemiwürschmidt; and [[hitchcock]] (an 11-limit amity extension), the rank-2 temperament which also tempers out [[2200/2187]]. The same can be said of the mapping for [[13/1|13]], with the 99ef val tempering out [[144/143]], [[196/195]], 352/351 and [[364/363]], and its patent val tempering out [[169/168]], [[351/350]] and [[352/351]]. Hence 99edo, in spite of the fact that it tunes 11 and 13 relatively badly, is an important 13-limit tuning in more than one way.
+Being a [[zeta peak edo]], 99edo is also a very strong no-11 no-13 system, where it is consistent to the [[29-odd-limit]] with a sharp tendency. This favors the sharp mapping of 11 and 13, and allows these relatively weak approximations to somewhat blend with the rest for a full [[29-limit]] (or [[31-limit]], using the sharp-tending 99efk val) temperament. In fact, the 99efk val is the first to achieve [[diamond monotone]] in the [[31-odd-limit]], though it fails in the [[33-odd-limit]] due to mapping [[33/32]] to 5 steps, while [[32/31]] is mapped to 4 steps.
+One step of 99edo is close to [[144/143]], the grossma. Unfortunately, neither 99ef nor the patent val map it consistently, though [[198edo]] does.
+=== Prime harmonics ===
+{{Harmonics in equal|99}}
+=== 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.
 == Intervals ==
-See [[Table of 99edo intervals]].
+{{Main| Table of 99edo intervals }}
+== Notation ==
+[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
+{{Sharpness-sharp10-qt1-szg}}
+=== Kite's ups and downs notation ===
+edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]]. Note that quip (quintuple-up) is the same as quudsharp (quadruple-down sharp) and that quid (quintuple-down) is the same as quupflat (quadruple-up flat):
+{{Ups and downs sharpness|99|true}}
+== Approximation to JI ==
+=== 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:
-== Just approximation ==
+{{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>
+}}
-{{Primes in edo|99|columns=11}}
+The 7-prime-limited 49-odd-limit is where non-distinctness first shows up: namely, ~49/48 = ~50/49 (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; 49/45;
+(*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; 144/125; 280/243;
+(*21*) 81/70; 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*) 60/49; 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*) 125/98; 245/192; 32/25;
+(*36*) 9/7;
+(*37*) 162/125; 35/27;
+(*38*) 125/96; 64/49; 98/75;
+(*39*) 450/343; 21/16; 320/243;
+(*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*) 243/160; 32/21; 343/225;
+(*61*) 75/49; 49/32; 192/125;
+(*62*) 54/35; 125/81;
+(*63*) 14/9;
+(*64*) 25/16; 384/245; 196/125;
+(*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; 49/30;
+(*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; 140/81
+(*79*) 243/140; 125/72; 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*) 90/49; 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 made equidistant by 99edo ===
+Runs of 7-prime-limited 45-odd-limit intervals separated by 1\99:
+# 36/35 ↔<sub>a</sub> 28/27 ↔<sub>b</sub> 25/24 ↔<sub>c</sub> 21/20
+# 16/15 ↔<sub>b</sub> 15/14 ↔<sub>c</sub> 27/25
+# 10/9 ↔<sub>c</sub> 28/25 ↔<sub>b</sub> 9/8
+# 32/27 ↔<sub>b</sub> 25/21 ↔<sub>c</sub> 6/5
+# 32/25 ↔<sub>b</sub> 9/7 ↔<sub>a</sub> 35/27
+# 25/18 ↔<sub>c</sub> 7/5 ↔<sub>b</sub> 45/32 ↔<sub>d</sub> 64/45 ↔<sub>b</sub> 10/7 ↔<sub>c</sub> 36/25
+The separating intervals (all equated):
+# ↔<sub>a</sub> = 245/243, the [[sensamagic]] comma
+# ↔<sub>b</sub> = 225/224, the [[marvel]] comma
+# ↔<sub>c</sub> = 126/125
+# ↔<sub>d</sub> = 2048/2025, the [[Diaschismic|diaschisma]]
