University of Wollongong Thesis Collections University of Wollongong Thesis Collection
University of Wollongong Year
Composition : pure data as a meta-compositional instrument
Michael L.G Barkl University of Wollongong
Barkl, Michael L.G, Composition : pure data as a meta-compositional instru- ment, PhD thesis, School of Music and Drama, University of Wollongong, 2009. http://ro.uow.edu.au/theses/794
This paper is posted at Research Online. http://ro.uow.edu.au/theses/794
COMPOSITION: Pure Data as a Meta-Compositional Instrument
A thesis submitted in fulfilment of the requirements for the award of the degree
Doctor of Creative Arts
from
UNIVERSITY OF WOLLONGONG by Michael Laurence Gordon Barkl B.Mus., M.Mus., Ph.D., Dip.Ed., F.T.C.L.
School of Music and Drama Faculty of Creative Arts January 2009
Certification
I, Michael Barkl, declare that this thesis, submitted in fulfilment of the requirements for the award of Doctor of Creative Arts, in the Faculty of Creative Arts, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution.
Michael Barkl
22 January 2009
ii Acknowledgements
Thanks are due to Dr Houston Dunleavy for encouraging me to “re-tool” (as he put it) in electronic music at the University, to Associate Professor Greg Schiemer for generously taking the time (most of one afternoon) to introduce me to Pd prior to my candidature and subsequently serving as my supervisor with equal support and generosity, and to the Professor and Head of the School of Music and Drama, Julian
Knowles, who supported my proposed project and permitted me to enrol.
I am grateful to John Gracen Brown for allowing me to use his poetry for purposes far removed from its original intention; and for accepting the results in good faith and in good humour. Thanks also to my family who allowed me to direct my attention to and pursue my interests in what appeared to be an arcane music.
Finally, thanks are due to Miller Puckette, the writer of Pd as an open source program, without which life would be a whole lot less fun.
iii
To my grandfather, Leslie Cum Chow Cook (1900-1977)
- audio engineer, inventor, inspiration-
iv Table of Contents
Certification ii Acknowledgements iii Dedication iv List of Figures viii Prologue x Abstract xiii Chapter 1 Developing Meta-Compositional Strategies 1 1.1 Background to the Project 1 1.2 Composition: Pure Data as a meta-compositional instrument 3 1.3 Progress 3 1.4 MIDI Studies 4 1.5 The paradox of Pythagoras 6 1.5.1 Complementary binary structures 7 1.5.2 Sine tones 7 1.5.3 The use of the harmonic series 8 1.6 Music of Grace 8 1.6.1 John Gracen Brown’s poetry 8 1.6.2 The use of primary material: a Bach chorale 9 1.6.3 The use of numbers: an analogue between MIDI note numbers and harmonic numbers 10 1.7 The application of programming conventions 11 1.8 Research Question 16 1.8.1 Aims 16 1.8.2 Significance 16 1.8.3 Approach 17 1.8.4 Originality 17 1.9 Pure Data Literature Review 19 1.9.1 Published findings 19 1.9.2 Externals developed by other composer-programmers 21 1.9.3 Areas requiring original research 22
v Chapter 2 The paradox of Pythagoras 23 2.1 Origins 23 2.2 The paradox of Pythagoras : screen prints 28 2.3 Music of the spheres 42 Chapter 3 Music of Grace 45 3.1 The cat dances and the moon shines brightly 45 3.2 The heavy dark trees line the streets of summer 48 3.3 The crystals in the cave absorb the light as if they have not seen it in a million years 51 3.4 Reflections on the compositional process 54 Chapter 4 Discussion and Conclusion 56 4.1 Discussion 56 4.2 Conclusion 61 Chapter 5 Epilogue: Here… 62 5.1 Origins 62 5.2 Here... 64 5.2.1 Panel 1 65 5.2.2 Panel 2 70 5.2.3 Panel 3 75 5.2.4 Panel 4 77 5.2.5 Panel 5 79 5.2.6 Panel 6 81 5.2.7 Panel 7 82 5.2.8 Panel 8 85 5.2.9 Panel 9 88 5.2.10 Panel 10 90 5.2.11 Panel 11 91 5.3 Discussion 93 Bibliography 96 Books and Dissertations 96 Chapters and Articles 98 Conference Proceedings 100 Music Recordings 102
vi Music Scores 103 WWW Discussion List Messages 103 WWW Documents and Pages 105 Attachments (CD data) 107 Appendices A-R 107 List of Appendix Figures 108 List of Appendix Tables 131 MP3 Recordings 132
vii
List of Figures
Figure 1.1 Befiehl du deine Wege 10
Figure 1.2 Rhythmic Durations as a Harmonic Series—Stockhausen 11
Figure 1.3 Haydn’s Sonata in G minor , Hob.xvi:44—Schenker 12
Figure 1.4 The cat dances Panels 1-5 13
Figure 1.5 The cat dances Subsections 1a and 1b within Panel 1 14
Figure 1.6 The cat dances Subsection 1a 15
Figure 2.1 The paradox of Pythagoras top canvas 29
Figure 2.2 [pd fundamental_of_9.13125Hz_/…] 30
Figure 2.3 [pd number_of_harmonics_128_*…] 31
Figure 2.4 [pd duration_1_2_5_10_15_20_30_40_50_60] 31
Figure 2.5 [pd oscillators] 32
Figure 2.6 [pd fm_two_chord_pair_odd_harm] 33
Figure 2.7 [pd random_x6] 35
Figure 2.8 [pd mixout_x6] 35
Figure 2.9 [pd fund_fm_osc_on_off_L] 37
Figure 2.10 [pd fund_fm_osc_on_off_R] 38
Figure 2.11 Music of the spheres top canvas 42
Figure 2.12 [pd fundamental_of_mercury…] 43
Figure 2.13 [pd number_of_harmonics_9.53307e+010…] 44
Figure 3.1 Extract from Befiehl used for The cat dances 46
Figure 3.2 The cat dances and the moon shines brightly top canvas 46
Figure 3.3 Extract/arrangement from Befiehl used for The heavy dark trees 48
viii
Figure 3.4 The heavy dark trees line the streets of summer top canvas 50
Figure 3.5 Chords from Befiehl used for The crystals in the cave 52
Figure 3.6 The crystals in the cave top canvas 53
Figure 4.1 Debugging 58
Figure 5.1 Extract from Befiehl used for Here… 64
Figure 5.2 Here… bars 1-2 65
Figure 5.3 Here… bars 3-4 66
Figure 5.4 Here… bars 12-14 69
Figure 5.5 Here… bars 15-16 71
Figure 5.6 Here… bars 21-22 73
Figure 5.7 Here… bars 23-24 74
Figure 5.8 Here… bars 33-34 75
Figure 5.9 Here… bars 39-40 76
Figure 5.10 Here… bars 42-43 77
Figure 5.11 Here… bars 49-50 80
Figure 5.12 Here… bars 55-56 81
Figure 5.13 Here… bars 63-64 83
Figure 5.14 Here… bars 69-70 84
Figure 5.15 Here… bars 72-73 85
Figure 5.16 Here… bars 75-76 86
Figure 5.17 Here… bars 78-80 87
Figure 5.18 Here… bars 81-82 89
Figure 5.19 Here… bars 87-88 90
Figure 5.20 Here… bars 92-93 92
Figure 5.21 Here… bars 97-98 93
ix
Prologue
One of the consistent features of electronic music is the absence of a “score”, and while this attribute is often regarded as a “freedom”, it has also inhibited the study of electronic works, especially their process of composition; indeed, at different times composers, most notably Karlheinz Stockhausen, have attempted to produce “study scores” of their electronic pieces.
