1. drift of summer
3. twine and a piece of twine
5. aux ombres
6. Chamber Music
Introduction My compositional work since 1996 can be divided into two main areas:
Beginning with the series of works entitled drift of summer, I set out to
explore the relationship between the composer, the score and the performer, seeking to allow a traditionally skilled performer a more active role. The main reasons for this were: •
A wish to underline the individual nature of each performance, both by different performers (to allow them to make the work ‘their own’) and the individuality of different performances by the same performer; to allow the personal, individual, characteristics of the players and local circumstances to influence the realisation of the piece.
A wish to open up aspects of the work, to allow it a life of its own; to find a sense of (limited) unpredictability or spontaneity for all involved (audience, player, composer).
An attempt to ensure a more involved and dedicated performance than is usually the norm, by allowing players to invest more in the work, often insisting on a certain amount of commitment in preparing for performance. This can be both through technical expectations (asking players to perform at some limit of their technique e.g. as fast as possible) and in the actual realisation/ making of parts of the piece.
Trying to move away from the restrictive notions of interpretation of works by the performer. If one allows that players participate in shaping / making the work in a limited sense, even in traditional circumstances, then it seems to me to be desirable to channel this involvement and build it into the work. This can be achieved by pointing the players’ attention to where their interpretative powers should be directed (e.g. by an absence of notational information such as pitch or rhythm).
Underlying all of the above factors is a basic wish to find a certain energy, tension and intensity in performance which are more often found in improvised musics than in ‘closed’ works for the concert hall, and to couple this with the more considered, ‘researched’ aspects of technique (general process, rhythmic patterning etc.) The ‘opening’ of drift of summer described here can be seen to have taken the following forms: •
Formal freedoms - pathways through set material.
Qualitative freedoms – phrasing, dynamic shaping of material.
Temporal freedoms – absence of rhythmic specificity.
More general freedoms, such as the withdrawal of certain notational parameters.
The drift of summer pieces were a deliberately extreme, experimental series of works which attempt to work through the ideas outlined above. They were followed by a shift of attention towards the redefinition of other aspects of my compositional technique, particularly pitch, rhythm and structure. However many of the aspects of the open work explored in this series have continued to influence subsequent pieces; in fact all works written after this point are open in some respect. This can be seen, for example, in the absence of pulsed, metric writing in both twine and fffppp.
The works which follow the drift of summer series see the development of a
more consistent basis for my work, drawing upon acoustic and spectral models and knowledge. One of the main reasons for this was an increasing dissatisfaction with the generally parametric compositional approach used before, and a wish to bring the different aspects of sound/music together, rather than treating them as separate entities. Through the use of acoustic and spectral models this becomes possible; basing music upon the structure and behaviour of sounds themselves. This was first seen in twine, which uses material developed from the common acoustical phenomenon of combination tones; here the process is recursively applied to generate
the overall shape of the piece, as well as the basic pitch information. Other works have built upon this, for example aux ombres which is based upon spectrum analysis of the sound of the lowest note of the instrument, almost all aspects of the work being derived from this. Having developed a wider range of compositional tools, these have been assimilated into my general technique and gradually begun to be used in a more flexible way, with several different compositional methods used in a piece such as trace. Finally, later works have taken these techniques and sought to bring them together with earlier compositional methods, as can be seen in Duo where a wide range of techniques, both acoustically and cyclically based, are used side by side, the contrast and differences between these techniques becoming one of the concerns of the piece itself. As well as the shared and overlapping techniques used in their creation, a number of other relationships exists between several of pieces included in the folio. The most obvious examples of this can be seen between twine and a piece of twine, which clearly use the same material, the latter piece modifying the earlier material to fit the new ensemble, and between drift of summer1 and the opening sections of trace, which realise material from the score of the earlier double bass piece. Both these examples show reworkings of earlier material and the transformation of this material in response to various instrumental forces and contexts. Trace itself, partly due to the length of time over which it was written (as well as its duration), contains many of the compositional methods used in other pieces. For this reason, it is placed at the centre of the folio, surrounded by the works with which it shares ideas and techniques.