+Runs of intervals separated by 2\99:
+# 28/27 ↔<sub>e</sub> 21/20 ↔<sub>f</sub> 16/15 ↔<sub>e</sub> 27/25 ↔<sub>g</sub> 35/32 ↔<sub>f</sub> 10/9 ↔<sub>e</sub> 9/8 ↔<sub>f</sub> 8/7
+# 7/6 ↔<sub>f</sub> 32/27 ↔<sub>e</sub> 6/5
+# 32/25 ↔<sub>g</sub> 35/27 ↔<sub>e</sub> 21/16 ↔<sub>f</sub> 4/3 ↔<sub>e</sub> 27/20 ↔<sub>f</sub> 48/35 ↔<sub>g</sub> 25/18  ↔<sub>e</sub> 45/32 ↔<sub>f</sub> 10/7
+The separating intervals (all equated):
+# ↔<sub>e</sub> = 81/80
+# ↔<sub>f</sub> = 64/63
+# ↔<sub>g</sub> = 875/864, the keema
+=== Interval mappings ===
+{{Q-odd-limit intervals|99}}
+{{Q-odd-limit intervals|99.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 99ef val mapping}}
+== Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br>8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{Monzo| 157 -99 }}
+| {{Mapping| 99 157 }}
+| −0.339
+| 0.339
+| 2.80
+|-
+| 2.3.5
+| 393216/390625, 1600000/1594323
+| {{Mapping| 99 157 230 }}
+| −0.451
+| 0.319
+| 2.63
+|-
+| 2.3.5.7
+| 2401/2400, 3136/3125, 4375/4374
+| {{Mapping| 99 157 230 278 }}
+| −0.416
+| 0.283
+| 2.33
+|- style="border-top: double;"
+| 2.3.5.7.11
+| 243/242, 441/440, 896/891, 3136/3125
+| {{Mapping| 99 157 230 278 343 }} (99e)
+| −0.694
+| 0.612
+| 5.05
+|- style="border-top: double;"
+| 2.3.5.7.11
+| 121/120, 176/175, 1375/1372, 2200/2187
+| {{Mapping| 99 157 230 278 342 }} (99)
+| +0.006
+| 0.881
+| 7.27
+|}
+* 99et is lower in relative error than any previous equal temperaments in the 7-limit. Not until [[171edo|171]] do we find a better equal temperament in terms of either absolute error or relative error.
-== Temperaments ==
+=== Rank-2 temperaments ===
-{| class="wikitable center-all right-3 left-5"
+{| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per octave
+|-
-! Generator<br>(reduced)
+! Periods<br>per 8ve
-! Cents<br>(reduced)
+! Generator*
-! Associated<br>ratio
+! Cents*
+! Associated<br>ratio*
 ! Temperament
+|-
+| 1
+| 2\99
+| 24.242
+| 686/675, 99/98
+| [[Sengagen]] (99e) / sengage (99ef)
 |-
 | 1
@@ Line 28: / Line 311: @@
 | [[Amicable]]
 |-
-|1
+| 1
 | 16\99
 | 193.939
 | 28/25
-| [[Hemiwürschmidt]] (99e) / Hemithir (99ef) / Hemiwur (99f)
+| [[Hemiwürschmidt]] (99e) / hemithir (99ef) / hemiwur (99f)
 |-
 | 1
@@ Line 53: / Line 336: @@
 |-
 | 1
-| 27\99
+| 26\99
 | 315.152
 | 6/5
-| [[Parakleismic]] / Parkleismic / Paradigmic (99e)
+| [[Parakleismic]] (99) / paralytic (99e) / parkleismic (99) / paradigmic (99e)
 |-
 | 1
@@ Line 62: / Line 345: @@
 | 339.394
 | 128/105
-| [[Amity]] (99ef) / Hitchcock
+| [[Amity]] (99ef) / stalagmite (99ef) / hitchcock (99)
 |-
 | 1
@@ Line 74: / Line 357: @@
 | 387.879
 | 5/4
-| [[Würschmidt]] / Whirrschmidt
+| [[Würschmidt]] / whirrschmidt
+|-
+| 1
+| 41\99
+| 496.970
+| 4/3
+| [[Undecental]]
 |-
 | 1
@@ Line 104: / Line 393: @@
 | 48.485
 | 36/35
-| [[Ennealimmal]] / ennealimnic (99ef) / ennealim (99e) / ennealiminal
+| [[Ennealimmal]] / enneabiotic (99ef) / ennealympic (99) / <br>ennealimnic (99ef) / ennealim (99e) / ennealiminal (99)
 |-
 | 11
@@ Line 110: / Line 399: @@
 | 496.970<br>(48.485)
 | 4/3<br>(36/35)
-| [[Hendecatonic]]
+| [[Hendecatonic (temperament)|Hendecatonic]]
 |}
+<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
-==Scales==
+== Octave stretch or compression ==
-*[[Tutone6]]
+edo's approximations of harmonics 3, 5, and 7 can all be improved if slightly [[stretched and compressed tuning|compressing the octave]] is acceptable, using tunings such as [[157edt]] or [[256ed6]]. 157edt is especially performant if the 13-limit of the 99ef val is intended, but the 7-limit part is overcompressed, for which the milder 256ed6 is a better choice.