The desire to document the compositional process has also been a longstanding personal interest of mine, and the electronic works in this folio, described in the thesis, are a creative response to this interest. The original works take the form of MP3 files that are provided on the companion CD in the sleeve of this volume. All works except one have been composed using an open source musical patching language called Pure Data or Pd, which was initially developed by Miller
Puckette.
The personal motivations for the compositions on the accompanying CD are explained in chapter 1. It describes the types of pieces composed for the folio and the means and resources used to develop and produce them. The notion of “reading” the graphic layout of Pure Data (Pd) patches is proposed as a way to document compositional process and structure. The poetry of John Gracen Brown provides a contextual “vision” for an extension and development of the sounds of The paradox of
Pythagoras into the series of three highly structured works that comprise Music of
Grace . My interest in pure sine tones, used in this case for an extended harmonic
x series based on a significant fundamental, is discussed in relation to these pieces and, finally, the whole project is reframed in “research” terms.
In chapter 2 The paradox of Pythagoras is discussed in detail (together with a variant of this piece entitled Music of the spheres ). The discussion not only describes
the work in terms of its structure and function, but addresses a range of aesthetic
choices that are maintained throughout the rest of the folio, especially with regard to
pitch (frequency) and the particular use of the harmonic series. For the purposes of
reference and comparison the appendices include a table showing the relationship
between all Pd patches created specifically for the work.
Chapter 3 briefly describes a series of three works collectively entitled Music of Grace and discusses the compositional development of each of these works.
Though the works were inspired by the poetry of John Gracen Brown their musical origins lie in a Bach chorale. A detailed examination of every one of the 1025 patches I developed in the process of composing Music of Grace can be found in the appendices, together with reference tables that show the structural relationship between all Pd patches created. This was intentionally organised so that technical detail essential to the composition process is made available without deterring a reader who is less conversant with the intricacies of Pure Data from understanding the musical character of these works.
Chapter 4 finally deals with the central question of my thesis—the inherent problem of electronic music composition and its inattention to the documentation of compositional process and structure. The programming and layout conventions of the
Pd patches are reassessed in the light of the works discussed in the previous chapters and the specific solutions devised for each individual piece. Difficulties are acknowledged and deviations from programming conventions are accounted for.
xi Chapter 4 concludes by recognising the capacity of Pd to suit large scale multi- sectional projects, and the value of the programming conventions as a benchmark for readability.
Chapter 5 serves as an epilogue, revisiting instrumental composition in the
light of the electronic works composed using Pure Data and reviewing some of the
special characteristics of instrumental writing. It describes the process of composing
a chamber work entitled Here… , a work written concurrently with The crystals in the
cave , discussed in chapter 3. As an epilogue to the project, after an intense period of
composing purely electronic music, this piece allowed a return to the issues identified
at the beginning of the project with a widened vision of composing. The strictures
and human limitations of instrumental music, which are acknowledged as “special” in
their own way, may now take their place alongside the “freedoms” of electronic music
in a complementary manner.
xii
Abstract
The aim of “Composition: Pure Data as a Meta-Compositional Instrument” was to compose a folio of original electronic pieces that used Miller Puckette’s open source program Pure Data (Pd) as a “meta-compositional instrument”: that is, as a vehicle for documenting the creative process in a graphical way as a type of analytical notation.
The pieces extended and explored creative aspects of my previous
compositional research into binary processes, symmetry, and complementary pairs,
using only sine tone frequencies based on the higher partials of sub-audio
fundamentals.
Published Pd programming conventions provided a standard benchmark with
regard to “common sense” signal flow conventions, and were only adjusted when
significant differences between purposes and methods were encountered.
Despite the “composition of the composition” being evident in the graphical
layout of the patches, it became clear that further “interpretive” commentary was
necessary to explain the artistic or musical purposes of different patches.
Nonetheless, it was shown that a composition in Pd can explicitly show its
own construction and interrelation of compositional elements, providing a kind of
descriptive analysis of the work. Moreover, Pd was shown to be suitable for large
scale, multi-sectional projects.
xiii
Chapter 1
Developing Meta-Compositional Strategies
1.1 Background to the Project
My introduction to electronic music in 1977 was through the traditional, and sometimes laborious, techniques of recording, tape splicing and mixing as one of
Martin Wesley-Smith’s students at the NSW State Conservatorium of Music. Later, while studying with Warren Burt, the Moog Modular V offered a dizzying array of possibilities. Finally, the new Fairlight Computer Musical Instrument (CMI) arrived and I earned the tiniest footnote in the history of electronic music in Australia by producing what is presumed to be the first so-called “serious” piece for it. 1
Working with the CMI was exciting, but my undergraduate years were complete and, in 1980, a Fairlight cost close to the equivalent of a small house in
Sydney. I devoted the next decade to orchestral and chamber music, and the decade after that, to musicology and education.
However, in 1988 I had a brief experience that stayed with me. I was invited to IRCAM in Paris for a lecture and performance of one of my chamber works 2 by the
resident Ensemble InterContemporain. As part of the visit a tour of the facility was
arranged and the place seemed to be abuzz with the word “Max”. There is nothing
like a visit to IRCAM to rekindle an interest in electronic music and I began to
fantasise how I could return there.
1 Rosalia (1980), using sampled drum sounds, was first performed on 29 November 1980 at the NSW State Conservatorium of Music and was subsequently featured in a performance at the International Music and Technology Conference, University of Melbourne, on 28 August 1981. 2 Ballade (1984) for flute, clarinet, vibraphone, piano, violin and cello.
1 Domestic and vocational activities, though pleasurable and satisfying, intervened for the next 17 years and I eventually moved to Wollongong in 2005.
After getting settled, one of my first actions was to contact the Faculty of Creative
Arts to discuss the possibility of studying electronic music.
There were two provisos:
1. Did I have sufficient background to resume the study of electronic music
composition at this stage?
2. Was it possible to run the required software on a laptop computer?
Firstly, I brought to this project a four-year undergraduate background in electronic music combined with a thorough post-graduate background in both composition and music analysis. At that level, my preparation for this project was reasonably good. However, I did not have a background as a computer programmer.
When I discussed with Greg Schiemer my interest in using accessible technology (a laptop computer) to develop algorithmic structures using a user-friendly program,
Miller Puckette’s Pure Data (Pd) was suggested. When I discovered that Pd was similar to Max the project was irresistible from my point of view. 3
In terms of “limits” to the project, it had to be acknowledged from the outset that
this was a composition project and not a software-development one. I did not expect
to add to the world’s knowledge of computer synthesis or even of Pd; I expected only
to add original music to that created using Pd. However, I did expect that the music I
created would not only use Pd but be integral to Pd. This is not to say that the music
would not be able to be realised by another program such as Csound, for example, but
that Pd was to be used for a particular purpose.
