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Tree of rank two temperaments: Difference between revisions

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**Imported revision 279549168 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
=The temperament tree=
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
Using the [[Normal_lists|normal comma list]] it is possible to define a [https://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 and the normal comma list. The number at the end of the row is a logflat badness measure. 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.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-28 00:35:29 UTC</tt>.<br>
 
: The original revision id was <tt>279549168</tt>.<br>
=The 5-limit top branches=
: The revision comment was: <tt></tt><br>
{| class="wikitable"
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
|-
<h4>Original Wikitext content:</h4>
! | Monzo
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">|-15 8 1&gt; [[Helmholtz node|helmholtz]] 4.25910
! | Ratio
|-4 4 -1&gt; [[Meantone node|meantone]] 7.38134
! | Temperament <br>name
|-3 -1 2&gt; [[Dicot node|dicot]] 13.02798
! | Badness
|-6 -5 6&gt; [[Hanson node|hanson]] 13.23353
|-
|4 -1 -1&gt; [[Father node|father]] 14.88434
| | {{Monzo|-15 8 1}}
|1 -27 18&gt; [[Ennealimmic node|ennealimmic]] 17.19058
| | 32805 / 32768
|11 -4 -2&gt; [[Diaschismic node|diaschismic]] 19.91485
| | [[Helmholtz_node|helmholtz]]
|38 -2 -15&gt; [[Luna node|luna]] 20.57600
| | 4.25910
|9 -13 5&gt; [[Amity node|amity]] 21.95959
|-
|7 0 -3&gt; [[Augmented node|augmented]] 22.31538
| | {{Monzo|-4 4 -1}}
|1 -5 3&gt; [[Porcupine node|porcupine]] 30.77769
| | 81 / 80
|23 6 -14&gt; [[Vishnu node|vishnu]] 31.18117
| | [[Meantone_node|meantone]]
|0 3 -2&gt; [[Bug node|bug]] 32.80131
| | 7.38134
|2 9 -7&gt; [[Sensipent node|sensipent]] 35.22030
|-
|-10 -1 5&gt; [[Magic node|magic]] 39.16293
| | {{Monzo|-3 -1 2}}
|-7 3 1&gt; [[Mavila node|mavila]] 39.55645
| | 25 / 24
|17 1 -8&gt; [[Würschmidt node|würschmidt]] 40.60312
| | [[Dicot_node|dicot]]
|-21 3 7&gt; [[Orson node|orson]] 40.80736
| | 13.02798
|8 14 -13&gt; [[Parakleismic node|parakleismic]] 43.27862
|-
|3 4 -4&gt; [[Dimipent node|dimipent]] 47.23052
| | {{Monzo|-6 -5 6}}
|8 -5 0&gt; [[Limmic node|limmic]] 63.76017
| | 15625 / 15552
|12 -6 -1&gt; [[Golic node|golic]] 72.65308
| | [[Hanson_node|hanson]]
|-14 3 4&gt; [[Negri node|negri]] 86.85590
| | 13.23353
|5 -6 2&gt; [[Okai node|okai]] 122.84790
|-
|12 -9 1&gt; [[Superpyth node|superpyth]] 135.14075
| | {{Monzo|4 -1 -1}}
|-2 13 -8&gt; [[Unicorn node|unicorn]] 150.48657764487502311
| | 16 / 15
|-4 7 -3&gt; [[Laconic node|laconic]] 161.79907
| | [[Father_node|father]]
|-25 7 6&gt; [[Ampersand node|ampersand]] 165.75484
