Mercator family: Difference between revisions

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@@ Line 6: / Line 6: @@
 Mapping: [{{val| 53 84 123 }}, {{val| 0 0 1 }}]
+Mapping generators:
 Wedgie: {{wedgie| 0 53 84 }}
@@ Line 14: / Line 16: @@
 =Cartography temperament=
-In terms of the normal comma list, Cartography is characterized by the addition of the schisma, 32805/32768, to Mercator's comma, which completely reduces all commas in the [[Schismic-Mercator equivalence continuum]] to the [[unison]], and thus, the 5-limit is exactly the same as the 5-limit of 53edo. Cartography can also be characterized as the 53&amp;159 temperament, with [[212edo]] being a possible tuning.
+In terms of the normal comma list, Cartography is characterized by the addition of the schisma, 32805/32768, to Mercator's comma, which completely reduces all commas in the [[Schismic-Mercator equivalence continuum]] to the [[unison]], and thus, the 5-limit is exactly the same as the 5-limit of 53edo. Cartography can also be characterized as the 53&amp;159 temperament, with [[212edo]] being a possible tuning.  It should be noted that the 7-limit is somewhat independent for this temperament and is only really fully nailed down in one way or another by extending to the 11-limit.
-Commas:
+Commas: 32805/32768
-POTE generator:
+POTE generator: ~225/224 = 5.3666
-Mapping:
+Mapping: [<53 84 123 0], <0 0 0 1]]
-Wedgie:
+Mapping generators: ~81/80, ~7/1
-EDOs:
+Wedgie: << 0 0 53 0 84 123 ]]
-Badness:
+EDOs: {{EDOs| 53, 159, 212, 689c, 901cc }}
-==7-limit==
+Badness: 0.0870
-Commas:
-POTE generator:
+==11-limit==
+-limit Cartography nails down the 7-limit by adding the symbiotic comma to the list of tempered commas.
-Mapping:
+Commas: 19712/19683, 32805/32768
-Wedgie:
+POTE generator: ~225/224 = 6.1430
-EDOs:
+Mapping: [<53 84 123 0 332 196], <0 0 0 1 -1 0]]
-Badness:
+Mapping generators: ~81/80, ~7/1
-==11-limit==
-Commas:
-POTE generator:
-Mapping:
 Wedgie:
-EDOs:
+EDOs: {{EDOs| 53, 106d, 159, 212, 371d, 583cde }}
-Badness:
+Badness: 0.0545
 ==13-limit==
-Commas:
+-limit Cartography adds the island comma to the list of tempered commas, and while this extension is connected to the 5-limit, it is independent of the 11-limit and 7-limit, so it can just as easily be added by itself to make a no-sevens no-elevens version of Cartography.
-POTE generator:
+Commas: 676/675, 19712/19683, 32805/32768
-Mapping:
+POTE generator: ~225/224 = 6.1430
-Wedgie:
+Mapping: [<53 84 123 0 332 196], <0 0 0 1 -1 0]]
-EDOs:
+Mapping generators: ~81/80, ~7/1
-Badness:
+Wedgie:
-=Pentacontatritonic=
+EDOs: {{EDOs| 53, 106d, 159, 212, 371df, 583cdeff }}
-Commas:
-POTE generator:
+Badness: 0.0300
-Mapping:
+==Pentacontatritonic==
+This temperament differs from Cartography in that it uses a different 11-limit extension to nail down the 7-limit- specifically, the swetisma.
-Wedgie:
+Commas: 540/539, 32805/32768
-EDOs:
+POTE generator: ~385/384 = 4.1494
-Badness:
+Mapping: [<53 84 123 0 481], <0 0 0 1 -2]]
-==7-limit==
+Mapping generators: ~81/80, ~7/1
-Commas:
-POTE generator:
-Mapping:
 Wedgie:
-EDOs:
+EDOs: {{EDOs| 53, 159e, 212e, 265, 318, 583c }}
-Badness:
+Badness: 0.1151
-==11-limit==
+==13-limit==
-Commas:
+-limit Pentacontatritonic adds the schismina to the list of commas being tempered out- this extension is connected to the 7-limit.
-POTE generator:
-Mapping:
-Wedgie:
+Commas: 540/539, 4096/4095, 13750/13689
-EDOs:
+POTE generator: ~385/384 = 3.9850
-Badness:
-==13-limit==
-Commas:
-POTE generator:
+Mapping: [<53 84 123 0 481 345], <0 0 0 1 -2 1]]
-Mapping:
+Mapping generators: ~81/80, ~7/1
 Wedgie:
-EDOs:
+EDOs: {{EDOs| 53, 159ef, 212ef, 265, 318, 583cf }}
-Badness:
+Badness: 0.0612