Greetings and welcome.
Part One of this Segment explores Inverted V7 chords, and their Natural Resolutions in
Major.
Further installments will explore inverted V7s in Minor Keys.
Writing exercises In between will provide you, the student, with opportunities to apply
and practice these skills.
Theory, and Practice!
Any of the three tones of a triad can be positioned as the bass note.
The three positions of a triad, therefore, are the root position, first inversion, and
second inversion.
The bass is figured as shown: 53 (meaning root position), 63 (1st inversion), and 64
(2nd inversion). [mus]
Since any of the four tones of the dominant
7th chord may occupy the bass position, reason dictates that the V7 must have not only a
first and second inversion, but also a THIRD INVERSION, for a total of four positions.
Complete figures of the thorough bass are as follows: 7, 653, 643, and 642.
[mus]
The Bass of the First Inversion V7 is the Third of the chord.
Adding the root, seventh, and fifth of the complete chord puts the upper voices at respective
intervals of 6th, 5th, and 3rd above the bass note.
Hence, the figuring 653, often abbreviated as 65.
This applies regardless of whether the upper voices are arranged in close position or open
position.
What counts is the fact that the Third of this seventh chord is situated in the LOWEST
voice. Close. [mus]
Open. [mus] The Bass of the Second Inversion is the Fifth
of the V7 chord.
The upper voices, assigned the Third, Root, and Seventh of the chord, are at the intervals
of 6th, 4th, and 3rd, respectively, above the bass note.
Hence, the figuring 643, often abbreviated as 43.
This applies regardless of whether the upper voices are arranged in close position, or
in open position.
What counts is the fact that the Fifth of the seventh chord is situated in the LOWEST
voice. Close [mus]
Open. [mus] The Bass of the Third Inversion is the Seventh
of the seventh chord.
The upper voices, assigned the Fifth, Third, and Root of the complete chord, are placed
at the respective intervals of 6th, 4th, and 2nd above the bass note.
Hence, the figuring 642, abbreviated as 42, often just 2.
It doesn't matter if the upper voices are arranged in close position, or in open position.
What is important is the fact that the Seventh of the V7 chord is situated in the LOWEST
voice. Close. [mus]
Open. [mus] In practice, the 7th of the V7 inverts as
a major second, and also forms a tritone (diminished 5th/augmented 4th) with the Third of the chord.
The Third, in turn, is the LT of the key.
These are dissonant intervals, and dissonance must be properly dealt with.
With regard to the Resolution of the V7 inversions, let us reconsider the paths of least resistance:
The Root of the V7 is also the 5th of the tonic triad.
It is the common tone between the two chords, which we should retain in the same voice.
Inverting the V7 does not alter this relationship.
Reconsider.
That the Third of the V7 is the LT.
With few exceptions, the LT MUST resolve up, to the tonic tone, especially when the LT
is in the bass or soprano.
Reconsider.
That the Fifth of the V7 is the Supertonic of the key, and as such may resolve by step
either down or up.
Upward resolution of the Fifth leads to doubling the Third of the subsequent tonic triad, which
is fine.
An upward leap of a fourth (or downward skip of a third) – to the dominant scale degree
– is sometimes encountered as well.
Here, the LT is in the bass, an outer voice.
It is for this reason that the First inversion or V65 chord must in practice resolve to the
root position I, or Tonic triad. [mus]
Observe that both Third and 7th of V7 resolve by diatonic step in contrary motion;
no skipping or leaping – and the root of the V7 is retained in the same voice on into
the I chord.
The same Principle applies to Open Position chord voicings; the LT in the bass – the
chord Third – must resolve upward, the 7th downward.
Observe again that both Third and 7th of V7 resolve by diatonic step, in contrary motion,
and the V7 root stays in the same voice.
Only the Fifth of the V7 has a choice of direction, whether up or down. [mus]
With the Fifth in the bass, there are two
possible chords of resolution: I, or I6.
In the first instance, resolving to the Root position I presents nothing unusual, whether
close or open voicing. [mus]
As for the second instance, resolving to the
I6, the third of the first inversion tonic chord is naturally doubled. [mus]
The V7 chord in Third inversion is figured
as shown: "six-four-two" or just "four-two" (or "two").This inversion must resolve
to the First Inversion Tonic or I6 chord.
Why?
7ths are dissonant; when the 7th of the chord is in the bass, it resolves its dissonance
by descending a step. [mus]
Here are V42s in which the Fifth of the chord
– the supertonic – resolves by an upward step.
The motion of remaining chord members follows the natural course of least resistance: common
tones, conjunct motion to nearest neighbors, and so forth. [mus]
On the other hand, here are a couple of V42-I6
progressions with a leap, or skip, to the dominant scale degree. [mus]
Perfectly acceptable.
Today, we discussed the three inversions of the dominant seventh chord, how they are figured
in the thorough bass – V65, V43, and V42 or V2 – and how to resolve the dissonances
inherent to the V7 chord.
Interestingly, these always work as complete chords, the inverted V7s, and their resolutions
to the I or I6.
Yes, it is sometimes necessary to double the Third of the tonic triad, but neither chord
needs to be incomplete; this is unlike the Root position cadence, where we often found
it better to omit the Fifth of the V7, in order to resolve to a complete tonic chord.
In a subsequent presentation, we'll present a few practical exercises on writing the various
inverted Dominant-Seventh-to-Tonic-Triad progressions.
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[Copyright © Mark Priest, 2017]
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