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Tree of rank two temperaments: Difference between revisions

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=The 5-limit top branches=
=The 5-limit top branches=
|-15 8 1> [[Helmholtz_node|helmholtz]] 4.25910
{| class="wikitable"
|-4 4 -1> [[Meantone_node|meantone]] 7.38134
|-
|-3 -1 2> [[Dicot_node|dicot]] 13.02798
! | Monzo
|-6 -5 6> [[Hanson_node|hanson]] 13.23353
! | Ratio
|4 -1 -1> [[Father_node|father]] 14.88434
! | Temperament <br>name
|1 -27 18&gt; [[Ennealimmic_node|ennealimmic]] 17.19058
! | Badness
|11 -4 -2&gt; [[Diaschismic_node|diaschismic]] 19.91485
|-
|38 -2 -15&gt; [[Luna_node|luna]] 20.57600
| | {{Monzo|-15 8 1}}
|9 -13 5&gt; [[Amity_node|amity]] 21.95959
| | 32805 / 32768
|7 0 -3&gt; [[Augmented_node|augmented]] 22.31538
| | [[Helmholtz_node|helmholtz]]
|-16 35 -17&gt; [[Minortone_node|minortone]] 29.76534
| | 4.25910
|1 -5 3&gt; [[Porcupine_node|porcupine]] 30.77769
|-
|23 6 -14&gt; [[Vishnuzmic_node|vishnuzmic]] 31.18117
| | {{Monzo|-4 4 -1}}
|0 3 -2&gt; [[Bug_node|bug]] 32.80131
| | 81 / 80
|2 9 -7&gt; [[Sensipent_node|sensipent]] 35.22030
| | [[Meantone_node|meantone]]
|-10 -1 5&gt; [[Magic_node|magic]] 39.16293
| | 7.38134
|-7 3 1&gt; [[Mavila_node|mavila]] 39.55645
|-
|17 1 -8&gt; [[Würschmidt_node|würschmidt]] 40.60312
| | {{Monzo|-3 -1 2}}
|-21 3 7&gt; [[Orson_node|orson]] 40.80736
| | 25 / 24
|24 -21 4&gt; [[Vulture_node|vulture]] 41.43092
| | [[Dicot_node|dicot]]
|8 14 -13&gt; [[Parakleismic_node|parakleismic]] 43.27862
| | 13.02798
|3 4 -4&gt; [[Dimipent_node|dimipent]] 47.23052
|-
|-14 -19 19&gt; [[Enneadecal_node|enneadecal]] 47.84488
| | {{Monzo|-6 -5 6}}
|5 -9 4&gt; [[Tetracot_node|tetracot]] 48.51756
| | 15625 / 15552
|8 -5 0&gt; [[Limmic_node|limmic]] 63.76017
| | [[Hanson_node|hanson]]
|12 -6 -1&gt; [[Uncle_node|uncle]] 72.65308
| | 13.23353
|-52 -17 34&gt; [[Chlorine_node|chlorine]] 77.072
|-
|-14 3 4&gt; [[Negri_node|negri]] 86.85590
| | {{Monzo|4 -1 -1}}
|-29 -11 20&gt; [[Gammic_node|gammic]] 87.75217
| | 16 / 15
|-13 17 -6&gt; [[Graviton_node|graviton]] 93.18426
| | [[Father_node|father]]
|-19 12 0&gt; [[Compton_node|compton]] 94.49449
| | 14.88434
|26 -12 -3&gt; [[Misty_node|misty]] 106.54043
|-
|13 5 -9&gt; [[Valensixthtone_node|valensixthtone]] 122.76461
| | {{Monzo|1 -27 18}}
|5 -6 2&gt; [[Okai_node|okai]] 122.84790
| | 7629394531250 / 7625597484987
|12 -9 1&gt; [[Superpyth_node|superpyth]] 135.14075
| | [[Ennealimmic_node|ennealimmic]]
|47 -15 -10&gt; [[Deco_node|deco]] 139.19066
| | 17.19058
|-2 13 -8&gt; [[Unicorn_node|unicorn]] 150.48658
|-
|-11 7 0&gt; [[Apotomic_node|apotomic]] 154.65113  
| | {{Monzo|11 -4 -2}}
|-4 7 -3&gt; [[Laconic_node|laconic]] 161.79907
| | 2048 / 2025
|-44 -3 21&gt; [[Unit_node|unit]] 162.46707
| | [[Diaschismic_node|diaschismic]]
|-25 7 6&gt; [[Ampersand_node|ampersand]] 165.75484
| | 19.91485
|20 -17 3&gt; [[Roda_node|roda]] 168.26415
|-
|-18 7 3&gt; [[Stump_node|stump]] 200.60049
| | {{Monzo|38 -2 -15}}