3 Puckette was working on Max at IRCAM during the late 1980s. I met a number of young Americans there and Puckette may have been among them.
2 The second proviso was a personal and pragmatic one. Having once experienced separation anxiety from the Fairlight CMI after enrolment at the NSW
Conservatorium ceased I did not want to have that happen again. The project had to be able to be realisable in my home studio, which, because I lived in a very small apartment, consisted of a laptop on a collapsible table beside my bed.
1.2 Composition: Pure Data as a meta-compositional instrument
My proposal was to create a folio of electronic pieces using the program Pure Data
(Pd) as a “meta-compositional instrument”.
By “instrument” I meant using the program as a machine or tool to make
music. By “meta-compositional” I meant using Pd to explicitly close the gap between
analysis and composition (the two subjects which have engaged me for the last 30
years): that is, the “notation” of the composition in Pd (taking advantage of its
graphic qualities) was intended to explicitly show its own construction and the nature
of its interrelations—in effect, the composition of the composition would become
evident. Pd already has a widely acknowledged value in real time synthesis. My
intention was to exploit its less acknowledged value by using its inherent graphic
qualities as a means of documenting the thought processes of the composer. 4
1.3 Progress
Initially, I proposed that I would work with MIDI only, and compose a folio of works for quasi-piano in the tradition of Conlon Nancarrow’s Studies for Player Piano
4 This expectation was thought to be reasonable since Pd was designed essentially as a “real-time” computer music system useable by so-called “non-computer scientists” (Puckette 1997). Significantly, Pd’s user interface is a screen-based patching language that imitates the modalities of a patchable analogue synthesiser through a graphic representation (not altogether unlike the Moog Modular V, for example).
3 through to Warren Burt’s Music for Microtonal Piano Sounds (1992-1998) 5 and Kyle
Gann’s Studies for Disklavier (1997-2004). 6 However, after six months learning Pd and composing a short quasi-piano piece I decided to expand my perspectives and a number of types of music emerged:
1. Two short MIDI pieces that functioned as experimental “studies”; 7
2. The paradox of Pythagoras : twenty-seven pieces of variable duration that are
clouds of slowly changing oscillator sound;
3. Music of the spheres : a work derived from The paradox of Pythagoras ,
consisting of nine pieces based on the orbits of the planets;
4. Music of Grace : a series of three gentle, but still austere, compositions 8
consisting of chains of “panels” that are re-readings of previous panels; 9
5. Here… : A single movement chamber work for clarinet, piano and cello,
serving as an “epilogue” to the electronic works and a re-engagement with
acoustic music. 10
1.4 MIDI Studies
The purpose of the MIDI studies was to separate the control functions of Pd from the synthesis, at least for the purposes of personal experimentation. The main issue that
5 See Burt, Warren. 39 Dissonant Etudes . CD, Tall Poppies TP093, 1993. 6 See Gann, Kyle. Nude Rolling Down an Escalator: Studies for Disklavier . CD, New World Records B0633-2, 2005. 7 Recordings of the short MIDI studies, Study#1 and Study#2 , are considered preparatory work and have not been included in this folio. 8 Each one of these compositions has its own title: 1. The cat dances and the moon shines brightly ; 2. The heavy dark trees line the streets of summer ; 3. The crystals in the cave absorb the light as if they have not seen it in a million years . 9 “Panels” is a description and application adopted from the Italian composer Franco Donatoni (1927- 2000). “‘Panel construction’ refers to composition that graphically (and often aurally) creates section breaks” (Haber 2004: 16). The significance of the use of this terminology is that my previous musicological research concentrated on the music of Donatoni (Barkl 1985) and Donatoni’s student Riccardo Formosa (Barkl 1994). My own composition techniques, both for instrumental music and for this Pd project, derive from that research. 10 The number series 27-9-3-1, articulated by the pieces in this folio, is not accidental; it is intended to subtly tie the pieces in the folio together.
4 arose surprised me by its intensity. Clearly, when writing for MIDI piano, the limitations of a human performer are of no consequence, let alone the foibles of an individual pianist. The efforts of louder, softer and faster mean nothing. My surprise was the realisation of just how much my personal compositional approach was entwined with the “physicality” of individual instruments, each imbued with a kind of historical “catalogue” of repertoire or idiomatic figures. In the past my compositional craftsmanship involved establishing a musical meaning through the connection of the instrument to the human performer, and then from the performer to the human listener in live performance.
My approach to composition technique meant nothing in the electronic music
context and I was devastated.
And then I saw this devastation as the most extraordinary opportunity. I had
previously researched composition and music-making from a social-economic and
psychological viewpoint (Barkl 1992) and had been struck by its transactional
component. Performers (including conductors) and audiences generally wished to
feel “rewarded” for their investment of effort and time. Even more directly, concert
producers required an economic return. As a composer I had been sensitive and
accepting of this and had consciously attempted to provide rewards via idiomatic
writing (for the performers) and astonishing sounds (for the audiences). I had no
sense of “selling out”; this was just my approach as a composer and my interpretation
of craftsmanship. The corollary of this point of view was that my music was
essentially demand driven: the live performance was the authentic music (a recording
5 being something else) and, if performers did not wish to perform the work, then there was little point composing. 11
The opportunity was that, while I had previously seen these strictures as
stimulating (to the point of being the foundation of my compositional approach), the
removal of them would allow a totally “free” music. For the first time I could create
music that I did not have to “sell” to a performer. I could create music that I, even if
it was only I, wished to hear.
Significantly, by acknowledging the authenticity of a recording of an
electronic work, as distinct from its live performance in a concert setting, 12 the music
remained unbound by the economic context of live performance and became available
for distribution via electronic means, such as web radio, whilst remaining in authentic
form. 13 While live interactivity remains one of the most outstanding and attractive
features of Pd, my interests are in the structuring of compositions in time and not in
interactivity or improvisation. 14
1.5 The paradox of Pythagoras
The initial purpose of The paradox of Pythagoras was to concentrate on sculpting sound; that is, to experiment with synthesis with minimal interference from Pd’s control functions. The concept was to create complementary (A-B) panels of sound using slowly changing sine tones based on higher partials in the harmonic series. 15
11 The aesthetic problems of electronic music and live audiences have been discussed at length (see Emmerson 1986, Davis 1996 and Holmes 2002). Cf the communicatory intentions behind Steve Reich’s “documentary” approach to electronic music (Reich 1996) and the research into speech synthesis (Chowning 1989). 12 Here I take my cue from Morton Subotnick, Silver Apples of the Moon (1967) (Wergo 2035, 1994), the first electronic composition conceived and recorded specifically for release as a commercial recording, as apposed to “live” or concert performance. 13 See Cosentino 2004 for web radio and Duckworth 2005 for other web based distribution.. 14 As a jazz player, my improvisatory urges are well satisfied elsewhere. 15 Because the music in this project is constructed solely from exact harmonics, for the purpose of this thesis, “partials” and “harmonics” have the same meaning, with the fundamental being counted as the first partial or the first harmonic. However, it is recognised that the word “partial” is often used to
6 These synthesis studies have taken on a life of their own, engaged my interest, and have grown from “panels” to “walls” of sound that vary from resembling various sounds ranging from tanpura drones to industrial noise. 16
1.5.1 Complementary binary structures
My interest in complementary structures as a compositional determinant is a personal one relating to my previous research into binary form and balance, and the notion of creating complex structures from simple binary opposites. 17 The current project serves to further that research.
