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Tree of rank two temperaments: Difference between revisions

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There are no wedgies here to begin with, but the page acts as if there are
 
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=The temperament tree=
=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.
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.


=The 5-limit top branches=
=The 5-limit top branches=
Line 114: Line 114:
| | [[Parakleismic_node|parakleismic]]
| | [[Parakleismic_node|parakleismic]]
| | 43.27862
| | 43.27862
|-
| | {{Monzo|39 -29 3}}
| | 68719476736000 / 68630377364883
| | [[Tricot_node|tricot]]
| | 46.09293
|-
|-
| | {{Monzo|3 4 -4}}
| | {{Monzo|3 4 -4}}
Line 132: Line 137:
| | {{Monzo|8 -5 0}}
| | {{Monzo|8 -5 0}}
| | 256 / 243
| | 256 / 243
| | [[Limmic_node|limmic]]
| | [[Limmic_node|limmic]] (blackwood)
| | 63.76017
| | 63.76017
|-
|-
Line 144: Line 149:
| | [[Chlorine_node|chlorine]]
| | [[Chlorine_node|chlorine]]
| | 77.072
| | 77.072
|-
| | {{Monzo|32 -7 -9}}
| | 4294967296 / 4271484375
| | [[Escapade_node|escapade]]
| | 83.77811
|-
|-
| | {{Monzo|-14 3 4}}
| | {{Monzo|-14 3 4}}
Line 187: Line 197:
| | {{Monzo|47 -15 -10}}
| | {{Monzo|47 -15 -10}}
| | 140737488355328 / 140126044921875
| | 140737488355328 / 140126044921875
| | [[Deco_node|deco]]
| | [[Deco_node|deco]] (qintosec)
| | 139.19066
| | 139.19066
|-
|-
Line 197: Line 207:
| | {{Monzo|-11 7 0}}
| | {{Monzo|-11 7 0}}
| | 2187 / 2048
| | 2187 / 2048
| | [[Apotomic_node|apotomic]]  
| | [[Apotomic_node|apotomic]] (whitewood)
| | 154.65113
| | 154.65113
|-
|-
Line 207: Line 217:
| | {{Monzo|-44 -3 21}}
| | {{Monzo|-44 -3 21}}
| | 476837158203125 / 474989023199232
| | 476837158203125 / 474989023199232
| | [[Unit_node|unit]]
| | [[Unit_node|unit]] (mutt)
| | 162.46707
| | 162.46707
|-
|-
Line 239: Line 249:
| | [[Amavil_node|amavil]]
| | [[Amavil_node|amavil]]
| | 232.48148
| | 232.48148
|-
| | {{Monzo|-28 25 -5}}
| | 847288609443 / 838860800000
| | [[Pental_node|pental]]
| | 240.04961
|-
|-
| | {{Monzo|9 9 -10}}
| | {{Monzo|9 9 -10}}
Line 244: Line 259:
| | [[Mynic_node|mynic]]
| | [[Mynic_node|mynic]]
| | 249.96513
| | 249.96513
|-
| | {{Monzo|19 10 -15}}
| | 30958682112 / 30517578125
| | [[Trisedodge_node|trisedodge]]
| | 252.72417
|-
|-
| | {{Monzo|25 -48 22}}
| | {{Monzo|25 -48 22}}
Line 289: Line 309:
| | [[Hemififths_node|hemififths]]
| | [[Hemififths_node|hemififths]]
| | 372.84807
| | 372.84807
|-
| | {{Monzo|10 23 -20}}
| | 96402615118848 / 95367431640625
| | [[Countermeantone_node|countermeantone]]
| | 373.47690
|-
|-
| | {{Monzo|-29 11 5}}
| | {{Monzo|-29 11 5}}
Line 329: Line 354:
| | [[Slender_node|slender]]
| | [[Slender_node|slender]]
| | 760.56781
| | 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}}
| | {{Monzo|46 -29 0}}
Line 349: Line 384:
| | [[Casablanca_node|casablanca]]
| | [[Casablanca_node|casablanca]]
| | 1423.73592
| | 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}}
| | {{Monzo|-49 31 0}}
Line 355: Line 400:
| | 4309.84584
| | 4309.84584
|}
|}
[[Category:Tables]]
[[Category:Lists of temperaments]]
Retrieved from "https://en.xen.wiki/w/Tree_of_rank_two_temperaments"