|-9 -6 8&gt; [[Doublewide_node|doublewide]] 226.75870
| | 274877906944 / 274658203125
|-5 -10 9&gt; [[Shibboleth_node|shibboleth]] 227.55270
| | [[Luna_node|luna]]
|28 -3 -10&gt; [[Amavil_node|amavil]] 232.48148
| | 20.57600
|9 9 -10&gt; [[Mynic_node|mynic]] 249.96513
|-
|25 -48 22&gt; [[Abigail_node|abigail]] 254.51011
| | {{Monzo|9 -13 5}}
|-13 -46 37&gt; [[Supermajor_node|supermajor]] 263.66615
| | 1600000 / 1594323
|10 -40 23&gt; [[Gamera_node|gamera]] 272.56201
| | [[Amity_node|amity]]
|-5 -32 24&gt; [[Octoid_node|octoid]] 285.05756
| | 21.95959
|-59 5 22&gt; [[Tertiaseptal_node|tertiaseptal]] 297.54417
|-
|25 15 -21&gt; [[Nessafof_node|nessafof]] 332.79289
| | {{Monzo|7 0 -3}}
|-17 2 6&gt; [[Lemba_node|lemba]] 334.71996
| | 128 / 125
|19 -9 -2&gt; [[Beatles_node|beatles]] 358.54157
| | [[Augmented_node|augmented]]
|35 -25 2&gt; [[Hemififths_node|hemififths]] 372.84807
| | 22.31538
|-29 11 5&gt; [[Tritonic_node|tritonic]] 378.52735
|-
|-31 2 12&gt; [[Wizard_node|wizard]] 386.36650
| | {{Monzo|-16 35 -17}}
|5 13 -11&gt; [[Nusecond_node|nusecond]] 466.49271
| | 50031545098999707 / 50000000000000000
|31 -21 1&gt; [[Leapday_node|leapday]] 523.18249
| | [[Minortone_node|minortone]]
|30 6 -17&gt; [[Semisept_node|semisept]] 630.57587
| | 29.76534
|-35 6 11&gt; [[Septimin_node|septimin]] 670.94722
|-
|-20 39 -18&gt; [[Mirkat_node|mirkat]] 751.58057
| | {{Monzo|1 -5 3}}
|-46 10 13&gt; [[Slender_node|slender]] 760.56781
| | 250 / 243
|46 -29 0&gt; [[Mystery_node|mystery]] 1020.55630
| | [[Porcupine_node|porcupine]]
|93 -3 -38&gt; [[Quasiorwell_node|quasiorwell]] 1303.61642
| | 30.77769
|72 0 -31&gt; [[31-5_node|31-5 node]] 1402.24568
|-
|22 14 -19&gt; [[Casablanca_node|casablanca]] 1423.73592
| | {{Monzo|23 6 -14}}
|-49 31 0&gt; [[31-3_node|31-3 node]] 4309.84584
| | 6115295232 / 6103515625
| | [[Vishnuzmic_node|vishnuzmic]]
| | 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|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]]
| | 63.76017
|-
| | {{Monzo|12 -6 -1}}
| | 4096 / 3645
| | [[Uncle_node|uncle]]
| | 72.65308
|-
| | {{Monzo|-52 -17 34}}
| |
| | [[Chlorine_node|chlorine]]
| | 77.072
|-
| | {{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]]
| | 139.19066
|-
| | {{Monzo|-2 13 -8}}
| | 1594323 / 1562500
| | [[Unicorn_node|unicorn]]
| | 150.48658
|-
| | {{Monzo|-11 7 0}}
| | 2187 / 2048
| | [[Apotomic_node|apotomic]]  
| | 154.65113
|-
| | {{Monzo|-4 7 -3}}
| | 2187 / 2000
| | [[Laconic_node|laconic]]
| | 161.79907
|-
| | {{Monzo|-44 -3 21}}
| | 476837158203125 / 474989023199232
| | [[Unit_node|unit]]
| | 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|9 9 -10}}
| | 10077696 / 9765625
| | [[Mynic_node|mynic]]
| | 249.96513
|-
| | {{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|-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|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|-49 31 0}}
| | 617673396283947 / 562949953421312
| | [[31-3_node|31-3 node]]
| | 4309.84584
|}
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