Talk:Fokker periodicity block

Tunings, Temperaments, and Scales (defunct)

This article is within the scope of WikiProject Tunings, Temperaments, and Scales, a project which is currently considered to be defunct.Tunings, Temperaments, and ScalesWikipedia:WikiProject Tunings, Temperaments, and ScalesTemplate:WikiProject Tunings, Temperaments, and ScalesTunings, Temperaments, and Scales articles

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)[reply]

Only equal tuning when cyclic[edit]

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 × 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 × 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)[reply]