Equivalence continuum: Difference between revisions

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=== Example (7-limit rank-2 temperaments in 31edo) ===

Let '''u'''''x'', '''u'''''y'', '''u'''''z'' = 81/80, 126/125, 1029/1024 be the basis for the kernel of 7-limit 31edo. Then:

* [[septimal meantone]] tempers out 81/80 = '''u'''''x'' = (1, 0, 0) and 126/125 = '''u'''''y'' = (0,1,0), thus corresponds to the plane ''z'' = 0. This corresponds to '''v''' = (0, 0, 1).

* [[septimal meantone]] tempers out 81/80 = '''u'''''x'' = (1, 0, 0) and 126/125 = '''u'''''y'' = (0, 1, 0), thus corresponds to the plane ''z'' = 0. This corresponds to '''v''' = (0, 0, 1).

* [[hemithirds]] tempers out 1029/1024 = '''u'''''z'' = (0, 0, 1) and 3136/3125 = 2'''u'''''x'' + '''u'''''y'' = (2, 1, 0). This corresponds to '''v''' = (1, −2, 0).

* [[miracle]] tempers out 1029/1024 = '''u'''''z'' = (0, 0, 1) and 225/224 = '''u'''''x'' − '''u'''''y'' = (1, −1, 0). This corresponds to '''v''' = (1, 1, 0).

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 === Example (7-limit rank-2 temperaments in 31edo) ===
 Let '''u'''<sub>''x''</sub>, '''u'''<sub>''y''</sub>, '''u'''<sub>''z''</sub> = 81/80, 126/125, 1029/1024 be the basis for the kernel of 7-limit 31edo. Then:
-* [[septimal meantone]] tempers out 81/80 = '''u'''<sub>''x''</sub> = (1, 0, 0) and 126/125 = '''u'''<sub>''y''</sub> = (0,1,0), thus corresponds to the plane ''z'' = 0. This corresponds to '''v''' = (0, 0, 1).
+* [[septimal meantone]] tempers out 81/80 = '''u'''<sub>''x''</sub> = (1, 0, 0) and 126/125 = '''u'''<sub>''y''</sub> = (0, 1, 0), thus corresponds to the plane ''z'' = 0. This corresponds to '''v''' = (0, 0, 1).
 * [[hemithirds]] tempers out 1029/1024 = '''u'''<sub>''z''</sub> = (0, 0, 1) and 3136/3125 = 2'''u'''<sub>''x''</sub> + '''u'''<sub>''y''</sub> = (2, 1, 0). This corresponds to '''v''' = (1, &minus;2, 0).
 * [[miracle]] tempers out 1029/1024 = '''u'''<sub>''z''</sub> = (0, 0, 1) and 225/224 = '''u'''<sub>''x''</sub> &minus; '''u'''<sub>''y''</sub> = (1, &minus;1, 0). This corresponds to '''v''' = (1, 1, 0).