Editing Modulatory space (section)

== Cylindrical modulatory spaces ==

A temperament of rank two which is not linear has one generator which is a fraction of an octave, called the period. We may represent the modulatory space of such a temperament as n chains of generators in a circle, forming a cylinder. Here n is the number of periods in an octave.

For example, [[diaschismic temperament]] is the temperament which tempers out the [[diaschisma]], or 2048/2025. It can be represented as two chains of slightly (3.25 to 3.55 cents) sharp fifths a half-octave apart, which can be depicted as two chains perpendicular to a circle and at opposite side of it. The cylindrical appearance of this sort of modulatory space becomes more apparent when the period is a smaller fraction of an octave; for example, [[ennealimmal temperament]] has a modulatory space consisting of nine chains of minor thirds in a circle (where the thirds may be only 0.02 to 0.03 cents sharp.)