Ringer scale: Difference between revisions

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 == Perfect Ringer scale ==
-A perfect Ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics to distinct numbers of steps up to [[octave equivalence]]. It is likely that only a small finite number of perfect Ringer scales exist. Here are the known ones so far (to be expanded as/if more are found):
+A perfect Ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics to distinct numbers of steps up to [[octave equivalence]]. It is conjectured that these are the only perfect Ringer scales:
 '''Ringer 1:''' 1:2
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 Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]].
+Also note that there is a "Perfect Pseudoringer 9" if we allow a pair of harmonics to be swapped/out of order in order to preserve the constant structure property.
 == Origin of Ringer scales ==