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

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 === Governing Rules ===
-'''Commatic Repulsion''' - This rule is best summed up in Flora Canou's statement that things repel the similar but not identical.  To illustrate this principle, let's take a look at the VImin chord as is present in [[meantone]] and contrast it to the situation outside of meantone.  Believe it or not, the meantone VImin chord has no fewer than three separate functions relative to the Tonic.  First of all, there's the Relative Minor functionality, which is 5/3–1/1–5/4 relative to the Tonic and can tonicize as a new Imin either temporarily, as in a deceptive cadence, or permanently as in a modulation.  Secondly, there's the Tertiary Dominant functionality, which is 27/16-81/80-81/64 relative to the Tonic and, as the name suggests, acts as the Dominant of the Dominant's own Dominant.  Finally, there's the Tensive functionality, which is 27/16-1/1-5/4 relative to the Tonic and is involved in interrupted cadences, as well as in starting cadences that "wind down" such as VImin-IVmaj-Imaj or even VImin-Vmaj-Imaj.  While all three of these are fused together in meantone, the first two of these three functions are separated exactly by the syntonic comma in non-meantone environments, while the third shares its root with the Tertiary Dominant and shares both its third and fifth with the Relative Minor, and the only way to use a VImin chord with all three functions is to temper out the syntonic comma.  As Flora Canou has stated:
+'''Commatic Repulsion''' - This rule is best summed up in Flora Canou's statement that things repel the similar but not identical.  To illustrate this principle, let's take a look at the VImin chord as is present in [[meantone]] and contrast it to the situation outside of meantone.  Believe it or not, the meantone VImin chord has no fewer than two separate functions relative to the Tonic.  First of all, there's the Relative Minor functionality, which is 5/3–1/1–5/4 relative to the Tonic and can tonicize as a new Imin either temporarily, as in a deceptive cadence, or permanently as in a modulation.  Secondly, there's the Tertiary Dominant functionality, which is 27/16-81/80-81/64 relative to the Tonic and, as the name suggests, acts as the Dominant of the Dominant's own Dominant.  While both of these are fused together in meantone, these two functions are separated exactly by the syntonic comma in non-meantone environments, and the only way to use a VImin chord with all three functions is to temper out the syntonic comma.  As Flora Canou has stated:
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+However, in non-meantone settings, it is possible to have a chord which shares its root with the Tertiary Dominant and shares both its third and fifth with the Relative Minor.  Since such an arrangement results in a wolf fifth, and since the wolf fifth is a dissonance requiring resolution, one could argue that such a chord has a function distinct from the more usual options- specifically one which involved in interrupted cadences, as well as in starting cadences that "wind down" such as VImin-IVmaj-Imaj or even VImin-Vmaj-Imaj.  This particular function is what I call the ''Major Contramediant Tensive''.
 '''Primary Adpositive Purity''' - This rule is that for every chord root located one step away from either the Tonic, Dominant or Serviant along the Circle of Fifths, there is a demand for the fifth of the chord in question to be within 3.5 cents of a just 3/2.  This means that the Tonic, Dominant, Serviant, Supertonic and Subtonic chords all demand a perfect fifth as the fifth of the chord, whether you are building the Tonality upwards or downwards.  One of the obvious applications of this is that chords built with wolf fifths must have roots located three or more steps away from the Tonic along the Circle of Fifths, and that when two notes within a given Diatonic system are separated by a wolf fifth, they both must likewise be located three or more steps away from the Tonic along the Circle of Fifths.