| | 14.88434
|-9 -6 8&gt; [[Doublewide node|doublewide]] 226.75870
|-
|-5 -10 9&gt; [[Shibboleth node|shibboleth]] 227.55270
| | {{Monzo|1 -27 18}}
|-17 2 6&gt; [[Lemba node|lemba]] 334.71996
| | 7629394531250 / 7625597484987
|19 -9 -2&gt; [[Beatles node|beatles]] 358.54157
| | [[Ennealimmic_node|ennealimmic]]
|-31 2 12&gt; [[Wizard node|wizard]] 386.36650
| | 17.19058
</pre></div>
|-
<h4>Original HTML content:</h4>
| | {{Monzo|11 -4 -2}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tree of rank two temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;|-15 8 1&amp;gt; &lt;a class="wiki_link" href="/Helmholtz%20node"&gt;helmholtz&lt;/a&gt; 4.25910&lt;br /&gt;
| | 2048 / 2025
|-4 4 -1&amp;gt; &lt;a class="wiki_link" href="/Meantone%20node"&gt;meantone&lt;/a&gt; 7.38134&lt;br /&gt;
| | [[Diaschismic_node|diaschismic]]
|-3 -1 2&amp;gt; &lt;a class="wiki_link" href="/Dicot%20node"&gt;dicot&lt;/a&gt; 13.02798&lt;br /&gt;
| | 19.91485
|-6 -5 6&amp;gt; &lt;a class="wiki_link" href="/Hanson%20node"&gt;hanson&lt;/a&gt; 13.23353&lt;br /&gt;
|-
|4 -1 -1&amp;gt; &lt;a class="wiki_link" href="/Father%20node"&gt;father&lt;/a&gt; 14.88434&lt;br /&gt;
| | {{Monzo|38 -2 -15}}
|1 -27 18&amp;gt; &lt;a class="wiki_link" href="/Ennealimmic%20node"&gt;ennealimmic&lt;/a&gt; 17.19058&lt;br /&gt;
| | 274877906944 / 274658203125
|11 -4 -2&amp;gt; &lt;a class="wiki_link" href="/Diaschismic%20node"&gt;diaschismic&lt;/a&gt; 19.91485&lt;br /&gt;
| | [[Luna_node|luna]]
|38 -2 -15&amp;gt; &lt;a class="wiki_link" href="/Luna%20node"&gt;luna&lt;/a&gt; 20.57600&lt;br /&gt;
| | 20.57600
|9 -13 5&amp;gt; &lt;a class="wiki_link" href="/Amity%20node"&gt;amity&lt;/a&gt; 21.95959&lt;br /&gt;
|-
|7 0 -3&amp;gt; &lt;a class="wiki_link" href="/Augmented%20node"&gt;augmented&lt;/a&gt; 22.31538&lt;br /&gt;
| | {{Monzo|9 -13 5}}
|1 -5 3&amp;gt; &lt;a class="wiki_link" href="/Porcupine%20node"&gt;porcupine&lt;/a&gt; 30.77769&lt;br /&gt;
| | 1600000 / 1594323
|23 6 -14&amp;gt; &lt;a class="wiki_link" href="/Vishnu%20node"&gt;vishnu&lt;/a&gt; 31.18117&lt;br /&gt;
| | [[Amity_node|amity]]
|0 3 -2&amp;gt; &lt;a class="wiki_link" href="/Bug%20node"&gt;bug&lt;/a&gt; 32.80131&lt;br /&gt;
| | 21.95959
|2 9 -7&amp;gt; &lt;a class="wiki_link" href="/Sensipent%20node"&gt;sensipent&lt;/a&gt; 35.22030&lt;br /&gt;
|-
|-10 -1 5&amp;gt; &lt;a class="wiki_link" href="/Magic%20node"&gt;magic&lt;/a&gt; 39.16293&lt;br /&gt;
| | {{Monzo|7 0 -3}}
|-7 3 1&amp;gt; &lt;a class="wiki_link" href="/Mavila%20node"&gt;mavila&lt;/a&gt; 39.55645&lt;br /&gt;
| | 128 / 125
|17 1 -8&amp;gt; &lt;a class="wiki_link" href="/W%C3%BCrschmidt%20node"&gt;würschmidt&lt;/a&gt; 40.60312&lt;br /&gt;
| | [[Augmented_node|augmented]]
|-21 3 7&amp;gt; &lt;a class="wiki_link" href="/Orson%20node"&gt;orson&lt;/a&gt; 40.80736&lt;br /&gt;