-*[[Tutone7]]
-*[[Tutone13]]
-*[[Zeus7tri]]
-*[[Zeus8tri]]
+If the 13-limit patent val is intended, then little to no compression, or even stretch, might be serviceable, such as in [[zpi|567zpi]].
-Since 99edo has a step of 12.1212 cents, it also allows one to use its MOS scales as circulating temperaments.
+== Scales ==
-{| class="wikitable"
+{{Main| List of MOS scales in 99edo }}
-|+Circulating temperaments in 99edo
-!Tones
+* [[Tutone6]]
-!Pattern
+* [[Tutone7]]
-!L:s
+* [[Tutone13]]
-|-
+* [[Zeus7tri]]
-|5
+* [[Zeus8tri]]
-|[[4L 1s]]
-|20:19
+== Instruments ==
-|-
+=== Skip fretting ===
-|6
+'''Skip fretting system 99 6 11''' is a [[skip fretting]] system for 99edo. The frets correspond to 16.5edo ([[33ed4]]). All intervals are for 7-string [[guitar]].
-|[[3L 3s]]
-|17:16
+; Harmonics
-|-
-| 7
+/1: string 2 open
-|[[1L 6s]]
-|15:14
+/1: string 5 fret 11
-|-
-|8
+/2: string 4 fret 6
-|[[3L 5s]]
-|13:12
+/4 is not easily accessible, but the next-best approximation is at string 5 open.
-|-
-|9
+/4: string 6 fret 6
-|[[9edo]]
-|equal
+/8: string 5 fret 2
-|-
-|10
+/8: string 5 fret 6
-|[[9L 1s]]
-|10:9
+=== Keyboards ===
-|-
+[[Lumatone mapping for 99edo|Lumatone mappings for 99edo]] are now available.
-|11
-|[[11edo]]
+== Music ==
-|equal
+; [[Bryan Deister]]
-|-
+* [https://www.youtube.com/watch?v=bYK8V07yyq4 ''microtonal improvisation in 99edo''] (2023)
-|12
+* [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025)
-|[[3L 9s]]
-|9:8
+; [[Mundoworld]]
-|-
+* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – zeus[7] in 99edo tuning
-|13
-|[[8L 5s]]
+; [[Gene Ward Smith]]
-| rowspan="2" |8:7
+* ''Nonaginta et Novem'' (archived 2010) [https://soundcloud.com/genewardsmith/nonaginta-et-novem SoundCloud] | [http://www.archive.org/details/NonagintaEtNovem details] | [http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/Nonaginta%20et%20Novem.mp3 play]
-|-
+* [http://micro.soonlabel.com/gene_ward_smith/transformers/benny.mp3 ''Benny''] Smith-Palestrina in [[zeus7tri]]
-|14
-|[[1L 13s]]
-|-
-|15
-| [[9L 6s]]
-| rowspan="2" | 7:6
-|-
-|16
-|[[3L 13s]]
-|-
-|17
-|[[14L 3s]]
-| rowspan="3" |6:5
-|-
-|18
-|9L 9s
-|-
-|19
-|4L 15s
-|-
-|20
-| 19L 1s
-| rowspan="5" |5:4
-|-
-|21
-|15L 6s
-|-
-|22
-|11L 11s
-|-
-|23
-| 7L 16s
-|-
-|24
-|3L 21s
-|-
-|25
-|24L 1s
-| rowspan="8" |4:3
-|-
-|26
-|21L 5s
-|-
-|27
-|18L 9s
-|-
-|28
-|15L 13s