1.5.2 Sine tones
Sine tones have an audible clarity where beats, difference tones and even residues may be expected to be heard. 18 I experimented with FM synthesis and, while the timbres were interesting for The paradox of Pythagoras , I found the sidebands distracting for the more “pure” intentions of Music of Grace and chose to leave the sine tones pure and unadorned for that series. 19
Additionally, sine tones have and maintain, for me, a strong aesthetic dimension, as expressed by Stockhausen in 1953: “It is unbelievably beautiful to hear
identify harmonics that are not exact integer multiples of the fundamental. For a similar reason, the word “overtone” is avoided, as it is commonly used to describe partials that do not have a relation to harmonics. 16 The use of the word “noise” here is not intended to imply any connection to Russolo’s (1986) concepts or ideas. Indeed, as I will show later, these pieces have very little in common with the more random frequencies associated with “noise”. Rather, they are more closely associated with notions of “purity”. 17 See Barkl 1994. 18 See Pierce 1989, Schneider et al. < http://www.klinikum.uni-heidelberg.de/Music-and-the-Auditory- Cortex.5503.0.html > and “How Do You Hear Tones?” 2006
7 such sounds, which are completely balanced, ‘calm’, static, and ‘illuminated’ only by structural proportions. Raindrops in the sun…” 20
1.5.3 The use of the harmonic series
Initially I did not have an interest in tuning systems. However, working in equal temperament with sine tones made the tuning anomalies of equal temperament distractingly apparent and seemingly out of place. Using higher partials in the harmonic series (and the equivalent partials in the sub-harmonic series) placed all frequencies, including summation and difference tones, in their “correct” relation.
The results enhanced aural clarity.
1.6 Music of Grace
The inspiration for Music of Grace comes from the American poet John Gracen
Brown and specifically his book of poetry The Return (2005). Music of Grace derives from a Bach chorale, and extends it to make a very different music.
Music of Grace uses the lessons learnt in the MIDI control studies and The
paradox of Pythagoras to make a series of pieces of some length and scale from basic
Pd principles; that is, without using externals developed by other composer-
programmers. 21 Certain Pd programming conventions, as proposed by Trevor Agus
(2004), 22 are acknowledged in order to document the composition process.
1.6.1 John Gracen Brown’s poetry
There is no special reason for the choice of this poet except for personal preference.
The notion of “The Return” is metaphorical (from my point of view) for my return to
20 Letter to Karel Goeyvaerts 7 September 1953, quoted in Toop 1979 (translation by Richard Toop). Stockhausen was writing of his experiences composing Studie I . 21 The use of externals is discussed later, in the Pure Data Literature Review. 22 See Appendix D. Agus’s conventions will be briefly described in the next section.
8 composition after a decade of near silence. It is through the “grace” of the computer
(that is, inexpensive hardware and open source software) that has made this return possible.
The titles of the three individual pieces that comprise Music of Grace are the complete text of three short poems by John Gracen Brown (2005: 5). 23 These poems,
which take the form of brief “visions”, 24 create a general context for the musical
works:
1. The cat dances and the moon shines brightly 25
2. The heavy dark trees line the streets of summer 26
3. The crystals in the cave absorb the light as if they have not seen it in a million
years .27
1.6.2 The use of primary material: a Bach chorale
As did countless music students, I spent a decade of childhood and adolescence emulating Bach chorale style, and tonal harmony became something of a personal strength. The particular chorale I have chosen, Befiehl du deine Wege ,28 is the only
one in the Riemenschneider collection to have a flute obbligato. 29
23 John Gracen Brown gave me permission to use his work in a letter dated 26 April 2006. Upon completion of Music of Grace I was concerned that the result may not meet with his approval, so I sent him a CD copy. After listening to the pieces, and with characteristic warmth and generosity, John Gracen Brown reaffirmed his permission in a letter dated 13 September 2008. 24 This is how John Gracen Brown described them (personal communication 13 September 2008). 25 “The Cat and the Moon”. 26 “Streets on a Summer Night”. 27 “Cavern Crystals”. 28 “Entrust thy Ways”, otherwise known as the melody of “Herzlich thut mich verlangen.” In this harmonisation it closes Cantata 161 “Komm, du süsse Todesstunde”, suggesting the awakening and resurrection of the body. 29 See Bach 1941: 66. Additionally, the melody from this chorale has been used for popular songs, notably Paul Simon’s “American Tune”, from There Goes Rhymin’ Simon (Warner Bros 1973/WEA 2004).
9
Figure 1.1 Befiehl du deine Wege
The flute obbligato became my licence to do my own troping. The extracted
pitches from Befiehl became numbers (as per standard MIDI assignment) and were
allocated to harmonic numbers.
1.6.3 The use of numbers: an analogue between MIDI note numbers and
harmonic numbers
In essence, I viewed MIDI number assignment as an ordering or ranking system,
placing one (available) pitch in relation to the next (where the actual numbers
themselves are of little significance). One may imagine that composers who typically
work with scales30 could view MIDI numbers as a chromatic scale and the harmonic
series as “just” another scale. The assignment of numbers from one parameter to
another is not unusual. See, for example, Stockhausen’s analogue of durations to the
harmonic series in How Time Passes.31 My use of numbers in this fashion is focused
on the relation between pitches rather than the pitches themselves.
30 Such as Warren Burt and Kyle Gann. 31 Stockhausen, Karlheinz. “…how time passes…” Die Reihe 3, Bryn Mawr: T. Presser (1959): 10-14 (p.16). Cited in London 2002: 716, Fig.22.10. Stockhausen’s article also includes an equivalent duration-pitch diagram for the sub-harmonic series. See also Xenakis 1992 and Gozza 2000 for number-sound relationships.
10
Figure 1.2 Rhythmic Durations as a Harmonic Series—Stockhausen
1.7 The application of programming conventions
The first thing that struck me about Pd’s patching language was its ability to
document compositional algorithms. It seemed to me that, with a little care, Pd
patches would be easily readable, not so much as a finished or publishable “score”,
but as a documentation of a composer’s sketches and evidence of process; that is,
serving as a kind of descriptive analysis of the piece. Using sketches or examples
from a musical score, with minimal annotations, as an analytical tool is well known.
Schenker is perhaps the most obvious example of this.32
32 Schenker, Heinrich. “Vom Organischen der Sonatenform,” in Das Meisterwerk in der Musik, Vol.II, Musich: Drei Masken, 1926; trans. W.Drabkin as “On Organicism in Sonata Form,” in The Masterwork in Music, Vol.II, Cambridge University Press, 1996; cited in Hyer 2002: 742. I have also previously developed my own techniques in this regard (see Barkl 1985 and Barkl 1994).