1. drift of summer1 for Double Bass(es) drift of summer2 for Percussionist(s)
These two studies are taken from a larger group of pieces which share the same title (of which there are currently five), and which set out to explore and focus upon a number of compositional issues. The most important of these concerns the relationship between the composer and performer, and particularly the role of freedom in performance. Two main factors were important in highlighting these issues, the first of which was the influence of free improvisation, witnessed in a number of live performances by people such as Fred Frith, Chris Cutler, Charles Hayward and John Zorn. Secondly, they were written after completing a number of acousmatic works and reflect a wish to bring experience gained from working electroacoustically to instrumental composition. Their designation as compositional studies also reveals a need to rethink, and as a result, to change certain ways of working through the writing of these pieces. Subsequently they can be seen as rather extreme pieces (particularly in comparison with my other instrumental pieces) which nevertheless have influenced all my subsequent writing. The work which immediately predates these studies, TANK (which was written for a contemporary dance performance1) consists of four separate tapes, each containing a different type of sound, which are played concurrently from the four corners of the performance space. Each tape was made independently and is approximately twice as long as the performance. Although the tapes are started together at the start of the performance, they should not all be played from the beginning. The unsynchronised relationship between the tapes allows each performance to be different, and provides a flexible sound environment for the dance. The experience of rehearsing and seeing the work in performance, with its variable 1
TANK was made collaboratively with choreographers Ben Wright and Andrew Robinson. It was commissioned by the â€˜Rhythm Methodâ€™ Festival in 1984 and given its premiere at the Purcell Room, South Bank Centre, London in September of that year. The Drift series was begun in February 1985.
resulting sound world, led directly on to the drift of summer group of pieces and the aim of writing instrumentally to create similarly flexible results. Although each piece in the series is written for a specific instrument or type of performer (e.g. percussionist), each of the pieces can be combined together with any of the others. Versions of the work range from solo realisations, through versions for multiple players of the same instrument, to performances using all the five available versions. In order to accommodate this flexibility of instrumentation, an overall time length for the piece was imposed (five minutes), as was an internal division of this duration (into ten second units). This temporal framework was created in order to allow some synchronisation between players (on a mid to large-scale) whilst allowing freedom within this, on a small scale. The absence of any large-scale articulated form in TANK (as a result of the temporal freedom between the tape material) is echoed in the repetitive structure of drift. At the start of each ten second unit all of the different parts are playing, gradually ceasing on one of the second divisions. The overall effect of this is of a repeated attack-decay gesture (every ten seconds), particularly with multiple instruments playing together. Within this overall gestural framework each instrument is given a specific type of freedom: for the percussionist, a specific instrumentation is not specified, only the required number of different instruments (five); the double bass has detailed instructions regarding the timbral nature of the sound produced and its dynamic, but no information regarding pitch. The avoidance of any pitch information in all of the versions of the piece shows a wish to rethink and reorganise compositional priorities. In earlier instrumental work there was a concern that pitch organisation was beginning to dominate my compositional method, so here I forced myself to work without notated pitch at all. This restriction particularly forced a rethinking of certain instruments, as can be seen in the double bass version, which is reinvented as the source of a wide variety of timbre.
The methods used to develop the material within the structural framework outlined above were deliberately kept simple and are mostly the result of the overlaying of two or three linear processes. Within the double bass version this consisted firstly of the creation of a catalogue of timbral resources and the devising of a notation for their representation. From this a thirteen step ‘scale’ was arrived at which moves timbrally from maximum noise content (hitting the body of the instrument) to maximum pitch content (arco, ord. bow position) and which is notated as follows:
noise ----------------------------------------------------------------------------------------> pitch
(An explanation of these symbols is given in the score of drift of summer1).
This scale is then subjected to a process whereby each element can either be replaced by one of its neighbours in the original scale or it can remain the same. This process was carried out repetitively, deforming the original scale to create fifteen different sequences (including the original scale, which can be seen on page 13 of the score). Each of these sequences forms the basis of a single page of the score.
fffppp for Six Pianos
The starting point for this work was the creation of a series of six chords which would form the harmonic and melodic basis for the piece:
These chords, which were freely devised, were mapped across the entire range of the piano keyboard to create six transpositions of each chord:
The next stage was to create a rhythmic framework for the distribution of this harmonic material. This framework was created through the 'interference' patterns which result from the layering of sequences of regular pulses. This device had been used in several previous pieces (monody (1991), Point and Line to Plane (1991) and verses and carillons (1993)) where the surface rhythmic detail was created by merging rhythmic layers. In fffppp by contrast, these layers are kept separate and instead this technique was used to create a structural, harmonic, rhythm. Indeed the aim was to write a piece without any metered or pulsed material - to make the rhythmic framework of the piece disappear from view, while still providing a strong and detailed formal framework.
