Maximal harmony epimorphic scales: Difference between revisions
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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. | 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 = | ||
== Five notes == | |||
[[semilim2]] | |||
[[semilim3]] | |||
[[ | |||
[[ | == Six notes, 6b val == | ||
[[dwarf6_5]] | |||
[[cluster6e]] | |||
[[ | |||
[[x-wing1|x-wing1]] | [[x-wing1|x-wing1]] | ||
| Line 17: | Line 16: | ||
[[x-wing2|x-wing2]] | [[x-wing2|x-wing2]] | ||
==Seven notes== | == Seven notes == | ||
[[ | [[zarlino]] | ||
[[ | [[mavchrome6]] | ||
==Eight notes== | == Eight notes == | ||
[[ | [[semimaj1]] | ||
[[ | [[semimaj2]] | ||
==Nine notes== | == Nine notes == | ||
[[ | [[mavdie1]] | ||
==Ten notes== | == Ten notes == | ||
[[ | [[blackchrome1]] | ||
[[ | [[blackchrome2]] | ||
=7 odd limit= | = 7 odd limit = | ||
== Seven notes == | |||
[[maxsev1]] | |||
[[maxsev2]] | |||
[[ | |||
[[ | = Seven limit marvel = | ||
== Seven notes == | |||
[[Gypsy_scale|Gypsy scale]] | |||
==Seven notes== | = Eleven limit marvel = | ||
[[ | == Seven notes == | ||
[[marvel11max7a]] | |||
[[marvel11max7b]] | |||
{{Navbox scale gallery}} | |||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
Latest revision as of 20:10, 11 February 2025
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
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