Tonic base. Dually he considers the discharge 6-5 of the
Subdominant agent into the Tonic associate. Both discharges are highly
significant for key determination. The “DualDischarge”-Denotator of the FormPiMod12DualSteps expresses this duality:
Function: Dominant - Subdominant. The initial inversion e711 maps the
G-Major-Triad onto the F-Minor-Triad and vice versa (see DualFunction1),
and it maps the G-Minor-Triad onto the F-Major-Triad and vice versa (see
DualFunction3). Furthermore it exchanges the G-“Dominant-Seventh-Chord
and the F-Minor-Chord with added Sixth (see DualFunction2).
Cadence: Authentic / Plagal. With respect to the functional dualism
between Dominant and Subdominant and the modal dualism between the two
Tonic variants as well as the two dominants there results a dualism between
certain authentic and plagal cadences, namely those which differ modally in
both chords:
Semicadences: These are obtained as retrograde versions of the
cadence steps. It is clear that the resulting denotators fit into the
PiMod12DualSetSteps-Form. We omit the details. The inner symmetry of all
four Dual-Forms makes clear, that it is not possible to formally decide upon
what is left and what is right in Harrison’s table.
Alteration: Sharpen / Flatten. Harrison lists two corresponding pairs of
alterations:
the flattening of the 7th scale degree in C-Major B Bb together
with the sharpening of the 6th scale degree AbA in C-Minor.
In modulations these alterations produce, for example, a 4th scale
degree in F-Major and a 2nd scale degree in G-Minor, respectively. The
alteration-pair as well as both resulting Scales are explained by suitable
denotators Alteration1 and DualAlteredScales1.