Six pulse layers are used in this piece, of 6, 7, 8, 9, 10 and 11 seconds, one layer initially assigned to each player. The resulting combined complex rhythmic sequence would take over 92 hours to run full cycle, but at 5'30" and 5'36" there are the first partial conjunctions of cycles (6, 10 and 11 at 5'30" and 6, 7 and 8 at 5'36") and so this was chosen as the completion point of the work.
Each player's harmonic and pulse layer was created through the following process:
each player's pulse layer cycles through the chords 1 to 6 repeatedly (upper layer in fig.3a)
each pulse layer cycles through the chord transposition i-vi repeatedly (lower layers in fig.3a), whenever players' pulse layers coincide they 'swap' position, taking the chord position with them, but adopting the chord number from the new position (see figure 3b). By this process, the six individual pulse layers are kept separate throughout but swapped between players.
The results of this process form the detailed rhythmic and harmonic structure of the piece. Furthermore, the lengths of subsections of the piece are, with slight modifications, dictated by coincidences between 3 pulse layers (fig.4). Section
[G1 (18") added later] G2 - 24"
10",11" (subsection of J)
+ 42" (50")
Having completed this process the final framework for the piece was arrived at, from the individual section lengths to the harmonic rhythm within these. The sections make different use of this material, ranging from strict presentation through to a freer implementation. The first two sections perhaps provide the clearest examples of these contrasting uses.
Section A. This initial section was written some months before the rest of the piece and in many ways is the freest section of the work. The idea behind this section was to present all of the basic harmonic material together in as dense a form as possible. Each player sweeps from top to bottom of the keyboard repeatedly, each starting on a different chord and cycling through the remaining chords in order. Although this section does not strictly use the harmonic distribution from the large scale plan, it is built upon the overlapping wave-like descent patterns which can be seen at the start of this plan (see fig.3a). This material then rotates around the ensemble until all six players have played all the six lines presented in the first instant (although this process is not completed until section C). This opening section presents the material for the rest of the work in a somewhat raw, unorganised state before the rather mechanistic organisational process outlined above can shape it.
Section B. This section directly and simply presents the material generated by the 'structural machine', firstly vertically as a simple chord (bar 2) followed by a melodic line. Where the rhythmic cycles coincide the two players share the available material, presenting it together, making audible the swapping or crossing-over process previously discussed.
3. twine for Soprano Saxophone Quartet. and a piece of twine for Saxophone Quartet (satb) Figure 1 presents a graphical overview of the structure of twine. This shows the piece to be made up of three different, but closely related material types. The most important of these, type c, was the product of my first attempt to work with acoustical knowledge to inform the writing of a piece. Amongst the main reasons for this was a wish to move away from ‘abstract’ forms of pitch organisation (previously serial/postserial methods) and to work more with the ‘sound’ rather than the notes of a piece, mainly as a result of working with electroacoustic music. In this case, the simple but flexible idea of difference tones and in particular sum tones is used. This phenomenon, whereby two pitched sounds can combine to produce a third pitch which is the sum of the original two frequencies, is well documented having been first discovered in the mid-eighteenth century 2. Figure 2 gives an example of this process, where the summing of the initial two G#’s produces a third pitch, an octave above. In twine, a modified version of this phenomena is used whereby the two initial pitches and the resulting sum tone pitch are placed in a feedback loop. Thus, the sum tone pitch is added again to one or other of the original pitches to produce a fourth new pitch. This process is then repeated to make a self-generating, ascending pitch sequence. Coupled with this process is the idea of loss of energy (showing itself musically as a diminuendo as the sequence continues) as the feedback material moves further away from the source tones. Figure 2 goes on to show three pitches being generated by this process, together with the realisation of the pitch material in the final score. The coupling of the upward sweep with a loss if dynamic energy can be seen in the repeated diminuendo through this bar. This idea of pitch ascent taken from this process was developed further, providing many of the organisational features of the work, most obviously in the overall pitch profile of the piece which moves from low to high. Figure 4 shows the structure behind the application of the feedback sum-tone process outlined above: 2
See Cambell and Greated (1987) for more details.
