User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions

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 === History ===
-The idea of extending Diatonic functional harmony to cover intervals between the standard scale degrees is one that has at least some roots in [[Wikipedia: Ivan Wyschnegradsky|Wyschnegradsky]]'s concept of [[Wikipedia: Major fourth and minor fifth|"Major Fourth" and "Minor Fifth"]].  However, I wanted to use LCJI as a basis for defining these intervals and thus decided to take [[11/8]] as being the just version of Wyschnegradsky's "Major Fourth", and while I drew up sketches based loosely on [[24edo]] for early versions of this concept, I also realized that that two instances of [[33/32]] added up to an interval smaller than [[2187/2048]] but which had a similar function.  Furthermore, since two instances of 11/8 resulted in an interval in the vicinity of a Major seventh, I decided to takes stacks of 11/8 to form a second navigational axis which works together with the Diatonic Axis in order to define the microtonal functions positioned roughly halfway between the German and Viennese Diatonic functions, though there are a few other microtonal functions as well that are not immediately covered by this second axis.
+The idea of extending Diatonic functional harmony to cover intervals between the standard scale degrees is one that has at least some roots in [[Ivan Wyschnegradsky|Wyschnegradsky]]'s concept of [[Wikipedia: Major fourth and minor fifth|"Major Fourth" and "Minor Fifth"]].  However, I wanted to use LCJI as a basis for defining these intervals and thus decided to take [[11/8]] as being the just version of Wyschnegradsky's "Major Fourth", and while I drew up sketches based loosely on [[24edo]] for early versions of this concept, I also realized that that two instances of [[33/32]] added up to an interval smaller than [[2187/2048]] but which had a similar function.  Furthermore, since two instances of 11/8 resulted in an interval in the vicinity of a Major seventh, I decided to takes stacks of 11/8 to form a second navigational axis which works together with the Diatonic Axis in order to define the microtonal functions positioned roughly halfway between the German and Viennese Diatonic functions, though there are a few other microtonal functions as well that are not immediately covered by this second axis.
 [[File:Diatonic_Function_Map.png|thumb|Initial diagram of paradiatonic function locations I made around the time of officially joining the Xenharmonic community.  Note that a number of the functions listed on this page are missing, while the Contralead, the Semicontralead, the Intersubiant, the Interregnant, the Misoserviant and the Misodominant initially had different names.]]