Kite's thoughts on antipodes: Difference between revisions

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 * If the edo is odd and the 5th is even, the antipodes are the mid-3rd (half-5th) and its octave complement a 4th higher. For example, [[17edo]]'s 5th is 10\17, and its antipodes are 5\17 and 12\17.
-In summary, the antipode is always the half-octave, the half-4th or the half-5th, whichever one exists in the edo. The proof that one and only only one of these will exist in any single-ring edo is left as an exercise for the reader.
+In summary, the antipode is always the half-octave, the half-4th or the half-5th, whichever one exists in the edo. Only one of these exists; or all three exist, in which case the edo is multi-ring.
 == Applications ==