11
Figure 1.3 Haydn’s Sonata in G minor, Hob.xvi:44—Schenker
Initially I intended to develop my own set of patching conventions, since patches can easily become impenetrable. However, within a few weeks of literature review I discovered that Trevor Agus (a British researcher into hearing science) had raised similar ideas, though from a rather different point of view,33 and had published
his own set of conventions. Agus’s brief conventions, comprising approximately half
a dozen pages, recommend concise comments, consistent data flow, consistent
naming of sub-patches, and avoidance of “sends” and “receives”34 and inline
monitoring or “debugging” objects.35 As a starting point it seemed sensible to apply
Agus’s conventions as far as possible and extend them if need be.
Examples of patches from The cat dances and the moon shines brightly
follow, which show some basic aspects of the principle in action.36 In Figure 1.4 data
33 “This is intended to apply to situations where Pd patches are being shared between users. … Specifically it is for a project in which 4 of us will be working on the same potentially large-scale patch.” (Agus 2004, 19:09:16 CET) 34 “Sends” and “receives” are connections that are not visible on screen. 35 That is, functional components should be “inline” and non-functional monitoring components should be offset. 36 See Appendix E “Pd Boxes” for a description of how Pd objects, messages, GUIs and comments are rendered in this thesis.
12 flows down the page from panel 1 to panel 5. The [bang) GUI signals that the previous section is complete as well as initiating the next section.
Figure 1.4 The cat dances Panels 1-5
Figure 1.5 shows what is inside the [pd panel_1] sub-patch. Again, data flow
is down the page and shows that panel 1 comprises two subsections.
13
Figure 1.5 The cat dances Subsections 1a and 1b within Panel 1
Figure 1.6 shows what is inside the [pd p_1a] sub-patch. Here the data flow is more complex, with feedback to [pd high_control_1-22].
14
Figure 1.6 The cat dances Subsection 1a
Opening further sub-patches, such as [pd high_control_1-22], [pd rests], [pd axis_50], [pd high_1-22], [pd low_1-22], [pd mixout_x6_d] and [pd no_of_voices_playing], would delve deeper into the structure down to the level of elemental operations.
The bulk of the written component of the thesis (and appendices H, J and L) will be concerned with the description and explanation of these kinds of patches. The cat dances has 50 different such “canvases” (as Pd calls them), some of which are
15 elementary (such as Figures 1.4 and 1.5) and some of which are more complex (such as Figure 1.6); The heavy dark trees has 257 and The crystals in the cave has 718.
1.8 Research question
Insofar as a folio of compositions can be thought of as “research”, the research question could be expressed as follows: 37
Do Agus’s conventions provide a viable method of plotting creative processes
in large scale Pd projects?
1.8.1 Aims
The aim of the project is to compose a folio of electronic pieces that, as far as
possible, use Pd as a vehicle for documenting creative process in a graphical way; that
is, as a kind of analytical notation.
1.8.2 Significance
Agus’s conventions have been proposed and discussed amongst Pd users, but as yet
there has been no documented specific implementation and therefore no consensus on
the matter. 38 However, such an approach to Pd would not only be of use for
collaborative projects, as flagged by Agus, 39 but for “archival” benefit to scholars, students and, most importantly, composers themselves.
37 The “thesis” is the “submission of creative work (research)…supported by written documentation…focusing on aspects such as origins of the work, structures and techniques used, and artistic theories underpinning the work.” See University of Wollongong. Creative Arts: 2006 Postgraduate Course Guide : 16. 38 See Barknecht 2004, 5 March 00:24:09 CET. The complete discussion on the subject may be found at the “Pure Data Mailing List,” last accessed 8 August 2005, < http://iem.at/mailinglists/pd-list >. 39 See Agus 2004, 4 March 22:50:17 CET. The issues are, in fact, a little more complex than outlined above. One of Agus’s principal concerns, for example, is that software is unlikely to be maintained for its whole life by the original author, and conventions allow later engineers to understand new code more quickly (Agus 2004).
16 1.8.3 Approach
The approach to this project is creative. There is no intention, for example, to produce pieces that illustrate Agus’s conventions. 40 Rather, the intention is to produce pieces that will conform to Agus’s conventions insofar as the conventions remain useful.
1.8.4 Originality
The project is original in the sense that the compositions are original. However, three aspects are worth considering in this context:
1. The use of “standard” Pd (as distinct from “extended” Pd)
2. The use of sine tones and higher partials (harmonics)
3. The application of Agus’s conventions
Firstly, the use of the “standard” 41 version of Pd is not original in itself.
Rather, it represents a particular value system and point of view of the composer (as
discussed previously).
Secondly, the use of sine tones and higher harmonics is also not original in
itself, but it does represent a particular aesthetic held by the composer. Sine tones
have been used since the birth of electronic music and their use in this project reflects
the tradition of the Cologne studio and elektronische Musik 42 rather than, for example, recent Japanese so-called onkyo music. 43 One of the most well known contemporary uses of higher sine tone harmonics is by La Monte Young in his Dream House project
40 Such a practice is not unusual. Compare, for example, Nattiez’s analysis of Varèse’s Density 21.5 for solo flute (Nattiez 1982). The purpose of Nattiez’s analysis was more to provide an example of the semiotic method of analysis than a response to the desire to analyse this particular work (see Barkl 1994: 34-5, 45). 41 “Standard”, as distinct from extended versions of Pd that include externals developed by other composer/programmers. 42 See Cologne— WDR: Early Electronic Music , CD. BVHAAST 9016. 43 See “[Japan] Titles at Aquarius Records” < http://www.aquariusrecords.org/cat/japan15.html >.
17 in New York. 44 I became aware of the Dream House only after working on The
paradox of Pythagoras and making the presumption that there must be other music
like this. 45 Unfortunately from my point of view, the Dream House is an installation
and there are no commercially released recordings to listen to. However, descriptions
and reports are quite detailed 46 and it would appear that, among other things, the tones
in the Dream House are static. Apparent changes and effects are perceived through either changes in perception over time, or changing one’s physical position in the room. Two major points of difference between the Dream House and The paradox of
Pythagoras and Music of Grace are that the pitches and amplitudes do change over time, and they are conceived as recordings, not live performances or installations.
Lastly, while applying Agus’s conventions is certainly not an original idea, the particular purpose for which they are applied may be. Notation for electronic music has been a point of interest for many composers, 47 and has recently become a focus
for Miller Puckette and Pd users. 48 Additionally, the notion of Pd’s “compositional”
qualities, as opposed to its more celebrated “performative” ones, has recently attracted
Puckette’s attention. 49 Scoring and notation have become topical subjects for Pd. As far as my own interests are concerned, using Agus’s conventions to document the creative process extends and develops my previous research using graphical analytic techniques. 50
In summary, it would be fair to say that, leaving the creative originality of the
compositions aside, the individual contributory components of “standard” Pd, higher
44 “La Monte Young”, Mela Foundation < http://www.melafoundation.org >. 45 I would like to thank Warren Burt for bringing the Dream House to my attention. 46 See Gann, Kyle. “The Tingle of p x m n – 1” < http://www.melafoundation.org/gann.htm >. Howard, Ed. “Dream House” < http://www.melafoundation.org/Howard_03.htm >. McCroskey, Sandy. “Dream Analysis” < http://www.melafoundation.org/mccroske.htm >. All pages last accessed 15 June 2006. 47 See, for example, Iannis Xenakis’s Mycenae Alpha and Cornelius Cardew’s Treatise . Cf also Stockhausen’s attempts to create, in retrospect, a “study score” of Studie I (Toop 1981). 48 See Puckette 2002 and Damien Henry 2004. 49 See Puckette 2004. 50 See Barkl 1985 and Haber 2004.
