Tree of rank two temperaments
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=The temperament tree= Using the [[Normal lists|normal comma list]] it is possible to define a [[http://en.wikipedia.org/wiki/Tree_structure|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 [[http://x31eq.com/temper/|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 node|helmholtz]] 4.25910 |-4 4 -1> [[Meantone node|meantone]] 7.38134 |-3 -1 2> [[Dicot node|dicot]] 13.02798 |-6 -5 6> [[Hanson node|hanson]] 13.23353 |4 -1 -1> [[Father node|father]] 14.88434 |1 -27 18> [[Ennealimmic node|ennealimmic]] 17.19058 |11 -4 -2> [[Diaschismic node|diaschismic]] 19.91485 |38 -2 -15> [[Luna node|luna]] 20.57600 |9 -13 5> [[Amity node|amity]] 21.95959 |7 0 -3> [[Augmented node|augmented]] 22.31538 |-16 35 -17> [[Minortone node|minortone]] 29.76534 |1 -5 3> [[Porcupine node|porcupine]] 30.77769 |23 6 -14> [[Vishnuzmic node|vishnuzmic]] 31.18117 |0 3 -2> [[Bug node|bug]] 32.80131 |2 9 -7> [[Sensipent node|sensipent]] 35.22030 |-10 -1 5> [[Magic node|magic]] 39.16293 |-7 3 1> [[Mavila node|mavila]] 39.55645 |17 1 -8> [[Würschmidt node|würschmidt]] 40.60312 |-21 3 7> [[Orson node|orson]] 40.80736 |24 -21 4> [[Vulture node|vulture]] 41.43092 |8 14 -13> [[Parakleismic node|parakleismic]] 43.27862 |3 4 -4> [[Dimipent node|dimipent]] 47.23052 |-14 -19 19> [[Enneadecal node|enneadecal]] 47.84488 |5 -9 4> [[Tetracot node|tetracot]] 48.51756 |8 -5 0> [[Limmic node|limmic]] 63.76017 |12 -6 -1> [[Golic node|golic]] 72.65308 |-14 3 4> [[Negri node|negri]] 86.85590 |-29 -11 20> [[Gammic node|gammic]] 87.75217 |-13 17 -6> [[Graviton node|graviton]] 93.18426 |-19 12 0> [[Compton node|compton]] 94.49449 |26 -12 -3> [[Misty node|misty]] 106.54043 |13 5 -9> [[Valensixthtone node|valensixthtone]] 122.76461 |5 -6 2> [[Okai node|okai]] 122.84790 |12 -9 1> [[Superpyth node|superpyth]] 135.14075 |47 -15 -10> [[Deco node|deco]] 139.19066 |-2 13 -8> [[Unicorn node|unicorn]] 150.48658 |-4 7 -3> [[Laconic node|laconic]] 161.79907 |-44 -3 21> [[Unit node|unit]] 162.46707 |-25 7 6> [[Ampersand node|ampersand]] 165.75484 |20 -17 3> [[Roda node|roda]] 168.26415 |-9 -6 8> [[Doublewide node|doublewide]] 226.75870 |-5 -10 9> [[Shibboleth node|shibboleth]] 227.55270 |9 9 -10> [[Mynic node|mynic]] 249.96513 |25 -48 22> [[Abigail node|abigail]] 254.51011 |-13 -46 37> [[Supermajor node|supermajor]] 263.66615 |10 -40 23> [[Gamera node|gamera]] 272.56201 |-5 -32 24> [[Octoid node|octoid]] 285.05756 |-59 5 22> [[Tertiaseptal node|tertiaseptal]] 297.54417 |25 15 -21> [[Nessafof node|nessafof]] 332.79289 |-17 2 6> [[Lemba node|lemba]] 334.71996 |19 -9 -2> [[Beatles node|beatles]] 358.54157 |35 -25 2> [[Hemififths node|hemififths]] 372.84807 |-29 11 5> [[Tritonic node|tritonic]] 378.52735 |-31 2 12> [[Wizard node|wizard]] 386.36650 |5 13 -11> [[Nusecond node|nusecond]] 466.49271 |30 6 -17> [[Semisept node|semisept]] 630.57587 |-35 6 11> [[Septimin node|septimin]] 670.94722 |-20 39 -18> [[Mirkat node|mirkat]] 751.58057 |-46 10 13> [[Slender node|slender]] 760.56781 |93 -3 -38> [[Quasiorwell node|quasiorwell]] 1303.61642
