Revision as of 04:40, 2 December 2024

If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the graph of the scale is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.