The lowest 6 pitches of the instrumentâ€™s register (chromatically Bb3-C#4) are used as the generating frequencies for all of this material in twine. The ascending pitch sequence is paired with each of the pitches above, once again in ascending order to create a sequence of sixteen pairs of pitches. This includes all of the possible pairings of different pitches plus the initial repeated G# pairing shown in figure 2. Only one of these repeated pairings is used, as the pattern of pitches generated is the same for each. This is used as the first sum pattern of the piece, presenting the simplest form of the process first. Figure 3 presents a further example of the application of the generated pitches within the piece. As with many of the pitches resulting from the governing sequence outlined above, those shown in this example do not conform to the equal-tempered scale. The first generated pitch is sharp of an equal-tempered G#4, in fact falling almost exactly between the G# (12 Hz sharp) and A (13 Hz flat). The second generated pitch is also â€˜out of tuneâ€™ being 12 Hz below E5 . The fact that many of the pitches made by this process fall between chromatic pitches meant that simply forcing them onto an equal-tempered grid would have removed much of the detail as well as acoustical connection of this generated data. Without wishing to resort to more detailed pitch notation and as a result make the final work much more difficult to perform3 the following approach was adopted in using the generated pitch material. Only chromatic notes are notated as attacks, but given the ease with which the
Previous experience of writing quarter-tone notated music and attending its rehearsal informed this view.
saxophone can perform small glissandi, slides to pitches just above or below are employed, so that the generated pitches are at least moved towards or over. This compromise has the advantages of being both easily read and performed by a player, as well as playing the generated pitches and weakening the sense of the equaltempered scale. The remaining two types of material were written after, are informed by and complement, the pitch sweep material. Material type b consists of two similar blocks near to the beginning and at the very end of the piece (the first block is interrupted by player oneâ€™s solo). They mark the extremes of high and low pitch over which the piece will move. Both blocks place the instruments in a confined pitch space focussing on 4 adjacent semitones (although unspecified pitches above and below this are required). The idea of the pitch cluster used here is taken from the controlling sequence for material type c (figure 4). Both blocks use four lines of material which are rotated around the ensemble upon repetition, each time rising in pitch by a semitone. Material type a also uses the repetition and re-reading of material. The opening solo can be included within this material type, given its linear, melodic nature. However with its broad pitch range and many trills it serves more generally to introduce the sound world of the piece and it is only at rehearsal E that this material type really begins. This melodic line, placed low in the instruments register (but not at its very bottom, as the upward movement of the piece has already begun) initially works within the pitch range of a perfect fourth, or six semitones (C#-F#), the same sized cluster as the controlling sequence for material c (shown in figure 4). At bar 24, this pitch group is extended downward with the addition of the low B which signals the ending of this sequence as the previous system is broken. The second monody, at rehearsal letter I, presents similar material although this time it is in the upper register of the ensemble (signalling the progress of the piece) and has a less restricted pitch. The central duets section of the work combines these two materials together simultaneously, the lower monody played by players one and two, the upper monody
by players three and four. Its central position in the work is signalled by the combination of these upper and lower pitch areas.