Original HTML content:
<html><head><title>Tree of rank two temperaments</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="The temperament tree"></a><!-- ws:end:WikiTextHeadingRule:0 -->The temperament tree</h1> Using the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> it is possible to define a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tree_structure" rel="nofollow">tree</a> 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 <a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow">temperament finder</a> 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.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="The 5-limit top branches"></a><!-- ws:end:WikiTextHeadingRule:2 -->The 5-limit top branches</h1> |-15 8 1> <a class="wiki_link" href="/Helmholtz%20node">helmholtz</a> 4.25910<br /> |-4 4 -1> <a class="wiki_link" href="/Meantone%20node">meantone</a> 7.38134<br /> |-3 -1 2> <a class="wiki_link" href="/Dicot%20node">dicot</a> 13.02798<br /> |-6 -5 6> <a class="wiki_link" href="/Hanson%20node">hanson</a> 13.23353<br /> |4 -1 -1> <a class="wiki_link" href="/Father%20node">father</a> 14.88434<br /> |1 -27 18> <a class="wiki_link" href="/Ennealimmic%20node">ennealimmic</a> 17.19058<br /> |11 -4 -2> <a class="wiki_link" href="/Diaschismic%20node">diaschismic</a> 19.91485<br /> |38 -2 -15> <a class="wiki_link" href="/Luna%20node">luna</a> 20.57600<br /> |9 -13 5> <a class="wiki_link" href="/Amity%20node">amity</a> 21.95959<br /> |7 0 -3> <a class="wiki_link" href="/Augmented%20node">augmented</a> 22.31538<br /> |-16 35 -17> <a class="wiki_link" href="/Minortone%20node">minortone</a> 29.76534<br /> |1 -5 3> <a class="wiki_link" href="/Porcupine%20node">porcupine</a> 30.77769<br /> |23 6 -14> <a class="wiki_link" href="/Vishnuzmic%20node">vishnuzmic</a> 31.18117<br /> |0 3 -2> <a class="wiki_link" href="/Bug%20node">bug</a> 32.80131<br /> |2 9 -7> <a class="wiki_link" href="/Sensipent%20node">sensipent</a> 35.22030<br /> |-10 -1 5> <a class="wiki_link" href="/Magic%20node">magic</a> 39.16293<br /> |-7 3 1> <a class="wiki_link" href="/Mavila%20node">mavila</a> 39.55645<br /> |17 1 -8> <a class="wiki_link" href="/W%C3%BCrschmidt%20node">würschmidt</a> 40.60312<br /> |-21 3 7> <a class="wiki_link" href="/Orson%20node">orson</a> 40.80736<br /> |24 -21 4> <a class="wiki_link" href="/Vulture%20node">vulture</a> 41.43092<br /> |8 14 -13> <a class="wiki_link" href="/Parakleismic%20node">parakleismic</a> 43.27862<br /> |3 4 -4> <a class="wiki_link" href="/Dimipent%20node">dimipent</a> 47.23052<br /> |-14 -19 19> <a class="wiki_link" href="/Enneadecal%20node">enneadecal</a> 47.84488<br /> |5 -9 4> <a class="wiki_link" href="/Tetracot%20node">tetracot</a> 48.51756<br /> |8 -5 0> <a class="wiki_link" href="/Limmic%20node">limmic</a> 