List of edo-distinct 29et rank two temperaments

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The temperaments listed are 29edo-distinct, meaning that they are all different even if tuned in 29edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator Wedgie Name Complexity Commas
29 12 <<1 -8 -15]] Helmholtz 3.103 32805/32768
29 6 <<2 13 16]] Immunity 4.157 1638400/1594323
29 4 <<3 5 1]] Porcupine 1.663 250/243
29 3 <<4 -3 -14]] Negri 2.739 16875/16384
29 14 <<5 18 17]] 5.519 409600000/387420489
29 2 <<6 -19 -44]] 8.646 18160335421875/17592186044416
29 10 <<7 2 -13]] 3.303 78125/73728
29 13 <<8 23 18]] 7.012 102400000000/94143178827
29 11 <<9 -14 -43]] 8.269 9341736328125/8796093022208
29 7 <<10 7 -12]] 4.455 9765625/8957952
29 9 <<11 -1 -27]] 5.836 146484375/134217728
29 1 <<17 9 -25]] 7.664 762939453125/660451885056
29 8 <<13 12 -11]] 5.857 1220703125/1088391168
29 5 <<15 -4 -41]] 8.498 2471923828125/2199023255552

7-limit temperaments

Period generator Wedgie Name Complexity Commas
29 12 <<1 -8 -14 -15 -25 -10]] Garibaldi 3.823 225/224 3125/3087
29 6 <<2 13 1 16 -4 -34]] Immunity 3.651 49/48 2240/2187
29 4 <<3 5 16 1 17 23]] Porky 3.362 225/224 250/243
29 3 <<4 -3 2 -14 -8 13]] Negri 2.245 49/48 225/224
29 14 <<5 18 17 17 13 -11]] 4.821 686/675 2240/2187
29 2 <<6 10 3 2 -12 -21]] Nautilus 2.943 49/48 250/243
29 10 <<7 2 18 -13 9 36]] 4.251 225/224 6125/5832
29 13 <<8 23 4 18 -16 -55]] 6.241 49/48 560000/531441
29 11 <<9 15 19 3 5 2]] Ammonite 4.506 250/243 686/675
29 7 <<10 7 5 -12 -20 -8]] 3.751 49/48 3125/3024
29 9 <<11 -1 20 -27 1 49]] 5.909 225/224 84035/78732
29 1 <<17 9 23 -25 -11 28]] 6.682 686/675 21875/20736
29 8 <<13 12 21 -11 -3 15]] 5.238 686/675 3125/3024
29 5 <<14 4 7 -26 -28 5]] 5.436 49/48 78125/73728

11-limit temperaments

Period generator Wedgie Name Complexity Commas
29 12 <<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]] Cassandra 3.897 100/99 225/224 245/242
29 6 <<2 13 1 -7 16 -4 -18 -34 -61 -23]] Immunity 3.977 49/48 55/54 896/891
29 4 <<3 5 16 4 1 17 -4 23 -8 -44]] Porky 3.020 55/54 100/99 225/224
29 3 <<4 -3 2 15 -14 -8 10 13 45 35]] Negroni 3.110 49/48 55/54 225/224
29 14 <<5 -11 -12 -3 -29 -33 -22 3 31 33]] Tritonic 4.596 121/120 225/224 441/440
29 2 <<6 10 3 8 2 -12 -8 -21 -16 12]] Nautilus 2.548 49/48 55/54 245/242
29 10 <<7 2 18 19 -13 9 6 36 37 -9]] 4.023 55/54 225/224 245/242
29 13 <<8 -6 4 1 -28 -16 -26 26 23 -11]] Wilsec 3.911 49/48 121/120 225/224
29 11 <<9 15 19 12 3 5 -12 2 -24 -32]] Ammonite 3.980 55/54 100/99 686/675
29 7 <<10 7 5 23 -12 -20 2 -8 29 47]] 4.064 49/48 55/54 625/616
29 9 <<11 -1 20 5 -27 1 -30 49 15 -55]] 5.264 121/120 225/224 1225/1188
29 1 <<17 9 23 13 -25 -11 -38 28 -1 -43]] 5.913 121/120 625/616 686/675
29 8 <<13 12 21 27 -11 -3 -2 15 21 3]] 4.823 55/54 245/242 625/616
29 5 <<14 4 7 9 -26 -28 -34 5 7 1]] 4.725 49/48 121/120 625/616

13-limit temperaments

Period generator Wedgie Name Complexity Commas
29 12 <<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]] Cassandra 3.911 100/99 105/104 196/195 245/242
29 6 <<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]] Impunity 3.934 49/48 91/90 100/99 352/351
29 4 <<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]] Porky 3.380 55/54 65/64 91/90 100/99
29 3 <<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]] Negroni 2.793 49/48 55/54 65/64 91/90
29 14 <<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]] 4.312 91/90 100/99 169/168 245/242
29 2 <<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]] Nautilus 2.806 49/48 55/54 91/90 100/99
29 10 <<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]] Roman 4.163 65/64 100/99 105/104 245/242
29 13 <<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]] Wilsec 3.527 49/48 65/64 91/90 121/120
29 11 <<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]] Ammonite 3.582 55/54 91/90 100/99 169/168
29 7 <<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]] 3.888 49/48 55/54 91/90 847/845
29 9 <<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]] 4.743 65/64 121/120 169/168 275/273
29 1 <<12 20 6 16 9 4 -24 -16 -30 -42 -32 -53 24 3 -28]] 4.724 49/48 55/54 245/242 343/338
29 8 <<13 12 21 27 17 -11 -3 -2 -21 15 21 -5 3 -30 -41]] 4.362 55/54 91/90 169/168 245/242
29 5 <<14 4 7 9 25 -26 -28 -34 -12 5 7 43 1 44 53]] 4.713 49/48 91/90 121/120 625/616