Talk:Fokker periodicity block

This article seems to me to need a complete rewrite, and I propose to give it one unless someone can explain why I shouldn't. Gene Ward Smith (talk) 05:42, 29 June 2010 (UTC)

Only equal tuning when cyclic
This only works to give an equal tuning system when the quotient group is cyclic. For example, try choosing as your two commas (in the two-dimensional version of this) the ratios 128/125 and 32/27. The resulting finite group has nine elements, but it is the non-cyclic group Z3 &times; Z3 rather than the cyclic group Z9, and it doesn't work as a way of getting a 9-equal tuning system (each pitch wants to be 1/3 or 2/3 of an octave so you only get three pitches instead of nine). The same thing happens e.g. for the less ridiculous choice of commas 128/125 and 531441/524288, giving the group Z3 &times; Z12 which again isn't cyclic. I hope this can be sourced properly and isn't original research. —David Eppstein (talk) 00:37, 14 August 2012 (UTC)