Maximal harmony epimorphic scales
Jump to navigation
Jump to search
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.
5-limit
Five notes
Six notes, 6b val
Seven notes
Eight notes
Nine notes
Ten notes
7 odd limit
Seven notes
Seven limit marvel
Seven notes
Eleven limit marvel
Seven notes
| V • T • EScale galleries | |
|---|---|
| JI scales | 12-tone JI scales • Combination product sets • CS scales • Maximal harmony epimorphic scales • MOS transversals • Non-octave JI scales • Wakalixes • Z-polygon transversals • Other JI scales Full list: Category:Just intonation scales |
| Tempered scales | 12-tone tempered scales • Clippers • Essentially tempered scales • Marvel woo scales • MOS cradle scales • Non-octave tempered scales • Scalesmith systematic scales • Other tempered scales Full list: Category:Tempered scales |
| ET subsets | 11edo modes, 19edo modes, 22edo modes, 24edo scales, 31edo modes |
All other scale gallery pages are included in Category:Lists of scales | |