Some technical aspects of my quintet ‘a new day in the desert’

I’m having to submit a bunch of stuff for my mid-candidature review for my PhD. Lots of fun, I can assure you. At the very least it forced me to write the piece below, which will be useful to me looking back in a couple of years and thinking to myself “oh god, I was an idiot back then!” More pragmatically, I currently still remember what I did in the piece, and when I have to talk about it in my final submission for my PhD, and my brain is foggy, it’s all here!

Anyway, here’s the draft score, if you like. It hasn’t been performed yet, but Ensemble Fractales plans to perform it in Belgium later this year.


Background

This work is the first piece that I wrote following Quite Early Morning, no. 2. This new piece inaugurates an approach to counterpoint the elaboration of which will be the subject of my final folio and thesis. The change in approach is marked. Where Quite Early Morning, no. 2 was aiming at a marginal polyphony emerging from gestalt ensemble gestures, and was almost entirely intuitively composed (i.e. no pre-compositional planning), this new approach aims at a far more thoroughgoing polyphonic texture, with a high degree of independence between lines, within which relations between lines can be drawn. The latter approach has a heavy degree of pre-compositional planning and a greater degree of complexity at many levels, in order to ensure: the independence of lines over time, their own self-development and internal contradiction, and their interrelation with each other.

Characters/vertical layout of voices

This work deals primarily with the vertical stratification of lines and, once this is established, its progressive easing across the course of the work. To achieve this stratification it attempts to distinctly define each line according to a ‘character’: essentially a bundle of parametric information forming a particular expressive identity. Obviously, in a mixed ensemble such as this, the instrument itself helps give this identity a long-range coherence by maintaining a relatively stable timbral identity over time. But beyond this initial identity, the registral placement of each instrument-line is very important for keeping each line perceptually distinct. In the opening of this work, the violin sits well above the rest of the ensemble, the cello is in the middle register, shadowed partly by the flute. On the other hand, the piano and the bass clarinet play across their entire registers, destabilising any simple vertical stratification.

Metric functions

One particular way to help define the different characters of the lines is to give each of them a different relationship to the global metre. I discuss this approach in my recent conference papers, so I won’t describe it in detail here. This is the basic arrangement at the beginning of the work:

Bass flute: Extra-metrically determined. Additive structures based on demi-semi-quaver durations.

Bass clarinet: Metrically determined. Measures are cut into unequal halves (generally ‘short-long’) that are then turned into the basis of a sequence of tuplets.

Violin: Metrically determined. Sequence of tuplets using entire bars as denominators

Cello: Outlining metre. Articulating a series of groupings (of 3 or 2 semiquavers) within each metre.

Piano line 1: Extra-metrically determined. In part it is a rhythmic diminution of the cello line.

Piano line 2: Metrically determined. Measures are divided into one or two parts, which form the denominator for a sequence of tuplets.

This is the opening relationship. These different metric functions, along with other characteristics, are increasingly shared between voices as the work progresses.

The global metric construction is based on repeating sequence of three different metric progressions, each of which begins by alternating between long and short bar-lengths and ends with repeated bar-lengths of 4 or 6 semiquavers. The idea, as outlined in my conference paper ‘The ideology of polyphonic time’, is to have a global metric structure that has its own trajectory and has an impact on the individual lines themselves. This is something I am developing in current pieces, and is somewhat undeveloped in this work.

Rhythmic processes

On top of the relationship of the individual lines to the metre, each line is given a particular set of rhythmic processes, potentially including phrase lengths, tuplet numerators (e.g. violin), number of notes in a gesture (e.g. clarinet), a deletion filter (e.g. violin), additive sequences in equal subdivisions (e.g. bass flute).

These give the basic rhythmic ‘tendency’ of the line: e.g. whether it is speeding up or slowing down, whether it is becoming more or less sparse, whether the gestures are growing shorter or longing.

Globally, the phrase lengths of each of the lines are slowly contracting across the course of the first major formal section, until there is a rapid staggering of entries from bar 51.

Interval structures/processes

For each line, I construct a particular process of melodic descent/ascent. Each process tends to have at its core a general descent or a general ascent, but over the top of this is added other numeric processes to give the line more shape on the local level:

Intervals: repeated notes
Ascending 3 0.5 2.5 1 2 1.5 2 1 2.5 0.5 3 0.5
Descending 0.5 0.5 1 0.5 1 1.5 0.5 1 1.5 2 0.5 1
Aux addition 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1
Result 2.5 0.5 2.5 0.5 1.5 1 1.5 0.5 2 -1.5 3 0.5

(Where ‘1’ equals an ascending semitone, ‘0.5’ an ascending quartertone, ‘-1’ a descending semitone, and ‘-0.5’ a descending quartertone)

In this example (taken from the precomposition of the violon part), there is a repeated sequence of ten numbers in palindrome 3,0.5,2.5,1,2,1,2.5,0.5. Added to this is a repeated sequence of three numbers: 0,0.5,1. Set against this, a process of growing subtraction 0.5 – 0.5,1 – 0.5,1,1.5 – 0.5,1,1.5,2 – etc. This produces a long-range interval sequence that begins by ascending, and gradually turns into a descending line. Yet due to the layers in the formation of this sequence, this basic logic (ascending/descending) is partially obscured by local level twists and turns.

