Diatonic functional harmony: Difference between revisions

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== Paradiatonic Functions ==

~~In addition~~ to ~~all~~ the ~~aforementioned Diatonic functions, Aura not only takes [[11/8]] to be a more just version of~~ [[Wikipedia:Ivan Wyschnegradsky|Wyschnegradsky]]'s [[Wikipedia:Major fourth and minor fifth|Major Fourth]] ~~interval (under~~ the ~~name~~ "~~paramajor fourth~~"), but ~~also~~ takes stacks of 11/8 to form a second navigational axis the "'''Paradiatonic 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.

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, Aura 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 he drew up sketches based loosely on [[24edo]] for early versions of this concept, he 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, Aura decided to takes stacks of 11/8 to form a second navigational axis, the "'''Paradiatonic 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 axis.

[[File:Diatonic_Function_Map.png|thumb|Initial diagram of paradiatonic function locations by Aura 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 and Interregnant initially had different names.]]

Through interactions with others in the Xenharmonic community, Aura was later influenced by others on Discord to take [[MOS]]-based structural considerations into account. This eventually resulted in the first formal definition of things like a "'''parachroma'''", an interval that can be easily tempered to equal half of a MOS-chroma.

=== Basic Paradiatonic Functions ===

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 == Paradiatonic Functions ==
-In addition to all the aforementioned Diatonic functions, Aura not only takes [[11/8]] to be a more just version of [[Wikipedia:Ivan Wyschnegradsky|Wyschnegradsky]]'s [[Wikipedia:Major fourth and minor fifth|Major Fourth]] interval (under the name "paramajor fourth"), but also takes stacks of 11/8 to form a second navigational axis the "'''Paradiatonic 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.
+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, Aura 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 he drew up sketches based loosely on [[24edo]] for early versions of this concept, he 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, Aura decided to takes stacks of 11/8 to form a second navigational axis, the "'''Paradiatonic 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 axis.
+[[File:Diatonic_Function_Map.png|thumb|Initial diagram of paradiatonic function locations by Aura 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 and Interregnant initially had different names.]]
+Through interactions with others in the Xenharmonic community, Aura was later influenced by others on Discord to take [[MOS]]-based structural considerations into account.  This eventually resulted in the first formal definition of things like a "'''parachroma'''", an interval that can be easily tempered to equal half of a MOS-chroma.
 === Basic Paradiatonic Functions ===