PhD Thesis - Folio of Compositions with Commentary

Chapter 6 Trio for Strings
by Robert Davidson

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I came to write a trio for violin, viola and double bass partly out of a desire to play in such a trio myself as a bassist.  It is a particularly resonant ensemble, and the bass is free to occupy a wide range with no cello as competition.

Like Tyalgum, the Trio realises the concept of framing.  The middle movement, which is the real "meat in the sandwich", is surrounded by miniatures of similar character.

Both are based on polyrhythms as a means of generating non-coinciding attacks.  These are very compatible with the Fuxian counterpoint I tend to favour because of their resemblance to ligatures of fourth species counterpoint.  A triadic basis constrains the harmony and allows for a sense of dissonance and resolution, the latter being delayed for long periods to give a sense of forward motion.  I find the polyrhythmic organisation attractive both for its separation of the parts into partitioned regions of time and for its large-scale palindromic rhythm.  Both of these aspects seem to me particularly effective in setting up conflicts between linear and nonlinear ways of dealing with time.  The texture is inspired by the mood created by Guillaume de Machaut's mid-fourteenth-century polyphonic work Hoquetus David.

In the first movement, the polyrhythm pattern is 4:5:7, a ratio which resolves to a coinciding downbeat after 140 rhythmic units.  Units being semiquavers, a resolution occurs after every seven five-four bars, at which point the instruments exchange roles, swapping to different subdivisions of seven, five or four.  Two of the three voices (in 5:4 ratio) coincide each bar, with a tendency to resolve to a consonance, so that the music progresses in five-beat phrases.

Each of the three sections, marked off by rhythmic resolution points, has a different harmonic focus.  An octotonic scale (alternating semitones and tones) is used throughout the first section.  The scale continues in the second section, but there is a more dissonant emphasis and use of sonorities suggesting b7#9 chords favoured in certain jazz genres.  The third section begins with a strong resolution to an open fifth chord and introduces a more relaxed natural minor scale, resolving in the last bar to the opening G major triad.

A 3:5:7 ratio runs through the third movement.  Again, the instruments exchange roles at each rhythmic resolution, which occurs after 105 quavers, or thirty-five beats organised as eleven nine-eight bars plus a single six-eight bar.  Unlike the first movement, bar-long phrases do not match the coincidences of the smaller ratio (3:5), which tend to set up a separate stratum of time.  The three sections of the movement are divided, as in the first movement, by harmony, with the first two sections sharing an A natural minor scale and the third section introducing an Eb into the scale to produce an F lydian b7 scale, as used by Bartok in Music for String Instruments and Percussion.  The first section returns as a coda to complete the overall harmonic progression of i III (V/VI) VI i.

It is in the second movement that the essence of the String Trio is located.  Indeed, this movement is often performed alone as an independent piece.  It carries on from the outer movements the notion of different strata of rhythm, but expressed in a freer, more intuitive way.  There are three strata of time at the beginning - a melody consisting of long notes in the violin, an additive process, constructed of quavers, in the viola, and a marking out of crotchet beats in the bass.  Each stratum operates in its own system of chained rhythmic cells of varying lengths.  The smallest element of division is not the note but the rhythmic cell, rather as a mosaic is built from small chunks of material.

There is some semblance of a series pattern in the chaining of rhythmic cells in each part, as is demonstrated in fig. 6-1.

Violin (crotchets): 5 5 5 5 3 3 5 3 5 5 3 2 2

Viola (quavers): 5 7 5 5 5 7 7 5 5 7 5 5 5 7 5 5 5 5 5 7 7 6 5 5

Bass (crotchets): 7 4 6 6 7 4 6 6 4 5 5 5 5

Figure 6-1 Rhythmic chains (beginning of pattern shown in score)

A clear pattern, however, does not emerge.  The character of each part derives instead from the preponderance of cells of a certain length, with cells of five units being the most prominent.  This preoccupation with the number five continues through the piece (and is suggested by the central place accorded subdivisions of five in the outer movements).

At different points the various strands serve to organise the rhythm for the whole ensemble, which changes for a time from its diversified rhythm to rhythmic unison, throwing a spotlight on what has been there all along, but buried in the texture.  This occurs, for example at bar 35, when the rhythm is centred on the viola's part.

As well as rhythmic strata there are tonal strata.  In the opening bars, the violin outlines a G minor triad, the viola plays in C minor and the bass in F minor, resulting in a frozen counterpoint texture of ii-V-i in F minor, continuing almost unabated until bar 80, when the stratification changes to vii-V-I in Ab major.  This sort of long term stability of harmony is typical throughout the movement, and the large scale harmonic structure may be analysed according to its stratification as in fig. 6-2.  Each of the tonal areas is stratified with combinations of I II V and VII in various forms.  The final three tonal areas - II vi i - look unusually nonlinear at first glance.  But examining the violin part, it becomes clear that there is an understated II V i progression occurring.  The violin stresses Cm as VII of Dm, but its prominence in the violin part gives it some weight as V of the following Fm, giving the cadence a sense of resolution.  Reinforcing it is the bass' Dm acting as v for the following section's G minor in the violin (and the continuance of D as the first note of the violin melody).

Much of the material is characterised by circling figures, often using the number five in some way, creating motion without real direction.  The short cells in the viola and bass at the opening have this quality of turning in upon themselves.  From rehearsal numbers 2-4, and 15-18, each instrument plays similar self-focused figures as if they are cogs spinning in a complex machine.

Restrictions are often placed on available notes, such as in the use of scales.  The violin and bass are limited to a pentatonic scale in bars 18-34, for example, and the viola solo at rehearsal number 18 uses a tonally ambiguous pelog-like six-note scale.  The passage includes allusions to C major, D major, B minor and G major, its most prominent tonal aspect being the third-fifth oscillation of D-F# to C-G.  At 20, the viola uses these same four notes, presented in varying orders, as a restricted region in the harmonic space.  The violin joins with a different four-note set, setting up its own pitch domain, with notes either a fifth or sixth above the viola notes, and the bass a different one again, a sixth below the viola.  Each is based on notes that are easily playable in one position on the lowest string.  When combined at 25 (the bass patterns transposed up an octave to clarify the harmony), the three patterns produce a series of highly resonant first- and second-inversion triads.

The gradual increase of textural density is one of several linear processes that give direction to the music.  A similar process occurs in the passage preceding it, from rehearsal numbers 13-18.  Agitated, dense motion is steadily reduced to a still, quiet drone.  The process occurs in stages: at 15, semiquaver motion is exchanged for a quaver-based rhythmic counterpoint, beginning staccato and ending legato.  Overlapping dotted crotchets replace the quavers at 16, and at 17, a slow 5:4 rhythm (alluding back to the first movement) reduces the density further, eventually resting at 18 on a drone.

The drone sets the stage for a meditative viola solo.  Each instrument is made the focus at different points. In performance, several of the solos are usually improvised, though a fully written out version of each is included in the score to allow performance by musicians uncomfortable with improvisation. An arch structure is created by the ordering of the solos - violin, viola, bass, viola, and again violin.  Following the final violin solo is a short recapitulation of the opening material featuring the violin.  The final bars strip back the harmonic material to the interval of a third in each instrument to represent the component triads (G minor in the violin, C minor in the viola, and F minor in the bass), forming a ii-v-i cadence frozen in a forever unresolved state.

© 2003 Robert Davidson