| | 22.31538
|8 14 -13&amp;gt; &lt;a class="wiki_link" href="/Parakleismic%20node"&gt;parakleismic&lt;/a&gt; 43.27862&lt;br /&gt;
|-
|3 4 -4&amp;gt; &lt;a class="wiki_link" href="/Dimipent%20node"&gt;dimipent&lt;/a&gt; 47.23052&lt;br /&gt;
| | {{Monzo|-16 35 -17}}
|8 -5 0&amp;gt; &lt;a class="wiki_link" href="/Limmic%20node"&gt;limmic&lt;/a&gt; 63.76017&lt;br /&gt;
| | 50031545098999707 / 50000000000000000
|12 -6 -1&amp;gt; &lt;a class="wiki_link" href="/Golic%20node"&gt;golic&lt;/a&gt; 72.65308&lt;br /&gt;
| | [[Minortone_node|minortone]]
|-14 3 4&amp;gt; &lt;a class="wiki_link" href="/Negri%20node"&gt;negri&lt;/a&gt; 86.85590&lt;br /&gt;
| | 29.76534
|5 -6 2&amp;gt; &lt;a class="wiki_link" href="/Okai%20node"&gt;okai&lt;/a&gt; 122.84790&lt;br /&gt;
|-
|12 -9 1&amp;gt; &lt;a class="wiki_link" href="/Superpyth%20node"&gt;superpyth&lt;/a&gt; 135.14075&lt;br /&gt;
| | {{Monzo|1 -5 3}}
|-2 13 -8&amp;gt; &lt;a class="wiki_link" href="/Unicorn%20node"&gt;unicorn&lt;/a&gt; 150.48657764487502311&lt;br /&gt;
| | 250 / 243
|-4 7 -3&amp;gt; &lt;a class="wiki_link" href="/Laconic%20node"&gt;laconic&lt;/a&gt; 161.79907&lt;br /&gt;
| | [[Porcupine_node|porcupine]]
|-25 7 6&amp;gt; &lt;a class="wiki_link" href="/Ampersand%20node"&gt;ampersand&lt;/a&gt; 165.75484&lt;br /&gt;
| | 30.77769
|-9 -6 8&amp;gt; &lt;a class="wiki_link" href="/Doublewide%20node"&gt;doublewide&lt;/a&gt; 226.75870&lt;br /&gt;
|-
|-5 -10 9&amp;gt; &lt;a class="wiki_link" href="/Shibboleth%20node"&gt;shibboleth&lt;/a&gt; 227.55270&lt;br /&gt;
| | {{Monzo|23 6 -14}}
|-17 2 6&amp;gt; &lt;a class="wiki_link" href="/Lemba%20node"&gt;lemba&lt;/a&gt; 334.71996&lt;br /&gt;
| | 6115295232 / 6103515625
|19 -9 -2&amp;gt; &lt;a class="wiki_link" href="/Beatles%20node"&gt;beatles&lt;/a&gt; 358.54157&lt;br /&gt;
| | [[Vishnuzmic_node|vishnuzmic]]
|-31 2 12&amp;gt; &lt;a class="wiki_link" href="/Wizard%20node"&gt;wizard&lt;/a&gt; 386.36650&lt;/body&gt;&lt;/html&gt;</pre></div>
| | 31.18117
|-
| | {{Monzo|0 3 -2}}
| | 27 / 25
| | [[Bug_node|bug]]
| | 32.80131
|-
| | {{Monzo|2 9 -7}}
| | 78732 / 78125
| | [[Sensipent_node|sensipent]]
| | 35.22030
|-
| | {{Monzo|-10 -1 5}}
| | 3125 / 3072
| | [[Magic_node|magic]]
| | 39.16293
|-
| | {{Monzo|-7 3 1}}
| | 135 / 128
| | [[Mavila_node|mavila]]
| | 39.55645
|-
| | {{Monzo|17 1 -8}}
| | 393216 / 390625
| | [[Würschmidt_node|würschmidt]]
| | 40.60312
|-
| | {{Monzo|-21 3 7}}
| | 2109375 / 2097152
| | [[Orson_node|orson]]  
| | 40.80736
|-
| | {{Monzo|24 -21 4}}
| | 10485760000 / 10460353203
| | [[Vulture_node|vulture]]
| | 41.43092
|-
| | {{Monzo|8 14 -13}}
| | 1224440064 / 1220703125
| | [[Parakleismic_node|parakleismic]]
| | 43.27862
|-
| | {{Monzo|39 -29 3}}
| | 68719476736000 / 68630377364883
