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The DOMINANT chord
A DOMINANT chord is one whose power comes from itsSecondary Notes,
the interval of diminished fifth between its third and its seventh (G7
).
Major Seventh (C+7
) and Minor Seventh (Dm7
) chords are not DOMINANTs
because they have the interval of perfect fifth between the third and the seventh.
They may be chromatically "DOMINANTIZED"
by either flattening the seventh (C7
) or sharpening the third (D7
).
Inversely, asixth chord(F(6)
) will be DOMINANTIZED by flattening the third (Fm(6)
).
The TONIC Chord
A TONIC chord is evidently a chord of rest,
preferably withoutMOTRIX(seventh or sixth),
rhythmically disposed on aBeat rather than on an Off-Beat.
The ANTE 1 Chord
A strong ANTE 1 chord is one whose power comes from itsPrimary Notes,
the interval of diminished fifth between its root and its fifth (Bm7-5
with flat five
-5
),
to produce the most satisfyingModulation 3.
It is diatonic as the BUCKLE chord [VIIm7-5
] where it is the ANTE 1 of Am [IIm7-5 of VI],
but the ANTE 1 of C [IIofI] should beDiminished, with the Ab,
to possess the required strength [IIm7-5
].
The Circle
The imposition of a Key is to be found in itscircle,
especially the end of the circle, the three ANTEs, with the DOMINANT and the
TONIC
[III,VI,II, withVandI].
Modulating to another Key is achieved by shifting into ITS circle in order to
use the end.
Anychromaticisminvolved in the Modulation will only be with respect to the original Key,
not with the new Key where everything is normal, being in its own circle.
To understand how Modulations "move" to a new circle, we must look back
to see howMetamorphoses"move" to a newswing,
and establish an inter-level relationship quite similar to that
between Addition and Multiplication in mathematicalNumerical Structure.
This will establishModulation 1and the others will develop from it.
Two levels
A. The circle is the result of repeated applications ofMetamorphosis 1.
It is the simplest Metamorphosis and it is applied once on each chord,
constantly changing Swing each time.
B1. Modulation 1 will consist of repeated applications of theDOMINANTchord [V7
].
It is the simplest Modulation and it is applied once on each chord,
constantly changing Circle each time.
B2. Modulation 2 will consist of repeated applications
of bothDOMINANT and TONICchords [V7 I].
It is the next Modulation in complexity and it is applied once every two chords,
changing Circle each time.
B3. Modulation 3 will consist of repeated applications
ofANTE 1, DOMINANT and TONICchords [II7-5 V7 I].
It is the next Modulation in complexity and it is applied once every three chords,
changing Circle each time.
B456. And so on, with Modulations 4, 5, and 6,
all the way back to the possibility of a complete circle.
Interior-Exterior
As is the case inMetamorphoses, we will find cases of Interior/Exterior in our Modulation Circles.
Modulations within a given circle will be considered Interior,
such as Modulations1,2,3, and456,
while Modulations between 2 different circles will be considered Exterior,
such as seen in the subsequent sections, starting withMajor To Major,
followed byMajor To Minor,Minor To Major, andMinor To Minor.
Voice-Leading
TwoVoice-Leadingsare currently used in the circle
Voice-Leading C, which is binary and more popular, as well as
Voice-Leading A, which is ternary and more musical.
We will be using both.
Performance Disposition
To achieve maximum strength at the end of all circles (for the present that of C Major),
Orbit 1toOrbit 1(the notes D - C) will be placed in the Soprano for Voice-Leading C, and
Orbit 2toOrbit 1(the notes B - C) will be placed in the Soprano for Voice-Leading A.
ToModulation 1
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