a piece of twine was made as an arrangement of material from twine, reworked for a standard saxophone quartet. This short piece, which contains only two brief sections of new material (at rehearsal figures E and F), modifies the earlier piece, mainly through transposition. The earlier pieceâ€™s concern with high and low are continued here in a slightly modified form, particularly in these new sections where unspecified very high and very low notes are notated. Unlike the ensemble for twine, which consists of the same instrument with the same transposition, a standard saxophone quartet contains four different instruments each with its own transposition. This factor is used to modify directly the material from the earlier piece in various ways, particularly around the idea of unisons, both written and played. As an example, at bar 7 the ensemble plays in (near) unison, whilst at the conclusion of this material, at bar 13, it is written as a unison, generating the chord as shown in figure5:
Trace for Ensemble (15 Players)
Trace was begin in June 1998, after the completion of drift of summer1, twine and aux ombres, works with which it has close relationships, principally through its borrowing of techniques and ideas used in these earlier pieces. The most obvious of these is the use of sum and feedback pitch sweeps, adopted from twine, which can clearly be seen in the woodwind material near to the start of the piece (bars 22, 25, 35, 38 etc.). Another, taken from aux ombres, is the use of spectrum (particularly MQ) analysis as the basis of musical material. The data derived from the analysis of a double bass low E, played pizzicato, forms the pitch material (combined with the pitch sweeps mentioned above) of the opening 47 bars. This section is also connected to drift of summer1, in that the gestural material in these opening sections is derived from a realisation of the instructions of this earlier piece. One of the aims in reusing these techniques within Trace, as well as developing them further, was to find ways of unifying a wide range of previously seperate compositional methods. Within the ensemble it was decided that two instruments would have particularly important roles: double bass at the start, and piano towards the end of the piece. From this idea developed the pitch framework shown in figure 1a, formed from the lowest notes of, firstly, the double bass and then the piano:
It was decided to use the pianoâ€™s A an octave above (amongst other reasons so that both instruments could play both these notes), providing a rising pair of pitches as shown. The interval between these was filled in chromatically as shown in figure 1b, and it is these six pitches (in pairs) that were used to generate the sum and feedback material mentioned above. One further modification to this set of pitches added an octave between each pitch, to create the ascending sequence shown in figure 1c. It is these two sets of pitches which provide the point of unification of the different techniques used with Trace, as well providing the pitch basis for the whole of the work. Two examples will be given here of ways in which these earlier techniques were developed within Trace, both of which are connected to the sum and feedback material from twine. Firstly, sections O and P, sparsely orchestrated passages towards the centre of the piece, were developed simply from difference tones between the opening pitches of this section (the cello F and F# generating the oboe F the octave above). Instead of only using the sum tones previous applied, here they are complemented by difference tones, and the pitch sequence is developed in a similar feedback manner. The inclusion of difference tones in this process allows a wider range of pitches with varied (not only ascending) register. The most significant development of these earlier ideas however can be seen in the harmonic framework of the remainder (and significant body) of the piece, which is derived through the use of the principle of frequency modulation. This clearly follows on from the technique developed in twine, once again applying a principle taken from acoustical knowledge of sound to instrumental composition, as well as involving the creation of new pitches from initial pairs of frequencies. Figure 2 shows the basic process of frequency modulation, with two sets of new frequencies being created, one through the addition of multiples of the second input frequency (known as the modulator) to the first (called the carrier) and one through their subtraction. This shows the simplest possible example, with the two input frequencies identical, which results in the harmonic series:
Figure 2 The differences between the previous technique, used in twine, are that frequency modulation allows for the creation of a much greater variety of pitch groups, as well as having a well developed and documented theoretical framework4. Within this are proposals, made by Truax (1987), for the organisation of f.m. generated spectra according to, amongst other criteria, harmonicity. This suggests a more consistent means of ordering and generating f.m. material than was available for the difference material alone. The f.m. generated material is itself also much more flexible in its possible uses than the previous technique which relied on a specific temporal ordering of pitches to maintain its logical basis. Frequency modulation, in its application in instrumental composition, provides a flexible but predictable means of generating harmony. Figure 3 lists the 22 pitch collections generated by frequency modulation used in Trace. These were developed from the pitch basis outlined above in figure 1, the first 12 chords generated from pairs of pitches taken from the untransposed pitches shown in figure 1b, the remaining chords created using those from the transposed second group (figure 1c). The first group of chords (which begins at rehearsal H) was ordered according to the following series to generate a stable but gradually developing series of chords which gradually move towards the harmonic series at it centre (1/1) before remaining basically static, except for a stepwise rise on its upper pitch through the remainder of the sequence (pitch numbers correspond to figure 1b): 5!
See Chowning (1973), Miranda (1998) and Truax (1987) for examples.
The second half of the f.m sequence is generated by a very different sequence. This consistently uses the low E, alternatively as carrier and modulator, to create contrasting harmonies which nevertheless have a sense of direction, particularly in its rising pitch content (echoing the ascent at the end of the previous sequence) as the difference between the number ratios become greater (pitch numbers correspond to figure 1c):
This sequence is used to provide the harmonic basis of the closing sections of the piece from rehearsal letter R (chord no.13) through to the end of the piece (chord no. 23, figure 3) and follows a recap of the previous f.m. sequence (chord 1-12) which takes place between rehearsal letters Q and R.
aux ombres for Amplified Solo Piano and Live Electronics.
