List of 29et rank two temperaments by badness

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Below are listed rank-two temperaments supported by the29edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments with badness below 0.1[edit]

Listed is the wedgie and the TE badness times 1000 for three temperaments with badness less than 0.1.

Rank Wedgie Name Badness Commas
1 <<1 -8 -15]] Helmholtz 4.259 32805/32768
2 <<3 5 1]] Porcupine 30.778 250/243
3 <<4 -3 -14]] Negri 86.856 16875/16384

7-limit temperaments with badness below 0.06[edit]

Listed is the wedgie and the TE badness times 1000 for 17 temperaments with badness less than 0.06.

Rank Wedgie Name Badness Commas
1 <<1 -8 -14 -15 -25 -10]] Garibaldi 21.644 225/224 3125/3087
2 <<4 -3 2 -14 -8 13]] Negri 26.483 49/48 225/224
3 <<5 -11 -12 -29 -33 3]] Tritonic 47.578 225/224 50421/50000
4 <<7 -56 -69 -105 -129 -3]] 48.081 32805/32768 52734375/52706752
5 <<3 5 16 1 17 23]] Porky 54.389 225/224 250/243
6 <<6 10 3 2 -12 -21]] Nautilus 57.420 49/48 250/243

11-limit temperaments with badness below 0.05[edit]

Listed is the wedgie and the TE badness times 1000 for 17 temperaments with badness less than 0.05.

Rank Wedgie Name Badness Commas
1 <<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]] Cassandra 23.556 100/99 225/224 245/242
2 <<5 -11 -12 -3 -29 -33 -22 3 31 33]] Tritonic 23.659 121/120 225/224 441/440
3 <<6 10 3 8 2 -12 -8 -21 -16 12]] Nautilus 26.023 49/48 55/54 100/99
4 <<3 5 16 4 1 17 -4 23 -8 -44]] Porky 27.268 55/54 100/99 225/224
5 <<6 -19 -26 -21 -44 -58 -54 -7 17 31]] Marvolo 28.965 225/224 441/440 4000/3993
6 <<0 29 29 29 46 46 46 -14 -33 -19]] Mystery 34.291 441/440 896/891 3388/3375
7 <<4 -3 2 15 -14 -8 10 13 45 35]] Negroni 35.296 49/48 55/54 225/224
8 <<14 -112 -138 -107 -210 -258 -218 -6 139 177]] 35.867 32805/32768 43923/43904 151263/151250
9 <<1 21 15 11 31 21 14 -24 -47 -21]] Leapday 38.6240 121/120 441/440 686/675
10 <<4 -3 2 -14 -14 -8 -36 13 -22 -46]] Negril 38.679 49/48 100/99 225/224
11 <<5 18 17 26 17 13 24 -11 -2 14]] 40.485 100/99 245/242 686/675
12 <<8 -6 4 1 -28 -16 -26 26 23 -11]] Wilsec 41.886 49/48 121/120 225/224
13 <<6 -48 -55 -50 -90 -104 -100 7 50 50]] 45.457 441/440 4000/3993 235298/234375
14 <<9 15 19 12 3 5 -12 2 -24 -32]] Ammonite 45.694 55/54 100/99 686/675
15 <<5 -40 -41 -32 -75 -79 -68 17 64 52]] 47.064 441/440 3388/3375 35937/35840
16 <<8 -93 -112 -86 -166 -200 -164 1 122 146]] 48.756 42592/42525 43923/43904 151263/151250
17 <<3 5 -13 4 1 -29 -4 -44 -8 56]] Coendou 49.669 55/54 100/99 525/512

13-limit temperaments with badness below 0.04[edit]

Listed is the wedgie and the TE badness times 1000 for 43 temperaments with badness less than 0.04.