18 sine tone harmonics and Agus’s conventions are not significantly original in themselves. However, my claim is that, when taken as a whole and combined with creative work, this project represents an original approach and an original contribution.
1.9 Pure Data Literature Review
1.9.1 Published findings
Significant milestones in Miller Puckette’s development of Pd are documented in his published papers, a list of which is included in Appendix A. Of particular interest are
“Pure Data” (1996) and “Pure Data: Another Integrated Computer Music
Environment” (1997) as they describe the early developmental aspects of the program. Later papers, such as “Synthesizing Sounds with Specified, Time-Varying
Spectra” (2001), “Low-Dimensional Parameter Mapping using Spectral Envelopes”
(2004) and “Phase Bashing for Sample-Based Formant Synthesis” (2005), are concerned with more recent problems that may be applied to Pd. Another is notable for its application to a practical outcome, “New Public-Domain Realizations of
Standard Pieces for Instruments and Live Electronics” (2001), and two others for what appear to be a particular interest of Puckette: “Using Pd as a Score Language”
(2002) and “A Divide between ‘Compositional’ and ‘Performative’ Aspects of Pd”
(2004).
The two major published sources related to Pd are Miller Puckette’s “Theory
and Techniques of Electronic Music” (2003) 51 and the Institut für Elektronische
Musik und Akustik’s (IEM) “Bang: Pure Data” (2006). Puckette’s text is essentially
51 Although the date is given as 2003 (the version used during this project), Puckette considers the text to be a “work in progress”, intending to improve, upgrade and extend it as required. Its free availability in soft copy on the web makes this approach possible.
19 a comprehensive textbook on electronic music that uses Pd to illustrate the concepts. 52
As an additional feature, the patches used in the book are included in the Pd program download.
“Bang: Pure Data” is a web based publication of a selection of the papers presented in the First International Pd Convention in 2004, and thus makes available a number of papers in a convenient source. 53 The papers range from the technical to the
sociological and any attempt to make a summary description of them here would be a
distortion. Part of their significance is that they provide a window to the wide range
of serious research interests related to Pd engaged in by academics and artists from
Europe and the USA. While no paper raises the notion of Pd being used as
documentation of the creative process, of particular interest is one that identifies and
describes the Pd community, giving numbers of members of various subscriber lists,
geographical spread, types and modes of communication, and motivations (Mayr
2006).
The “Pd Help and Tutorials” section of the program is another significant
source of information. All “Help” files use working examples from Pd to illustrate
objects and functions. Extensive example patches, such as additive synthesis, FM and
reverberation, are also included in the Help download. Websites, associated with the
Institut für Elektronische Musik und Akustik at Graz provide further access to
tutorials and mailing lists. 54
52 General sources on computer music are more available than one would perhaps think. Until quite recently, authors of doctoral dissertations in electronic or computer music felt the need to include full descriptions of synthesis and underpinning theory before describing the actual doctoral project; see for example Ashton 1971 and Malouf 1985, which include sections describing general waveform generation and control. For this Pd project Roads 1996 was also consulted. 53 See “References—Conference Proceedings” for sources of Graz Conference papers from Barknecht, Bouchard, Cosentino, Czaja, Grill, Cyrille Henry, Damien Henry, Hollwerweger, Jurish, Pichlmair, Puckette, Savirsky, Smölnig, Steiner and Tittle, 2004. 54 See Appendix B “Pd Help and Tutorials”.
20 1.9.2 Externals developed by other composer-programmers
The resource of a world wide community of Pd-users sharing patches is an exciting and stimulating prospect, and for some period of time I worked with Olaf Matthes’s
MaxLib externals (2004). 55 However, for the purposes of this project, I reverted to the “standard” release of Pd, as provided by Miller Puckette, 56 for two reasons.
Firstly, I found myself drifting from my objectives and methods. My
objectives included exploiting the opportunity to produce the music I wish to hear,
irrespective of external aesthetics or economics. My method to achieve this objective
was to draw the music from my imagination, and to use Pd to construct the music in a
planned or architectural sense, rather than be distracted by adopting an exploratory
“trial and error” approach to available materials that had been created by others
motivated by a different aesthetic. 57 More specifically, my objective at this stage was
not to “learn” Pd per se , but to use it to achieve my compositional aims. Indeed, it is
likely that learning Pd thoroughly would take significantly longer than the time
allocated to this project. 58
Secondly, after adopting a freely available program designed for widespread
use, I had no wish to personalise it to the extent that my patches would not load
without special compiling. My intention was to ensure that my work would always
load on the “standard” version of Pd; complexity will be developed through the
building up of basic processes.
55 See also “Pure Data External Repository” < http://pure-data.sourceforge.net/ > and Smölnig “How to Write an External for Puredata ” < http://iem.at/pd/externals-HOWTO/pd-externals-HOWTO.pdf >. 56 See < http://crca.ucsd.edu/~msp/software.html >. An extended package of Pd may be downloaded from < http://pure-data.info >. The version of Pd used for this project is 0.38.3. 57 This is not to cast an implicit judgement on the “trial and error” approach, but to make a distinction between it and a “planned” approach. 58 Some advice in this regard has been offered by Frank Barknecht, journalist for Deutschland Radio and the computer magazine c’t and an experienced software developer and Pd programmer: “I gave myself a span of 4 years in which I would not even try to do any real music with Pd but instead just invest time to learn it” (2004, 5 March 00:57:42 CET).
21 1.9.3 Areas requiring original research
There has been some general doubt expressed by Pd practitioners as to the ability of
Pd to “scale up”; that is, its ability to be effective in larger scale projects. 59
The extension of Pd practice and documentation into larger scale compositions
has not specifically been addressed in the literature and was consequently chosen as a
focus for this project. The first stage in this process was to explore and develop the
general sound world of the project through manipulation of multiple oscillators. This
is discussed in chapter 2.
59 See, for example, Steiner: “Graphical programming languages don’t scale well into larger projects. Their strength is in getting highly customized things done quickly and instinctively. From what I’ve seen…they are generally not the right tool for creating large, general purpose, modularized applications” (2004, 23 March 14:29:19 CET) and Barknecht’s reply pointing out patcher languages’ relation to scripting languages (2004, 23 March 17:07:00 CET). Agus remains confident of Pd’s capacity to “scale up” (personal email 2 November 2006, see Appendix O).
22 Chapter 2
The paradox of Pythagoras
Chapter 2 discusses The paradox of Pythagoras in detail. In addition to describing
the work’s structure and function, it identifies significant aesthetic choices that are
maintained throughout the rest of the folio, particularly with regard to the choice of
fundamental pitch and use of the harmonic series. MP3 recordings of the 27
“movements” are included on the companion CD to this volume. Also included on
the companion CD, in order to facilitate cross referencing, is the related Appendix F.