Before writing this piece, I had previously written a number of works for instruments and live electronics (Vindauga (1989), verses and carillons (1993), Point and Line to Plane (1991)). Each of these had used preset multi-effects processing units 5 to extend the sound of the live instrument, but due to the technical limitations of such set-ups the live electronics role had remained rather inflexible and static. As a result of this, the specific aims in writing this piece were: to make use of recently available computer-based sound processing6 to create a more flexible, responsive sound processing ‘instrument’ than would have been previously been possible, to write a work which was built specifically upon the instrument for which it was written. These were realised in the following ways. Firstly, spectrum analyses were made of the sound of the piano 7, specifically of the lowest note of the instrument (A0). These analyses revealed details of the anatomy of the sound of the piano and of the way these change in time (see figure 1)8 . This inner-life of a single note revealed graphically becomes the substance of the work and is written large, as the structure of the note comes to form the basis of structure of the whole work. This happens in both detailed and general ways. For instance, much of the pitch material of the piece is derived from the analysis data, whilst on a more general level, the eddying, wavelike, self-similar patterns found near the start of figure 1, suggested the type of material that the piano would play, as well as the nature of its processing, by granulation. The ‘shadows’ of the title (which translates literally as ‘of / about 5
For instance the Yamaha SPX90 and Boss SE50.
This piece uses James MaCartney’s SuperCollider, a real-time audio synthesis environment for Apple Macintosh Computers, which became available in 1996. 7
These analyses were made using Lemur, a freeware computer programme which carries out M.Q. Sinusoidal Analysis, running on the Apple Macintosh computers. It was written by K. Fitz, B. Holloway, E. Tellman and L. Hakken at the University of Illinois CERL Sound Group. 8This
diagram should be read from right to left, as the analysis was carried out on a reversed piano sound, for the reason that this gives a more accurate analysis of the sound.
shadows’) can be seen musically in the piece in several ways, particularly in the return and repetition of material (often in modified form). This can be especially found in the electronic treatments of the piano sound which consist of three different types of ‘delay’: 1.Simple delay (rehearsal figure K).
Here the piano chorale material is delayed by 10 seconds, the pianist playing against what they have already played. This is the type of processing previously offered by the preset effects units mentioned above, but whereas these units would only allow delays in the region of a couple of seconds, here the computer allows a much greater time delay.
Recording and playback with speed change (recording=bars 74-84, playback=rehearsal figures O and P).
A 23” section of piano material is recorded and stored by the computer. It is then triggered for replay twice, each time at a slower speed. Each time the pianist is asked to follow, as closely as possible, this slowed version of what has previously been played. The slowed playback of the recorded material alters the pitch of the recorded sound, as well as its timbre. These timbral changes are emphasised by the slight pitch discrepancies between the playback pitches and the piano. These changes become more noticeable the greater the amount of speed change. The pitch/speed changes were calculated as follows (figure 2):
Record/Playback Speed q
Bar = Initial Played Pitch Piano Pitch Actual Playback Pitch
Recording 1 60
Playback 1 0.75 45
Playback 2 0.66 40
2” E4 329.6Hz
2 2/3” B3 246.9Hz 247.2Hz
3” A3 220Hz 219.73Hz
Recording and granulation of sound (rehearsal figures B-J).
This is the most complex sound processing used in the piece and consists of a repeated sequence of events, the details of which are controlled in real-time. A short section of piano material (6”) is recorded by the computer. Simultaneously this sound is read through by an index point, at a slower rate than that at which it was recorded. As a result the playback rate created by the index point results in a time stretching of the recorded sound. However the stored sound is not simply played back at a slower rate, as in the previous example. Here the index point is used to identify where short ‘grains’ of sound (between 8 and 24 milliseconds) are to be played back from, and as each of these individual grains is replayed at the same speed that it was recorded at, no pitch change occurs. This basic process is modified by allowing control over the overlap between grains and further by allowing a level of randomness around the index point; the higher the level of this, the more blurred the resulting sound will be when compared with the original, the randomness creating a kind of aural ‘smearing’ of the sound. In total, five parameters, grain length, overlap (density) and time dispersion already
mentioned, plus control of the overall volume of the effect and the amount of timestretching which takes place, are controlled through this first section of the piece. In order that these parameters can be modified in real time, a MIDI-fader controller is used to alter the settings of the onscreen sliders (which can be seen in figure 3), modifying the nature of the processed sound as a result. Although the type of parameter changes written in the score are all linear (moving one or more faders from one value to another) the real-time nature of these changes allows a more detailed response and a certain level of freedom is left to the electronics operator. The clearest example of this is in the control of the overall volume levels, where no specific information is given as the operator is expected to balance the proportion of the live and treated sound as the piece progresses. The instant feedback and quick response offered by the electronics set-up here means that after a certain amount of rehearsal time it becomes possible to predict how the first three faders (which control time dispersion, grain duration and grain overlap) interact and in performance to play with the detail of the given score instructions, enriching the relationship between the live piano and its electronic treatment.
