CHAPTER 3 (PART 2)
NON-FUNCTIONAL CHORDS
Auxiliary Chords
Auxiliary chords are formed by the stepwise movement (up or down) of one or more of the voices away from a harmony note in one chord to form a new chord. The voice(s) then return to the originals note(s) to re-form the original harmony. Normally the auxiliary chord is made up solely of notes from the original chord plus notes involved in the auxiliary movement. In this case they arise totally out of voice leading. (But see note below on auxiliary chords in root position). These auxiliary chords are non-functional whereas the chords surrounding them are functional. This is because the auxiliary chord merely elaborates the main functional chord, its purpose being to prolong the functional harmony. Auxiliary chords are used extensively to prolong the tonic harmony in static harmony (see chapter 2). They can also be used to extend the dominant to form a dominant prolongation. (See chapter 5.). Sometimes auxiliary chords can be used to decorate individual chords in dynamic harmony especially where this is slow moving.
The auxiliary chord is named by analogy with the auxiliary note. The following example contains auxiliary notes marked with an *:
The short duration of the auxiliary note does not create a feeling of
a change in the harmony. An auxiliary chord, is an extension
of the auxiliary note such that the duration of the auxiliary note and
the way the note sounds in conjunction with the other notes of the chord,
creates a sense of a change in harmony. This type of chord has its origins
in 16th century polyphony. See voice leading
appendix for more details.
Using the analytical symbols introduced earlier, the following harmonic outlines indicate some of the possible auxiliary chords within the diatonic major scale:
.
The examples marked a) are not very common (at least in the inversions shown) as they generate the secondary triads VI and III.
The examples marked b) are very common since they generate the primary triads IV and V by the simultaneous auxiliary movement of two voices.
The beaming of the white headed notes to black headed notes in these
and other harmonic outlines is used to indicate the melodic movement in
the parts. White headed notes are components of the functional chords
and the black headed notes are components of the non-functional chords.
The following example includes both chords of b) and also an example of the V7 chord used as an auxiliary chord (second of c)):
In bar 3 the E rises to F and returns to the E whilst the G rises to A and returns to G. The C major chord is thus transformed temporarily to an F major auxiliary chord. In bar 4 the E and C descend to D and B and return to E and C thus creating an auxiliary dominant G chord. In bar 2 the additional movement of the E to F and back creates a dominant 7th auxiliary chord.
Similar auxiliary chords may be drawn up for the minor key, In this case,
the 7th degree of the scale is usually sharpened to form the major chord
V.
The following figure shows some of the common possibilities involving chromatic harmonies:
.
The examples a) and b) involve movement in one direction only.
a) contains two auxiliary notes: one diatonic, E rises
to F and returns to E, and one chromatic: G rises to A-flat and returns
to G. The auxiliary chord formed is the minor subdominant
chord which occurs naturally in the minor key. In b)
all three notes of the tonic triad rise a semitone and then return to
the original notes. This chord is usually referred to as the Neapolitan
6th chord and is usually deployed in first inversion to avoid the
parallel 5ths that would otherwise arise.
The next three auxiliary chords in c) (i), (ii), (iii) are the three possible diminished 7th chords. I've shown all three for completeness and to introduce the terminology to be used in this book. (i) and (ii) are common auxiliary formations, (iii) is more usually deployed as a passing chord between I and II as the C - B-flat movement has a tendency to continue downward to A rather than to return to the C. (see next section - passing chords).
Auxiliary Chords in Root Position
Sometimes auxiliary chords are used in root position (could be any triadic chord). In this situation, they are not composed entirely of voice leading (notes of the main chord plus auxiliary notes) because of the way the bass moves from one root to another. These chords will still be referred to as auxiliary chords, by analogy with the auxiliary note, because of the way the chord returns to its preceding chord. These root position chords are also used to create static harmony. In this situation, it is possible to have passing chords that fill in between the main chord and the auxiliary chord. So there are really two types of auxiliary chord: those that are in root position and are capable of further elaboration are really functional chords and those that arise totally out of voice leading which are non-functional. In either case, they can be used to create static harmony. In different styles of music, many different chords (diatonic and chromatic) have been used as auxiliary chords to create static harmony and in this way, the choice of auxiliary chords contributes significantly to the style and mood of the music. I will include further examples at a later date but the distinction between these two types of auxiliary chords does not normally create too much difficulty because both types are used in similar ways.
Description of Chromatic Chords
This is an appropriate point to introduce the terminology to be used in this book for chromatic harmonies, in particular the diminished seventh chord. The following figure demonstrates some of the possible diminished 7th chords in C major. Most books treat these as borrowed from a related or unrelated minor keys or as dominant substitute chords. However as neither of these designations accurately describes the true function of the chords, I will introduce an alternative, simpler, terminology here which acknowledges the melodic rather than harmonic function of the these chords. I will use the terms: tonic leading, dominant leading and supertonic leading to describe the three possibilities regardless of the particular spelling of the chord. The tonic leading diminished seventh chord is named in this way because it contains the leading note which leads to the tonic, the dominant leading diminished seventh chord contains the sharpened 4th degree of the scale which leads to the dominant and the supertonic leading diminished seventh chord, because it contains the sharpened tonic which leads to the supertonic note. This terminology makes identification and discussion easier.
In the following example, Tchaikovsky uses the tonic leading diminished
7th chord as an auxiliary chord in the static harmony in Valse Des
Fleur. The static nature of the harmony is emphasised by the use of
a tonic pedal.
Note: There is also a description of the auxiliary note and auxiliary chords in the Voice Leading Appendix at: Auxiliary Notes and Linear Progressions and in subsequent sections.