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The temperament tree

Using the normal comma list it is possible to define a tree of temperaments of a given rank. Below is given the top level of a tree for rank two temperaments in the form of a 5-limit monzo, followed by a link to a 7-limit node of the tree. This in turn may be followed, via the hyperlinks, to further nodes in higher prime limits. Temperaments are denoted via names, wedgies, and the normal comma list. The wedgies, for those with the proper software, can be used to do all of the basic regular temperament operations, and their presence allows them to be searched for using the "Search Wiki" function. By putting together the commas in the normal list, Graham Breed's temperament finder gives an alternative to wedgies for finding the properties of the temperament. The number at the end of the row is a logflat badness measure (1000 times wedgie badness.) The branches near the top tend to favor the 5-limit part of the temperament in terms of complexity, while those near the bottom tend to favor higher limits after the links are followed to those limits.

The 5-limit top branches

|-15 8 1> helmholtz 4.25910
|-4 4 -1> meantone 7.38134
|-3 -1 2> dicot 13.02798
|-6 -5 6> hanson 13.23353
|4 -1 -1> father 14.88434
|1 -27 18> ennealimmic 17.19058
|11 -4 -2> diaschismic 19.91485
|38 -2 -15> luna 20.57600
|9 -13 5> amity 21.95959
|7 0 -3> augmented 22.31538
|-16 35 -17> minortone 29.76534
|1 -5 3> porcupine 30.77769
|23 6 -14> vishnuzmic 31.18117
|0 3 -2> bug 32.80131
|2 9 -7> sensipent 35.22030
|-10 -1 5> magic 39.16293
|-7 3 1> mavila 39.55645
|17 1 -8> würschmidt 40.60312
|-21 3 7> orson 40.80736
|24 -21 4> vulture 41.43092
|8 14 -13> parakleismic 43.27862
|3 4 -4> dimipent 47.23052
|-14 -19 19> enneadecal 47.84488
|5 -9 4> tetracot 48.51756
|8 -5 0> limmic 63.76017
|12 -6 -1> uncle 72.65308
|-52 -17 34> chlorine 77.072
|-14 3 4> negri 86.85590
|-29 -11 20> gammic 87.75217
|-13 17 -6> graviton 93.18426
|-19 12 0> compton 94.49449
|26 -12 -3> misty 106.54043
|13 5 -9> valensixthtone 122.76461
|5 -6 2> okai 122.84790
|12 -9 1> superpyth 135.14075
|47 -15 -10> deco 139.19066
|-2 13 -8> unicorn 150.48658
|-11 7 0> apotomic 154.65113
|-4 7 -3> laconic 161.79907
|-44 -3 21> unit 162.46707
|-25 7 6> ampersand 165.75484
|20 -17 3> roda 168.26415
|-18 7 3> stump 200.60049
|-9 -6 8> doublewide 226.75870
|-5 -10 9> shibboleth 227.55270
|28 -3 -10> amavil 232.48148
|9 9 -10> mynic 249.96513
|25 -48 22> abigail 254.51011
|-13 -46 37> supermajor 263.66615
|10 -40 23> gamera 272.56201
|-5 -32 24> octoid 285.05756
|-59 5 22> tertiaseptal 297.54417
|25 15 -21> nessafof 332.79289
|-17 2 6> lemba 334.71996
|19 -9 -2> beatles 358.54157
|35 -25 2> hemififths 372.84807
|-29 11 5> tritonic 378.52735
|-31 2 12> wizard 386.36650
|5 13 -11> nusecond 466.49271
|31 -21 1> leapday 523.18249
|30 6 -17> semisept 630.57587
|-35 6 11> septimin 670.94722
|-20 39 -18> mirkat 751.58057
|-46 10 13> slender 760.56781
|46 -29 0> mystery 1020.55630
|93 -3 -38> quasiorwell 1303.61642
|72 0 -31> 31-5 node 1402.24568
|22 14 -19> casablanca 1423.73592
|-49 31 0> 31-3 node 4309.84584