PhD Thesis - Folio of Compositions with Commentary

Chapter 3 String Quartet
by Robert Davidson

Scores | Articles | Recordings | Gigs | Contact | Home

Relevant scores and recordings:
String Quartet PDF | String Quartet MP3 | MP3 Player | Acrobat Reader

The String Quartet represents a new level of emotional expression in my music.  In previous compositions I have tended to distrust overt expression, but in the String Quartet I wanted to deal with questions of how the individual makes meaning in an environment where there is little possibility of certainty.

An unstable, unresolved fourth opens and closes the work.  The sonority underlying this fourth is an A minor triad in second inversion combined with an E major triad.  i and V are superimposed - tension and resolution are mixed together but remain unresolved.  This sonority is stretched out for two-and-a-half minutes at the beginning of the piece.  Harmonic rhythm, here at the beginning and throughout the piece, is very slow, with large expanses constructed upon single static sonorities; the first seven minutes contains only four chords.

The piece may be divided into four sections - a long opening alteration of canons and melodic passages (from the beginning until letter H), a gradually cumulative counterpoint and a series of instrumental solos (letter H to letter T), an exuberant texture dominated by arpeggiated figures (letter T to letter Z) and a recapitulation of earlier material (letter Z to the end).

The principle of gradual disclosure is a thread that runs through the piece.  Alap­-like, [1] each of the four sonorities of the opening section is explored from the peripheries before being put together clearly, note by note, as accompaniment for the first violin's melody.  The chords are suggested in canons before being definitely stated.  Similarly, the contrapuntal texture at letter J is put together part by part, accumulating its energy gradually.  In another instance, the dense, twelve-part chords at letter X only appear after they are suggested by the six-part chords of the preceding arpeggios.

The four sonorities expounded in the opening section, articulated first in canons between the viola and cello and then as pulses accompanying the first violin, are each based on a seven- or eight-note mode.  The first is the ascending form of the A melodic minor scale (the bass on the dominant), the second is an E phrygian with raised third and seventh (resulting in two augmented seconds), the third is F# lydian with flattened seventh, and the fourth is a B octotonic scale alternating minor and major seconds.  The bass notes - E, C#, F#, B - are patterned as the expansion of a third to a fifth.

Figure 3-1 Progression of sonorities in opening section

In parallel with the construction of sonorities from overlapped triads, the texture is constructed from overlapped melody in canon.  Canon is an effective method of balancing familiarity and surprise, as each new bar is a mixture of old and new material.  Each of the canons explores a small number of motifs in a way reminiscent of an Indian musician exploring a raga.  These motifs reappear in different forms throughout the piece, binding together diverse material with an organic sense of unity.  An examination of some of the motifs will illustrate this.

A rising motif opens each of the canons.  The opening interval varies in each canon - in turn a fourth, a fifth, an augmented fourth and a minor third (fig. 3-2).

Figure 3‑2 Occurrences of rising motif

The motif is taken up in various forms to launch each of the first violin melodies of the opening section.  In the second section, the underlying cello part, which forms the foundation for the section, is based on the rising first part of the motif (letter H), and each of the instrumental solos, excepting that of the second violin, begins with the motif (letters O, Q and R).  The opening of the third section at T also features the motif, used throughout the melodic duets which follow. In bars 309 and 313, and in the viola and cello at V, the last four notes of the original motif are transformed.

Another motif features the characteristic shape of a falling small interval followed by a rising large interval.  Appearing first in the opening canon, it is transformed in various ways throughout the piece with a focus on its characteristic falling-rising shape.  In some instances, the lower two notes are inverted (fig. 3-3).

A motif introduced in the first violin solo is referred to for both rhythm and contour.  Its falling thirds are inverted, expanded by interposing notes, and its quintuplet rhythm is expanded into sextuplets or septuplets (fig. 3-4). 

Figure 3‑4 Occurrences of thirds motif

Contracting intervals are used as a means to approach a single pitch in another motif.  First heard in the first violin, it is inverted, augmented, joined with the quintuplet rhythm of the thirds motif, and varied in its intervallic content.  Its implication of contrary motion links it with passages such as the transition at the end of the first section (letter G), and the expansion to an octave which marks the end of each violin solo in the first section (bars 49, 81 and 116).

Figure 3‑5 Occurrences of contracting motif

All of these motifs converge at the beginning of the second section in the cello line.  This bass is the foundation upon which a dense web of counterpoint is gradually assembled, the other parts emerging from it in a manner reminiscent of 14^th century motet writing, in which the upper parts often decorate the tenor.  According to Johannes de Grocheo, the tenor is "that part upon which all the others are based, just as the parts of a house or building are placed upon a foundation.  And it regulates them and gives them their quantity, just as the bones support the other parts of the body." [2]   As in medieval motets, the counterpoint here is constructed line by line, a process which is made evident as the parts accumulate.  This results in a sense of gathering and growth, intensified by the increasing use of semiquavers with each successive part.

The chord progression that takes up the first section reappears as accompaniment to the instrumental solos in the second section, with one chord for each instrument.  The notion of chord progression as a focus is taken up again at the end of the third section.  Here there is a much quicker succession of chords (glissandi between certain chords creating a curious sense of vertigo), and a greater density within the chords themselves; each of the chords is a combination of triads, partitioned by instrument.  In the first chord, for example, at bar 383, each instrument plays a triad in open voicing: the cello sounds C minor, the viola Eb major, the two violins D minor and Bb major, or i, ii, bVII and III.  Each chord in the progression similarly compounds the fundamental functions of tonic (I), pre-dominant (ii or IV) and dominant (V or VII).  There are important exceptions, found in the chords at bars 393, 404 and 407.  These sonorities do mix triads, but they are not in functional (or diatonic) relationship.  Rather, the roots of each triad are separated by a succession of either major or minor thirds.  Each triad is voiced with its third at the top, its pitch doubling as the root of the next-highest triad, and the entire sonority is bounded at its extremes by notes of the same pitch class.  All of the other chords in the progression, however, are combinations of functional triads.  This, then, is a clear case of stratified or "frozen" counterpoint, functional triads being partitioned not sequentially, as in traditional harmony, but by instrumental assignment and registral placement.  The structure of each chord in the progression is easily seen in table form (fig. 3-6).

Figure 3‑6 Tonal stratification in arpeggio chords

Cohesion in the chord progression is derived from the bass.  The lowest notes of the cello move in a simple rising contour, moving through an octave from C to C, and then outlining a V-I cadence from E to A, returning to the work's opening key.  Sequential movement also gives direction to the progression.  The cello part, for example, is characterised by a series of sixths and fifths arranged in stepwise motion.  The violin moves in parallel downward steps for a few chords at a time before rising to a higher pitch and repeating the process. 

Figure 3‑7 Sequential movement in the cello part, bars 383-92

Succeeding the chord progression is a recapitulation of earlier material.  First to return is the second section's contrapuntal passage with the entry sequence reversed, concluding with the bass line played in unison.  Still earlier material - the opening canon - is then restated, but now in four parts.  Following a reprise of a transitional passage, the work closes in an understated way, maintaining the unresolved second-inversion harmony heard in the opening bars.  This is a typical example of my tendency to leave pieces open ended, as if they are finishing with a question mark rather than a full stop.

© 2003 Robert Davidson