2.1 Origins
The origins of The paradox of Pythagoras lie in the experiments I did in synthesis, building up banks of oscillators that will behave in interesting musical ways. The rather presumptuous title for this patch comes from a self-published book “composed”
(as he writes on the cover) by Michael O’Halloran: Revisiting the Ancient Musical
Scale and the Paradox of Pythagoras (2004). My intention was to choose a
frequency on which to base the harmonic series used for this patch as well as the
subsequent Music of Grace . One option was to adopt something approximating the
legendary Chinese huang chung ( hwangjung ) tone that was said to maintain ancient
Chinese civilisation in harmonious alignment. 60
My choice, however, came from O’Halloran’s book, as a kind of tribute to him as an enthusiast for the proportions articulated by ancient measures and as proprietor
60 I had been introduced to the huang chung tone, the “yellow bell” or “primal sound”, some twenty years ago through the rather polemical book The Secret Power of Music (Tame 1984) and remembered it as an attractive notion. For a more contemporary review of Tame (1984) and the huang chung see Gray (“Frequently Asked Questions: The Secret Power of Music,
23 of the Old Goulburn Brewery. 61 If his book was “composed”, then my piece may be considered a “variation” on his composition, and I chose a fundamental of “D” in the fifth octave below middle-C, or 9.13125 Hz, tuned according to O’Halloran’s calculations.
The fundamental can also be represented as D ,,, using a convention adopted in this thesis. In this convention specific pitches are given in the text using apostrophes and commas or strokes: c ’=middle-C; an octave below c ’ is c; an octave below c is C; and an octave below C is C ,. D ,,, is therefore four octaves and a minor seventh below middle-C. 62
O’Halloran’s complete calculations and description of the “paradox” are rather complex and require some clarification before they are of any use in this context. In summary, O’Halloran relates the musical scale to the architectural referent, the 2x2 geographic-foot “mason’s module”, two modules being analogous to what are normally referred to as two tetrachords (O’Halloran 2004, 3). The proportions are applied to the dimensions of the Great Pyramid of Giza and the frequency of a’=438.30414 Hz is derived (2004, 47), where the scale passes from a ’ to g ’’ .
When the mason’s module is “tweaked” with reference to the Sothic Great Year
61 It should be made clear that O’Halloran is not a scholar in the academic sense, but an enthusiast, and there has been no attempt on my part to challenge his writings in a systematic academic manner (though it can be seen that questionable results may have been the result of judicious rounding of decimals). The Old Goulburn Brewery, claimed by O’Halloran to be designed by Francis Greenway and imbued with significant architectural and structural proportions (see also O’Halloran 2002), was the venue of many musical events during my 18-year residence in Goulburn, and the source of many happy memories. His pronouncements are accepted in good faith and their technical or historical accuracy (or otherwise) has no bearing on the nature of this project. 62 This is the so-called “Helmholtz pitch notation” because of the use of it in his Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (Brunswick 1863). Commas, or strokes, change to Roman numerals for five and above. The apparent awkwardness of assigning c ’ to middle-C is explained by the assignation of the pitch C for the bottom note of an 8-foot stop on organ manuals. Helmholtz’s notation is used as a conventional standard in the Grove’s Dictionary of Music and Musicians (Grove [ed.] 1878, 1880, 1883, 1899, Fuller-Maitland [ed.] 1900, Colles [ed.] 1927, 1940, Blom [ed.] 1954, Sadie [ed.] 1980, 2000) and the Harvard Dictionary of Music (Apel [ed.] 1944, 1969, 1970, 1976). It is, perhaps, particularly relevant to use it here in acknowledgement of Helmholtz’s analysis of overtones (including combination and summation tones and beats).
24 (2004, 53), 63 the proportion becomes 2:2.0292186 (2004, 54) rather than 2:2. That is,
according to O’Halloran, the fundamental, characterised as 2, has a Sothic twin
formed from the addition of 2 to the “gnomon” residual 0.0292186 expressive of the
Great Year (2004, 54), the twin being the “foundation of all measures” (2004, 62).
With a ’=438.30414 Hz, O’Halloran derives all notes except d ’’ from whole number
multiples of 12.1751, 64 and then derives d ’’ from the difference between c# ’’ (44 multiples) to d# ’’ (52 multiples): that is, 48 multiples of 12.1751 (2004, 64). The note d ’’ becomes 584.4 Hz and “therefore resonates with the fundamental tone. …
∆65 or D represents ‘nothing’ and ‘everything’. Like the very name of God in ancient
thinking, it reverberates in and through everything, yet is utterly and ultimately
inexpressible” (2004, 64). 66 Whether true or not, such assertions were more
romantically compelling than the prospect of my choosing a fundamental frequency at
random. 67
The frequency d ’’ =584.4 Hz was not, however, an appropriately low
frequency on which to base a harmonic series. I chose, therefore, to divide the
frequency by the required number to reduce it to an approximation of the lowest MIDI
D,,, which I was gratified to note was MIDI number 2, and therefore coincidentally referential to the notion of the 2x2 mason’s module and the “foundation of all
63 The Sothic Year refers to the fixed year of the ancient Egyptians, determined by the heliacal rising of Sirius and equivalent to 365 ¼ days. 64 12.1751*36=a ’; *40=b ’; *42=c ’’ ; *46.66=d ’’ ; *54=e ’’ ; *57=f ’’ ; *63=g ’’ . 65 ∆ (Delta) is also the Egyptian sigil (signet) for Sirius (O’Halloran 2004, 62). 66 According to O’Halloran, the significance of the number 584.4 is that it is double 292.2: “This is immediately recognised as the numeric of the Great Year of 29,220 years; and as a simple multiple of the residual component of the fundamental Sothic tone, 2 plus 0.02922…” (2004, 64). 67 Additionally, without ever mentioning the huang chung tone, O’Halloran had arrived precisely at the pitch, if not the exact frequency, of the huang chung for the last Chinese dynasty (suggested by fixed pitch instruments and identified by J.A. van Aalst in 1884): d ’’ of 601.5 Hz (Aalst 1933). By comparison, at the “Stuttgart Pitch” of a ’=440 Hz, the equal tempered d ’’ =587.33 Hz. O’Halloran’s d’’ is therefore 8.65674 cents lower than Stuttgart Pitch.
25 measures” referred to above. My D ,,, fundamental therefore became 9.13125 Hz 68 instead of the standard equal temperament D ,,, of 9.17702 Hz.
The second stage of my thinking was to choose how many numbers of the harmonic series to include as the patch was running. The lowest MIDI D ,,, suggested the use of 128 harmonics to further reflect the MIDI note system (and this is, in fact, the number I have adhered to in Music of Grace ). I noted that the theorist
Joseph Sauveur 69 claimed to hear up to the 128 th harmonic (Cook 2002, 85) (a
remarkable coincidence, in comparison to the 128 available MIDI notes from
C,,, =0 to g VI =127) and was initially quite content with this.
However, as time progressed, I wished to hear further harmonics and so
halved the fundamental frequency more and more times, allowing higher and higher
harmonics. Hypothetically, the fundamental could be almost infinitely low, allowing
an almost infinite number of harmonics. At present, when performing the patch, I
tend to favour using a fundamental of 9.13125/2 16 , that is
9.13125/65536=0.000139332 Hz, and up to the 1,000,000 th harmonic.
