5edo: Difference between revisions

Despite its lack of accuracy, 5edo is the second [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]], after 2edo. It also is the smallest equal division representing the [[9-limit]] [[consistent|consistently]], giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how [[4edo]] can be used, and which is discussed in that article, it can be used to represent [[7-limit]] intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the [[The_Seven_Limit_Symmetrical_Lattices|lattice]] of tetrads/pentads together with the number of scale steps in 5edo. However, while [[2edo]] represents the [[3-limit]] consistently, [[3edo]] the [[5-limit]], [[4edo]] the [[7-limit]] and 5edo the [[9-limit]], to represent the [[11-limit]] consistently with a [[patent val]] requires going all the way to [[22edo]]. Nevertheless, because the comma tempered out for this edo's circle of fifths is [[256/243]], and since this interval is smaller than half a step, 5edo is the second edo to demonstrate 3-to-2 [[telicity]].

== Intervals ==