Rank Wedgie Name Badness Commas
1 <<0 29 29 29 29 46 46 46 46 -14 -33 -40 -19 -26 -7]] Mystery 18.591 196/195 352/351 364/363 676/675
2 <<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]] Cassandra 20.749 100/99 105/104 196/195 245/242
3 <<6 -19 -26 -21 -10 -44 -58 -54 -38 -7 17 47 31 68 43]] Marvolo 21.470 169/168 225/224 364/363 441/440
4 <<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]] 21.559 49/48 55/54 65/64 91/90
5 <<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]] Nautilus 22.285 49/48 55/54 91/90 100/99
6 <<5 -11 -12 -3 -18 -29 -33 -22 -47 3 31 -1 33 -6 -51]] Tritonic 22.993 105/104 121/120 196/195 275/273
7 <<4 -3 2 -14 3 -14 -8 -36 -10 13 -22 18 -46 1 62]] Negril 24.383 49/48 65/64 91/90 875/858
8 <<1 21 15 11 8 31 21 14 9 -24 -47 -59 -21 -33 -13]] Leapday 24.732 91/90 121/120 169/168 441/440
9 <<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]] Wilsec 25.192 49/48 65/64 91/90 121/120
10 <<6 -48 -55 -50 -39 -90 -104 -100 -84 7 50 87 50 94 50]] Sextilififths 25.276 364/363 441/440 676/675 10985/10976
11 <<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]] 26.543 55/54 65/64 91/90 100/99
12 <<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]] 26.929 91/90 100/99 169/168 245/242
13 <<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]] Ammonite 27.168 55/54 91/90 100/99 169/168
14 <<8 -93 -112 -86 -81 -166 -200 -164 -158 1 122 156 146 187 38]] 27.440 676/675 1001/1000 10648/10647 10985/10976
15 <<2 -16 -28 -7 -13 -30 -50 -18 -28 -20 39 29 77 67 -19]] 27.464 121/120 169/168 225/224 275/273
16 <<2 13 30 22 16 16 42 28 18 33 6 -11 -42 -66 -26]] 28.521 100/99 169/168 225/224 275/273
17 <<2 -45 -57 -36 -42 -76 -96 -64 -74 -6 72 69 96 93 -12]] 28.632 352/351 676/675 1001/1000 1331/1323
18 <<3 5 16 4 24 1 17 -4 27 23 -8 37 -44 8 68]] 29.097 55/54 100/99 105/104 196/195
19 <<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]] 30.043 65/64 100/99 105/104 245/242
20 <<3 5 -13 4 -5 1 -29 -4 -19 -44 -8 -30 56 34 -32]] 30.233 55/54 65/64 100/99 105/104
21 <<5 -11 -12 -3 11 -29 -33 -22 -1 3 31 66 33 75 49]] 32.324 65/64 91/90 121/120 441/440
22 <<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]] 32.611 65/64 105/104 121/120 275/273
23 <<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]] 33.196 49/48 91/90 100/99 847/845
24 <<1 -8 -14 -18 8 -15 -25 -32 9 -10 -14 48 -2 74 94]] 33.610 65/64 91/90 100/99 245/242
25 <<6 10 3 8 -10 2 -12 -8 -38 -21 -16 -60 12 -39 -64]] 33.723 49/48 55/54 65/64 100/99
26 <<9 -72 -97 -75 -73 -135 -179 -150 -149 -23 75 97 125 154 25]] 33.754 1375/1372 1575/1573 2080/2079 2200/2197
27 <<3 -24 -42 -25 -34 -45 -75 -50 -65 -30 25 10 75 60 -25]] 33.849 225/224 275/273 847/845 1331/1323
28 <<2 -16 1 -7 -13 -30 -4 -18 -28 47 39 29 -23 -40 -19]] 34.066 49/48 91/90 121/120 352/351
29 <<11 -30 -38 -24 -28 -73 -91 -76 -85 -4 48 46 64 62 -8]] 34.213 225/224 441/440 847/845 1001/1000
30 <<9 -14 -10 -17 -15 -43 -41 -58 -57 16 9 17 -13 -5 11]] 34.616 105/104 196/195 245/242 1001/1000
31 <<9 -101 -126 -104 -102 -181 -225 -196 -195 -9 108 137 144 180 32]] 34.999 1575/1573 2080/2079 2200/2197 31250/31213
32 <<4 26 31 15 32 32 38 10 36 -1 -55 -22 -65 -25 55]] 35.601 121/120 196/195 275/273 572/567
33 <<8 -64 -83 -57 -52 -120 -154 -118 -112 -13 89 116 127 161 31]] 35.729 676/675 1001/1000 1375/1372 10648/10647
34 <<8 23 33 30 35 18 30 20 26 12 -10 -4 -30 -24 10]] 36.319 100/99 196/195 275/273 1331/1323
35 <<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]] 36.654 49/48 55/54 91/90 847/845
36 <<2 13 1 -7 16 16 -4 -18 18 -34 -61 -11 -23 41 81]] 37.078 49/48 55/54 91/90 896/891
37 <<7 -27 -40 -39 -31 -59 -83 -86 -75 -17 3 28 29 61 37]] 37.123 225/224 364/363 441/440 1875/1859
38 <<3 34 45 33 24 47 63 42 27 9 -41 -70 -63 -99 -39]] 37.629 169/168 352/351 364/363 1001/1000
39 <<11 -59 -67 -53 -57 -119 -137 -122 -131 10 81 86 83 88 -1]] 37.907 441/440 847/845 1001/1000 13365/13312
40 <<3 -53 -71 -54 -63 -91 -121 -96 -111 -16 58 50 94 86 -18]] 38.480 352/351 847/845 1375/1372 1575/1573
41 <<2 42 59 51 45 62 88 74 64 19 -27 -51 -61 -92 -33]] 38.801 352/351 364/363 676/675 1375/1372
42 <<4 -32 -27 -14 -26 -60 -54 -36 -56 27 78 58 54 27 -38]] 39.125 121/120 196/195 352/351 676/675
43 <<1 -8 -14 11 8 -15 -25 14 9 -10 53 48 79 74 -13]] 39.411 55/54 65/64 91/90 847/832
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