-|-
-| 29
-|[[12L 17s]]
-|-
-|30
-|9L 21s
-|-
-|31
-|[[6L 25s]]
-|-
-| 32
-|3L 29s
-|-
-|33
-|[[33edo]]
-|equal
-|-
-|34
-|31L 3s
-| rowspan="16" |3:2
-|-
-|35
-|29L 6s
-|-
-|36
-|27L 9s
-|-
-|37
-|25L 12s
-|-
-|38
-|23L 15s
-|-
-|39
-|21L 18s
-|-
-|40
-|19L 21s
-|-
-|41
-|17L 24s
-|-
-|42
-|15L 27s
-|-
-|43
-|13L 30s
-|-
-|44
-|11L 33s
-|-
-|45
-|9L 36s
-|-
-|46
-|7L 39s
-|-
-|47
-|5L 42s
-|-
-|48
-|3L 45s
-|-
-|49
-|1L 48s
-|-
-|50
-|49L 1s
-| rowspan="30" |2:1
-|-
-|51
-|48L 3s
-|-
-|52
-|47L 5s
-|-
-|53
-|46L 7s
-|-
-|54
-|45L 9s
-|-
-|55
-|44L 11s
-|-
-|56
-|43L 13s
-|-
-|57
-|42L 15s
-|-
-|58
-|41L 17s
-|-
-|59
-|40L 19s
-|-
-|60
-|39L 21s
-|-
-|61
-|38L 23s
-|-
-|62
-|37L 25s
-|-
-|63
-|36L 27s
-|-
-|64
-|35L 29s
-|-
-|65
-|34L 31s
-|-
-|66
-|33L 33s
-|-
-|67
-|32L 35s
-|-
-|68
-|31L 37s
-|-
-|69
-|30L 39s
-|-
-|70
-|29L 41s
-|-
-|71
-|28L 43s
-|-
-|72
-|27L 45s
-|-
-|73
-|26L 47s
-|-
-|74
-|25L 49s
-|-
-|75
-|24L 51s
-|-
-|76
-|23L 53s
-|-
-|77
-|22L 55s
-|-
-|78
-|21L 57s
-|-
-|79
-|20L 59s
-|}
-==Music==
-*[http://www.archive.org/details/NonagintaEtNovem Nonaginta et Novem] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/Nonaginta%20et%20Novem.mp3 play]'' by [[Gene Ward Smith]]
-*[http://micro.soonlabel.com/gene_ward_smith/transformers/benny.mp3 Benny] Smith-Palestrina in [[zeus7tri]]
-==See also==
+== See also ==
-*[[157edt]] - relative EDT
+* [[58edf]] – relative [[edf]]
-*[[58edf]] - relative EDF
+* [[157edt]] – relative [[edt]]
-*[[87edo]], [[94edo]], [[111edo]] - similarly sized edos all with consistency in higher harmonics.
+* [[87edo]], [[94edo]], [[111edo]] – similarly sized edos all with consistency in higher harmonics.
-*[[198edo]], the half-sized edo to reconcile the mappings of 11 and 13.
+* [[198edo]], the half-sized edo to reconcile the mappings of 11 and 13.
-*[[105edo]], a similarly sized edo that supports meantone, septimal meantone, undecimal meantone and grosstone
+* [[105edo]], a similarly sized edo that supports meantone, septimal meantone, undecimal meantone, and grosstone
-[[Category:Theory]]
+[[Category:Aberschismic]]
-[[Category:Equal divisions of the octave]]
-[[Category:99edo| ]] <!-- main article -->
-[[Category:Hemifamity]]
 [[Category:Hemififths]]
 [[Category:Hendecatonic]]
 [[Category:Hitchcock]]
+[[Category:Listen]]
 [[Category:Zeus]]
-[[Category:Listen]]

99edo: Difference between revisions