SuperCollider Screen Controls for aux ombres Figure 3 28
Chamber Music for Mixed Sextet
This piece is divided into two clear halves. The first alternates fast upbeat flourishes in rhythmic unison, with freer, unmeasured material, the gestural impetus from these upbeats being released in the subsequent, slower senza misura sections. This pattern, of moving from fast to slower material, which occurs repeatedly in the first part of the piece, is used as an obsessive, archetypal shape throughout Chamber Music on both small and large scales. It occurs only once in the second part of the piece, but lasts through its entire duration, as the ensemble moves from the maximum density of the start of the second half, gradually unwinding towards the calmer, slower ending. The way in which each of these sections is built and organised is outlined below, but before moving to look at this some mention should be made of the main influences upon this gestural conception of the material within Chamber Music. These principally come from electroacoustic music and in particular, spectromorphology 9, with its concepts of morphological archetype (attack/decay, continuant etc.) and gestural stringing (whereby these units are grouped into larger units). The aim, particularly in the first part of the piece, was to apply these electroacoustically-based ideas to instrumental material, in the shaping of individual sections and building them into a larger structure, rather than through any detailed means of pre-organisation. The pitch material for the piece reuses the chord matrix created for fffppp but here with very different results. Instead of treating each chord in each register as a separate unit, here the six different columns (each containing six chords) are used together rather as scales or large sets of pitches as follows (figure 1):
9 A term
developed by Smalley as an extension of Schaefferâ€™s Typomorphology. See Smalley, D. (1987 and 1997).
Basic Pitch Material of Chamber Music. Figure 1
These pitch collections are used in the following pattern in the first half of the piece, itself formed of two halves, the first which moves from the first to last group adding pairs of pitch groups together, and the second which gradually moves towards near chromatic saturation, as all the groups are added together by its end (figure 2):
1! a! ! ! 2! a+b! ! ! 3! b+c! ! 4! c+d! ! 5! d+e!! 6! e+f! 7! f!
! ! ! ! ! ! !
(8! a ) ! 9! a+b !! 10!a+b+c! ! ! 11!a+b+c+d! ! ! 12! b+c+d+e!! ! 13! c+d+e+f! ! 14! b+c+d+e+f! ! 15!a+b+c+d+e+f! !
1! 3 5 7 8 9 10
omitted 11 12 14 16 18 20 22
The second half of the work takes a different approach to this pitch material and, instead of treating the ensemble as a single group, which is harmonically consistent, each individual instrument has its own independent harmonic pattern which cycles through each of the pitch groups. The cumulative effect of this, whereby all harmonic material can be presented together, was introduced in the previous section and led up to by the process of harmonic saturation which took place through the first section, linking the two sections of the work harmonically. The overall aim of this second part of the piece was to move from a maximum level of rhythmic density,
as slowly and gradually as possible to less dense material. In order to realise this the following technique was adopted, using a descending binary number sequence. This was converted to rhythmic information, each number having the duration of a demisemiquaver, by treating 1â€™s as rhythmic points, 0â€™s as rests, as the following example shows (figure 3):
Part two of the piece begins with rhythmic material which uses a much longer sequence than in the given example, moving from 111111 to 000000 over the period of 38 bars (not including the two additional bars of material inserted at rehearsal figure E). This is presented as a six-part rhythmic canon with one rhythmic unit (7 demi-semiquavers) delay between the instruments, which enter in the following order: flute, clarinet, cello, violin 1, violin 2 and finally piano. Figure 4 gives an example of how this process is realised in the piece, showing the interaction of the separate pitch and rhythmic processes as well as the canonic relationship between the two given parts:
This process, which ends at bar 65, is followed by three further sections which also pursue this process but with shorter generating sequences as follows: 00000--> 11111, 1111--> 0000, 000 ---> 111, alternating the direction of the patterns to create as seamless a rhythmic process as possible.
