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Maximal harmony epimorphic scales: Difference between revisions

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If we look at all periodic scales [[Periodic_scale#Epimorphic|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-theoretic_properties_of_scales|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.
If we look at all periodic scales [[Periodic_scale#Epimorphism|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-theoretic_properties_of_scales|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=
=5-limit=
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