| | [[Tricot_node|tricot]]
| | 46.09293
|-
| | {{Monzo|3 4 -4}}
| | 648 / 625
| | [[Dimipent_node|dimipent]]
| | 47.23052
|-
| | {{Monzo|-14 -19 19}}
| | 19073486328125 / 19042491875328
| | [[Enneadecal_node|enneadecal]]
| | 47.84488
|-
| | {{Monzo|5 -9 4}}
| | 20000 / 19683
| | [[Tetracot_node|tetracot]]
| | 48.51756
|-
| | {{Monzo|8 -5 0}}
| | 256 / 243
| | [[Limmic_node|limmic]] (blackwood)
| | 63.76017
|-
| | {{Monzo|12 -6 -1}}
| | 4096 / 3645
| | [[Uncle_node|uncle]]
| | 72.65308
|-
| | {{Monzo|-52 -17 34}}
| |
| | [[Chlorine_node|chlorine]]
| | 77.072
|-
| | {{Monzo|32 -7 -9}}
| | 4294967296 / 4271484375
| | [[Escapade_node|escapade]]
| | 83.77811
|-
| | {{Monzo|-14 3 4}}
| | 16875 / 16384
| | [[Negri_node|negri]]
| | 86.85590
|-
| | {{Monzo|-29 -11 20}}
| | 95367431640625 / 95105071448064
| | [[Gammic_node|gammic]]
| | 87.75217
|-
| | {{Monzo|-13 17 -6}}
| | 129140163 / 128000000
| | [[Graviton_node|graviton]]
| | 93.18426
|-
| | {{Monzo|-19 12 0}}
| | 531441 / 524288
| | [[Compton_node|compton]]
| | 94.49449
|-
| | {{Monzo|26 -12 -3}}
| | 67108864 / 66430125
| | [[Misty_node|misty]]
| | 106.54043
|-
| | {{Monzo|13 5 -9}}
| | 1990656 / 1953125
| | [[Valensixthtone_node|valensixthtone]]
| | 122.76461
|-
| | {{Monzo|5 -6 2}}
| | 800 / 729
| | [[Okai_node|okai]]
| | 122.84790
|-
| | {{Monzo|12 -9 1}}
| | 20480 / 19683
| | [[Superpyth_node|superpyth]]
| | 135.14075
|-
| | {{Monzo|47 -15 -10}}
| | 140737488355328 / 140126044921875
| | [[Deco_node|deco]] (qintosec)
| | 139.19066
|-
| | {{Monzo|-2 13 -8}}
| | 1594323 / 1562500
| | [[Unicorn_node|unicorn]]
| | 150.48658
|-
| | {{Monzo|-11 7 0}}
| | 2187 / 2048
| | [[Apotomic_node|apotomic]] (whitewood)
| | 154.65113
|-
| | {{Monzo|-4 7 -3}}
| | 2187 / 2000
| | [[Laconic_node|laconic]]
| | 161.79907
|-
| | {{Monzo|-44 -3 21}}
| | 476837158203125 / 474989023199232
| | [[Unit_node|unit]] (mutt)
| | 162.46707
|-
| | {{Monzo|-25 7 6}}
| | 34171875 / 33554432
| | [[Ampersand_node|ampersand]]
| | 165.75484
|-
| | {{Monzo|20 -17 3}}
| | 131072000 / 129140163
| | [[Roda_node|roda]]
| | 168.26415
|-
| | {{Monzo|-18 7 3}}
| | 273375 / 262144
| | [[Stump_node|stump]]
| | 200.60049
|-
| | {{Monzo|-9 -6 8}}
| | 390625 / 373248
| | [[Doublewide_node|doublewide]]
| | 226.75870
|-
| | {{Monzo|-5 -10 9}}
| | 1953125 / 1889568
| | [[Shibboleth_node|shibboleth]]
| | 227.55270
|-
| | {{Monzo|28 -3 -10}}
| | 268435456 / 263671875
| | [[Amavil_node|amavil]]
| | 232.48148
|-
| | {{Monzo|-28 25 -5}}
| | 847288609443 / 838860800000
| | [[Pental_node|pental]]
| | 240.04961
|-
| | {{Monzo|9 9 -10}}
| | 10077696 / 9765625
| | [[Mynic_node|mynic]]
| | 249.96513
|-
| | {{Monzo|19 10 -15}}
| | 30958682112 / 30517578125
| | [[Trisedodge_node|trisedodge]]
| | 252.72417
|-
| | {{Monzo|25 -48 22}}