I discuss this idea in a blog post of October 14, 2015.[1] In this post I called it ‘complex motion’, since each line of the polyphonic discourse itself moves in a variety of directions almost simultaneously, adding up to an “interesting set of ever-shifting relations between linear directions”.

As opposed to earlier, more intuitive, works, this approach allows for the control of the long-range trajectory of a line, without resorting to a simple uni-directionality.

In the highly stratified section of ‘desert’, there is no precompositionally conceived global harmonic framework guiding the voices, as one would find in traditional counterpoint. This question of harmony is something that I am exploring in current and future pieces, and is treated in only a very rudimentary way in this piece (see below: ‘Global form’).

Other parametric processes

Each line also tends to have further parameters that are turned into processes in order to strengthen each line’s identity as well as to provide a greater sense of trajectory and development within each character. These other parametric processes usually concern the overlayering or intervention of particular playing techniques on the various instruments: left-hand tapping, harmonics, pizzicato, trills, piano clusters, and so on. Each of these is layered in according to its own complex process akin to the one above for violin pitches.

Unanticipated connections

With this heavily stratified discourse set up, it is inevitable that, in the compositional process, I will begin to perceive ‘emergent’ connections between lines that were unanticipated during the precompositional phase. These could be, for example, rhythmic unisons, phrases beginning or ending at the same time, obvious pitch relations (unisons or octaves being the most obvious), or similar melodic motion (both lines ascending or descending).

As I mentioned in my October 14 blog post, many parameters in the composition are left undetermined so that they can be used to highlight or disguise these emergent links between voices:

A number of parameters (such as dynamics and articulation/playing technique) are left open, which allows me to make the line relate to other events taking place in the texture once I’ve begun to write them all in and seeing what possible relations emerge. (At this stage this is one of the primary means by which I’m creating some form of ‘drama’ in the work…).

Similarly, I was willing also to ignore the precompositional processes if they were leading to undesired outcomes, or if I wanted to create new links between parts: e.g. create rhythmic unisons where precompositionally there were none.

Global form (as contrapuntal function)

Apart from the spontaneous, unanticipated connections between lines, I decided on global formal processes that cut against this stratification and put common constraints on the direction of the lines. In this sense, global form is not something separate from contrapuntal or polyphonic ‘material’ that could be just as well filled by some other kind of material, but instead is a function of counterpoint, one way in which the independence of the lines is mediated by a global common concern.

As part of its fundamental conception, the work alternates between total stratification (tempo quaver=75) and more integrated texture with a looser division of material, more rhythmic unification, and a harmonic structure of I-V7-I-IV-I inspired by the Irish folk song Limerick Lament (tempo quaver=120). This latter is initially indistinct from the other material, but across the course of the work, it slowly becomes more and more itself, increasingly revealing the harmonic progression and slowly undoing the rigid stratification between lines, allowing more sharing of materials between them.

To further shape this across time, I group these alternating sections, of which there are 21 total, into 3 major divisions. These provide points of relative climax and change of general deployment of materials: the first, ending at bar 63, brings to a close the overall development of the highly stratified first section; this is followed by a section that alternates between different groupings of the quintet, accompanied by sustained notes, building up to a climax at bar 105, with sustained notes in all instruments. After an insertion of quite different material, this section is characterised by an extreme difference between the two tempo sections, alternating highly stratified full ensemble textures with more fluid textures comprising smaller groupings of instruments.

The insertion occurs twice. Initially it enters between bars 35-56 (within the first major formal section) and is taken up only by piano and bass clarinet, while the flute, violin and cello continue their prior materials; the next time it returns, beginning in bar 109, all the instruments of the ensemble join in this material, slowly transforming and generally slowing down until the earlier materials returns at bar 145.

Navigating these three, non-synchronised precompositional structures (and their concomitant processes) gives the developing polyphonic discourse its particular global shape, which is not fully identifiable with any one of these layers, but with their interaction.

The non-synchronisation of these formal points gives passages unexpected directions. For instance, the second intervention finishes at bar 144 and the original material of the work returns at bar 145, but since there is a tempo change three bars later, this ‘restatement’ of materials is (from the listeners’ standpoint) unexpectedly cut off, moving immediately into smaller groupings of voices.

The compositional process in this sense is not unlike an elaborate obstacle course for five lines. I set up several (moving) obstacles, and then the concrete compositional process is getting through them in relation to the developmental logic of each individual line.

[1] https://usageandcontinuation.com/2014/10/14/a-new-day-in-the-desert-music-in-complex-motion/

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