63.76017<br /> |12 -6 -1> <a class="wiki_link" href="/Golic%20node">golic</a> 72.65308<br /> |-14 3 4> <a class="wiki_link" href="/Negri%20node">negri</a> 86.85590<br /> |-29 -11 20> <a class="wiki_link" href="/Gammic%20node">gammic</a> 87.75217<br /> |-13 17 -6> <a class="wiki_link" href="/Graviton%20node">graviton</a> 93.18426<br /> |-19 12 0> <a class="wiki_link" href="/Compton%20node">compton</a> 94.49449<br /> |26 -12 -3> <a class="wiki_link" href="/Misty%20node">misty</a> 106.54043<br /> |13 5 -9> <a class="wiki_link" href="/Valensixthtone%20node">valensixthtone</a> 122.76461<br /> |5 -6 2> <a class="wiki_link" href="/Okai%20node">okai</a> 122.84790<br /> |12 -9 1> <a class="wiki_link" href="/Superpyth%20node">superpyth</a> 135.14075<br /> |47 -15 -10> <a class="wiki_link" href="/Deco%20node">deco</a> 139.19066<br /> |-2 13 -8> <a class="wiki_link" href="/Unicorn%20node">unicorn</a> 150.48658<br /> |-4 7 -3> <a class="wiki_link" href="/Laconic%20node">laconic</a> 161.79907<br /> |-44 -3 21> <a class="wiki_link" href="/Unit%20node">unit</a> 162.46707<br /> |-25 7 6> <a class="wiki_link" href="/Ampersand%20node">ampersand</a> 165.75484<br /> |20 -17 3> <a class="wiki_link" href="/Roda%20node">roda</a> 168.26415<br /> |-9 -6 8> <a class="wiki_link" href="/Doublewide%20node">doublewide</a> 226.75870<br /> |-5 -10 9> <a class="wiki_link" href="/Shibboleth%20node">shibboleth</a> 227.55270<br /> |9 9 -10> <a class="wiki_link" href="/Mynic%20node">mynic</a> 249.96513<br /> |25 -48 22> <a class="wiki_link" href="/Abigail%20node">abigail</a> 254.51011<br /> |-13 -46 37> <a class="wiki_link" href="/Supermajor%20node">supermajor</a> 263.66615<br /> |10 -40 23> <a class="wiki_link" href="/Gamera%20node">gamera</a> 272.56201<br /> |-5 -32 24> <a class="wiki_link" href="/Octoid%20node">octoid</a> 285.05756<br /> |-59 5 22> <a class="wiki_link" href="/Tertiaseptal%20node">tertiaseptal</a> 297.54417<br /> |25 15 -21> <a class="wiki_link" href="/Nessafof%20node">nessafof</a> 332.79289<br /> |-17 2 6> <a class="wiki_link" href="/Lemba%20node">lemba</a> 334.71996<br /> |19 -9 -2> <a class="wiki_link" href="/Beatles%20node">beatles</a> 358.54157<br /> |35 -25 2> <a class="wiki_link" href="/Hemififths%20node">hemififths</a> 372.84807<br /> |-29 11 5> <a class="wiki_link" href="/Tritonic%20node">tritonic</a> 378.52735<br /> |-31 2 12> <a class="wiki_link" href="/Wizard%20node">wizard</a> 386.36650<br /> |5 13 -11> <a class="wiki_link" href="/Nusecond%20node">nusecond</a> 466.49271<br /> |30 6 -17> <a class="wiki_link" href="/Semisept%20node">semisept</a> 630.57587<br /> |-35 6 11> <a class="wiki_link" href="/Septimin%20node">septimin</a> 670.94722<br /> |-20 39 -18> <a class="wiki_link" href="/Mirkat%20node">mirkat</a> 751.58057<br /> |-46 10 13> <a class="wiki_link" href="/Slender%20node">slender</a> 760.56781<br /> |93 -3 -38> <a class="wiki_link" href="/Quasiorwell%20node">quasiorwell</a> 1303.61642</body></html>