| |
| | [[Abigail_node|abigail]]
| | 254.51011
|-
| | {{Monzo|-13 -46 37}}
| |
| | [[Supermajor_node|supermajor]]
| | 263.66615
|-
| | {{Monzo|10 -40 23}}
| | 12207031250000000000 / 12157665459056928801
| | [[Gamera_node|gamera]]
| | 272.56201
|-
| | {{Monzo|-5 -32 24}}
| | 59604644775390625 / 59296646043258912
| | [[Octoid_node|octoid]]
| | 285.05756
|-
| | {{Monzo|-59 5 22}}
| | 579357147216796875 / 576460752303423488
| | [[Tertiaseptal_node|tertiaseptal]]
| | 297.54417
|-
| | {{Monzo|25 15 -21}}
| | 481469424205824 / 476837158203125
| | [[Nessafof_node|nessafof]]
| | 332.79289
|-
| | {{Monzo|-17 2 6}}
| | 140625 / 131072
| | [[Lemba_node|lemba]]
| | 334.71996
|-
| | {{Monzo|19 -9 -2}}
| | 524288 / 492075
| | [[Beatles_node|beatles]]
| | 358.54157
|-
| | {{Monzo|35 -25 2}}
| | 858993459200 / 847288609443
| | [[Hemififths_node|hemififths]]
| | 372.84807
|-
| | {{Monzo|10 23 -20}}
| | 96402615118848 / 95367431640625
| | [[Countermeantone_node|countermeantone]]
| | 373.47690
|-
| | {{Monzo|-29 11 5}}
| | 553584375 / 536870912
| | [[Tritonic_node|tritonic]]
| | 378.52735
|-
| | {{Monzo|-31 2 12}}
| | 2197265625 / 2147483648
| | [[Wizard_node|wizard]]
| | 386.36650
|-
| | {{Monzo|5 13 -11}}
| | 51018336 / 48828125
| | [[Nusecond_node|nusecond]]
| | 466.49271
|-
| | {{Monzo|31 -21 1}}
| | 10737418240 / 10460353203
| | [[Leapday_node|leapday]]
| | 523.18249
|-
| | {{Monzo|30 6 -17}}
| | 782757789696 / 762939453125
| | [[Semisept_node|semisept]]
| | 630.57587
|-
| | {{Monzo|-35 6 11}}
| | 35595703125 / 34359738368
| | [[Septimin_node|septimin]]
| | 670.94722
|-
| | {{Monzo|-20 39 -18}}
| | 4052555153018976267 / 4000000000000000000
| | [[Mirkat_node|mirkat]]
| | 751.58057
|-
| | {{Monzo|-46 10 13}}
| | 72081298828125 / 70368744177664
| | [[Slender_node|slender]]
| | 760.56781
|-
| | {{Monzo|0 -19 13}}
| | 1220703125 / 1162261467
| | [[Bohpier_node|bohpier]]
| | 860.53382
|-
| | {{Monzo|65 -41 0}}
| |
| | [[41-3_node|41-3 node]]
| | 934.30950
|-
| | {{Monzo|46 -29 0}}
| | 70368744177664 / 68630377364883
| | [[Mystery_node|mystery]]
| | 1020.55630
|-
| | {{Monzo|93 -3 -38}}
| |
| | [[Quasiorwell_node|quasiorwell]]
| | 1303.61642
|-
| | {{Monzo|72 0 -31}}
| |
| | [[31-5_node|31-5 node]]
| | 1402.24568
|-
| | {{Monzo|22 14 -19}}
| | 20061226008576 / 19073486328125
| | [[Casablanca_node|casablanca]]
| | 1423.73592
|-
| | {{Monzo|-56 9 18}}
| | 75084686279296875 / 72057594037927936
| | [[Ennea_node|ennea]]
| | 2019.43349
|-
| | {{Monzo|104 -70 3}}
| |
| | [[Satin_node|satin]]
| | 2853.04905
|-
| | {{Monzo|-49 31 0}}
| | 617673396283947 / 562949953421312
| | [[31-3_node|31-3 node]]
| | 4309.84584
|}
[[Category:Tables]]
[[Category:Lists of temperaments]]
Retrieved from "https://en.xen.wiki/w/Tree_of_rank_two_temperaments"