1

Contents

Introduction 2

1. drift of summer 4

2. fffppp 8

3. twine and a piece of twine 13

4. Trace 19

5. aux ombres 24

6. Chamber Music 29

7. Duo 34

Bibliography 39

2

Introduction

My compositional work since 1996 can be divided into two main areas:

i. 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).

3

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.

ii. 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

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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.

5

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 ‘Rhythm Method’ 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.

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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.

7

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:

∗ ♦ … ⊕ × + ↑ ↓ ο ◊ Δ ∇ •

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.

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2. 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:

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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.

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11

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 Cycle

length coincidence

A - 50"

B - 22" 6",8",9"

C - 18" 6",9",10"

D - 30" 6",8",10"

E - 6" 6",7",9"

F - 18" 6",8",9"

[G1 (18") added later]

G2 - 24" 6",7",8"

H - 12" 6",9",10"

I - 18" 6",9",11"

J - 18" 6",8",9"

K - 4" 10",11" (subsection of J)

L - 20" 6",8",10"

M - 12" 6",7",9"

N - 12" 6",8",11"

O - 6" 6",9",10"

P - 10" 7",8",10"

Q - 8" 6",8",9"

+ 42" (50") 6",10",11"

Figure 4.

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.

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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.

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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/post-

serial 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 century2.

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.

14

15

16

The lowest 6 pitches of the instrument’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 ‘out of tune’ 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

3 Previous experience of writing quarter-tone notated music and attending its rehearsal informed this view.

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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 equal-

tempered 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 one’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

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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 piece’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:

Figure 5

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4. 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:

Figure 1

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It was decided to use the piano’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:

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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! 4! 3! 2! 3! 1! 1! 2! 3! 4! 5! 6

6! 5! 4! 3! 5! 2! 1! 1! 1! 1! 1! 1

fig.3

4 See Chowning (1973), Miranda (1998) and Truax (1987) for examples.

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23

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):

1! 1! 2! 1! 3! 1! 4! 1! 5! 1! 6

1! 2! 1! 3! 1! 4! 1! 5! 1! 6! 1

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.

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5. 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

units5 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 piano7, 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, wave-

like, 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.

6 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.

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26

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.

2. 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):

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Recording Playback 1 Playback 2Record/Playback Speed 1 0.75 0.66 q = 60 45 40

Bar = 2” 2 2/3” 3”Initial Played Pitch E4 B3 A3

Piano Pitch 329.6Hz 246.9Hz 220HzActual Playback Pitch 247.2Hz 219.73Hz

Figure 2

3. 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

28

mentioned, plus control of the overall volume of the effect and the amount of time-

stretching 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

29

6. 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,

spectromorphology9, 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 Schaeffer’s Typomorphology. See Smalley, D. (1987 and 1997).

30

Basic Pitch Material of Chamber Music.Figure 1

31

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):

pitch groups bar

1! a! ! ! ! 1! ! ! 2! a+b! ! ! ! 3 3! b+c! ! ! 5 4! c+d! ! ! 7 5! d+e!! ! 8 6! e+f! ! 9 7! f! ! 10

(8! a ) ! omitted 9! a+b !! 11 10!a+b+c! ! ! 12 11!a+b+c+d! ! ! 14 12! b+c+d+e!! ! 16 13! c+d+e+f! ! 18 14! b+c+d+e+f! ! 20 15!a+b+c+d+e+f! ! 22

Figure 2

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,

32

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 demi-

semiquaver, by treating 1’s as rhythmic points, 0’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:

33

Figure 4

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.

34

7. 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 cyclic-

overlay 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

10 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).

35

36

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 series11, 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 x2 x3 x4 etc.27.5 Hz 55 Hz 92.5 Hz 110 Hz A1 A2 E2 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 Stretch Number Factor

1 0.7 2 0.8 ‘Shrunk’ Series 3 0.9 4 1.0 Harmonic Series 5 1.1 6 1.2 7 1.3 ‘Stretched’ Series 8 1.4 9 1.5

11 See Cambell and Greatred (1987).

12 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.

37

Thus the data for the last spectrum (number 9) is generated as follows:

Fundamental = 27.5

x1 x2 x3 x4 27.5 1.5 55 1.5 92.5 1.5 110 1.5 etc. 144.2 407.9 749.3 1153.7 D3 G#4 F#5 D6

These nine spectra, which are used separately by the two instruments, first

appear briefly, at bar 74 (figure 2):

38

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.

39

Bibliography

Boros, J & Toop, R. (eds) Brian Ferneyhough - Collected Writings.Amsterdam: Harwood Academic Publishers,1995.

Cambell, M. & Greated, C. A Musician’s Guide to Acoustics. London: J.M.Dent, 1987

Chowning, J. The synthesis of complex audio spectra by means of frequency modulation.Journal of the Audio Engineering Society 21(7):1973 (526-534)

Lemur (Apple Macintosh version 4.01), [Computer Program] (1998) Available URL:ftp://ftp.cerlsoundgroup.org/pub/lemur/lemurPro-401.hqx

Miranda, E.R. Computer Synthesis for the Electronic MusicianOxford:Focal Press 1998

Smalley, D. Spectromorphology and the Structuring Process. S. Emmerson (Ed.) The Language of Electroacoustic Music. London, MacMillan,1987.

Smalley, D. Spectromorphology: explaining sound-shapes. Organized Sound 2(2) 1997,pp 107-26.

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