Duo for Violin and Piano
Duo continues the pattern begun in Trace, of writing pieces which use a variety of different techniques in their realisation. In this work, these compositional methods can be divided into two groups: cyclic ‘interference’ techniques (like those documented regarding fffppp) and those techniques which have some basis in acoustical knowledge (such as the spectrum analysis used in aux ombres). One of the large-scale concerns of the piece is a movement away from the former ‘abstract’ methods of organisation and patterning, which are used at the opening of the work, to those based upon ideas and (acoustic) knowledge of sound, which are found at the end. Coupled with this is a consideration of how the information generated from these techniques can be transformed into musical material. At one extreme is free writing, where information generated by the system is freely interpreted and further shaped. At the other, automatic10 writing. Both ways of writing are used with both types of material. For example, section A is generated automatically by two separate cyclicoverlay systems (similar to those previously documented), one for pitch and one for rhythm. Material from the same system forms the basis of the material for both instruments until rehearsal figure D, as they attempt to forge a relationship based on shared material. However the implementation of this material becomes gradually freer until bar 56, where the instruments begin to use separately generated material. The piano continues using the previous systems, but the violin now ‘comments’ upon this, with pitch information generated from the piano’s material through difference tones. Thus, the gradual shift towards acoustics-based techniques (as well as the ensemble’s search for a workable relationship) is begun. For the most part these are based upon the material shown in figure 1. These nine pitch collections are a series of artificial spectra, which were developed by a
This term, borrowed from Ferneyhough, rather than having any Surrealist connections, is used to designate generative systems which produce detailed material which can be directly transcribed into notation, with little or no further intervention from the composer, once the system has been set up. See Boros, J & Toop, R. (1995).
modification of the harmonic series (which forms the fourth pitch group), either through its contraction or expansion. The sound of many instruments has been found to be made up of a series of overtones which do not exactly conform to a perfect harmonic series. This is particularly the case with the piano, which has a slightly stretched overtone series 11, and so it was decided to use this feature, in an exaggerated form, to generate a harmonic basis for the latter part of the piece. The harmonic series itself is generated by a stepwise multiplication of the fundamental frequency:
x1 27.5 Hz A1
x2 55 Hz A2
x3 92.5 Hz E2
x4 110 Hz A2
In the remaining pitch sequences, which are all built upon the same fundamental pitch (the piano’s low A, 27.5 Hz), the harmonic series is distorted through the use of a power12 function:
Spectra Number 1 2 3 4 5 6 7 8 9
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
‘Shrunk’ Series Harmonic Series
See Cambell and Greatred (1987).
That is it is raised to the power of the stretch factor. This technique was used over simple multilplication as instrumental spectra, particularly the piano’s, which has been shown to conform to a spectrum distorted in this way.
Thus the data for the last spectrum (number 9) is generated as follows:
Fundamental = 27.5 x1 27.5 1.5 144.2 D3
x2 55 1.5 407.9 G#4
x3 92.5 1.5 749.3 F#5
x4 110 1.5 1153.7 D6
These nine spectra, which are used separately by the two instruments, first appear briefly, at bar 74 (figure 2):
After the brief presentation of pitch group six by the piano at the start of this example, the two instruments begin to work with spectra from opposite ends of the list, the piano with shrunk spectra (beginning with 1), the violin with the stretched versions (beginning with 9). With this new material is introduced a concern for timbre and timbral change, prompted by a move away from note-based to sound-based techniques (examples can be found at bars 109, 114 and 115). Underlying this is the idea that the spectral material can be seen both as a collection of individual pitches (which can be used melodically) as well as having the possibility of fusing together to create a timbre or colour. The process of the two instruments moving from the opposite extremes of the spectral material reaches a logical conclusion at the end of the piece, where the two instruments finally come together to share the same harmonic material, spectrum four, that is, the unmodified harmonic series. The instruments, having gradually moved towards more similar spectra, reach a stable, shared sound world at the close of the piece.
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