Editing Modulatory space (section)

== Circles of generators ==

Other models of pitch class space, such as the [[circle of fifths]], attempt to describe the special relationship between pitch classes related by perfect fifth.  In [[equal temperament]], twelve successive fifths equate to seven octaves exactly, and hence in terms of pitch classes closes back to itself, forming a circle.   We say that the pitch class of the fifth generates – or is a [[generating set of a group|generator]] of – the space of twelve pitch classes.

By dividing the octave into n equal parts, and choosing an integer m<n such that m and n are [[relatively prime]] – that is, have no common [[divisor]] – we obtain similar circles, which all have the structure of finite cyclic groups. By drawing a line between two pitch classes when they differ by a generator, we can depict the circle of generators as a [[cycle graph]], in the shape of a regular [[polygon]].{{example needed|date=December 2018}}