The general effect of The paradox of Pythagoras is of overlapping chords
slowly changing over time. The chords are comprised of random selections of odd
numbered harmonics above the fundamental, ensuring that there will be no “octaves”.
Each frequency will therefore be “unique”. The choice of fundamental and the choice
of the number of harmonics are up to the initiator of the patch: that is, the
“performer”. Additionally, the envelope of each frequency (duration of attack,
duration and dynamic of sustain, and duration of decay) is random within prescribed
limits, making each articulation unique. Finally, the timbre of each frequency,
68 Halved six times. 69 Joseph Sauveur (1653-1716) is famous for devising the logarithmic method of pitch calculations.
26 modified by frequency modulation (FM), changes or moves between two randomised control frequencies making each timbre unique.
It will be noticed that, when moving one’s head while listening, the sensory
experience changes, different pitches becoming more or less apparent. The reason for
this is not clearly understood, but it is presumed to be the effect of masking or
residual tones in the ear ( cf . Pierce 1989 and Parncutt 1989).
One of the first things that will be noticed is that, for ease of operation, I have provided a simple performance interface (see Figure 2.1 The paradox of Pythagoras top canvas), despite my intention not to “hide” the processes behind GUIs. While sophisticated GUIs are an area of research in themselves, quite outside the scope of this project, 70 this simple example facilitated experimentation.
Secondly, upon opening the first three pd objects on the top canvas, it will become apparent that Agus’s convention has not been strictly adhered to, since each uses the [send] object. When attempting to provide choices as to the fundamental, the number of harmonics (the “range”) and the duration, it was found that avoiding [send] was impractical. This is one instance where, in effect, Agus’s convention would have obscured clarity. If the three criteria were fixed, a [loadbang] on each oscillator would have been sufficient, with a [bang) to start. However, with variable criteria,
“beaming” the values to each oscillator remains a simple and consistent method to adopt, without unduly diminishing the clarity of the signal path to the reader. 71
70 See, for example Benson, Calum, Adam Elman, Seth Nickell and Colin Z Robertson. “GNOME Human Interface Guidelines 2.0: the GNOME Usability Project.” Accessed 21 September 2006
27 A discussion of the patches in detail follows. The complete patch structure of
The paradox of Pythagoras , showing the placement of all embedded sub-patches in relation to each other, is given in Appendix F on the companion CD to this volume.
MP3 recordings of the 27 “movements” in the piece are also provided on the CD.
2.2 The paradox of Pythagoras : screen prints
The top canvas (Figure 2.1 The paradox of Pythagoras top canvas) provides three pd objects from which to choose the parameters of the patch. Firstly, the frequency of the fundamental may be chosen from 27 options as listed in the pd object [pd fundamental_of_9.13125Hz_/…]; 72 that is, the fundamental 9.13125 Hz divided by each of the numbers given. 73 The default frequency (if no other fundamental is selected) is 9.13125 Hz (D ,,, ).
“Good Pd Programming Practice?” 21 March 2004, 22:35:14 CET. Online Posting. Pd. Accessed 21 September 2006 < http://lists.puredata.info/pipermail/pd-list/2004-03/018468.html >). 72 The names of the first two objects on the top canvas have been truncated for the purposes of the discussion in the thesis. [pd fundamental_of_9.13125Hz_/…] and [pd number_of_harmonics_128_*…] have lengthy names in order to document the actual denominators of 9.13125 Hz and the number of harmonics used. Additionally, they allow for the length required to differentiate 27 inlets along the top of the objects. 73 Dividing by 0.015625 is equivalent to multiplying by 64; likewise /0.03125=*32; /0.0625=*16; /0.125=*8; /0.25=*4; /0.5=*2. The 27 actual fundamental frequencies are: 584.4 Hz, 292.2 Hz, 146.1 Hz, 73.05 Hz, 36.525 Hz, 18.2625 Hz, 9.13125 Hz, 4.56563 Hz, 2.28281 Hz, 1.14141 Hz, 0.570703 Hz, 0.285352 Hz, 0.142676 Hz, 0.0713379 Hz, 0.0356689 Hz, 0.0178345 Hz, 0.00891724 Hz, 0.00445862 Hz, 0.00222931 Hz, 0.00111465 Hz, 0.000557327 Hz, 0.000278664 Hz, 0.000139332 Hz, 6.96659*10 -5 Hz, 3.4833*10 -5 Hz, 1.74165*10 -5 Hz, 8.70821*10 -6 Hz.
28
Figure 2.1 The paradox of Pythagoras top canvas
Secondly, the number of harmonics may be chosen from the pd object [pd
number_of_harmonics_128_*…]. Again, there are 27 options, with 128 being the
default number. The multiples of 128 have a complementary function to the
fundamentals so that the upper frequency limit remains stable if the corresponding
[bang)s are clicked. 74 That is, if the first [bang) is clicked of both the “fundamental” and the “number of harmonics” pd objects, the result is
9.13125/0.015625*128*0.015625 = 1168.8 Hz as the upper limit. Similarly, clicking the 27 th [bang) of both pd objects results in 9.13125/1.04858*10 6*128*1.04858*10 6 =
74 The actual number of harmonics selected for each [bang) 1-27 are as follows: 2; 4; 8; 16; 32; 64; 128; 256; 512; 1,024; 2,048; 4,096; 8,182; 16,384; 32,768; 65,536; 131,072; 262,144; 524,288; 1.04858*10 6; 2.09715*10 6; 4.1943*10 6; 8.38861*10 6; 1.67772*10 7; 3.35544*10 7; 6.71089*10 7; 1.34218*10 8.
29 1168.8 Hz. 75 Of course, this arrangement is merely for orientation, and quite different
effects can be gained by assigning different fundamentals to different numbers of
harmonics. 76
The desired [bang) enters [pd fundamental_of_9.13125Hz_/…] (Figure 2.2)
via the [inlet], and the calculation is made and sent to every appropriate receive object
[r fundamental] inside [pd oscillators]. Note the [loadbang] connected to [9.13125( to
provide the default setting.
Figure 2.2 [pd fundamental_of_9.13125Hz_/…]
[pd number_of_harmonics_128_*…] (Figure 2.3) shows the calculations made when the chosen [bang) enters via the [inlet] in order to establish the frequency range. The result is sent via [s range] to [pd oscillators]. Note the [loadbang] connected to [128( to provide the default setting.
75 1168.8 Hz is MIDI note 85.9134 (that is, MIDI note 86 due to the lower D ,,, fundamental) which is d ’’’ . 76 The 27 movements recorded on the companion CD to this volume match the 27 fundamentals to the “equivalent” number of harmonics in the normal manner.
30
Figure 2.3 [pd number_of_harmonics_128_*…]
[pd duration_1_2_5_10_15_20_30_40_50_60] (Figure 2.4) sends the approximate duration, calibrated in minutes, to [pd oscillators] via [s duration].
Figure 2.4 [pd duration_1_2_5_10_15_20_30_40_50_60]
[pd oscillators] (Figure 2.5) receives the selected duration and converts it to
milliseconds [* 60000] before sending it to the three banks of oscillators [pd
31 fm_two_chord_pair_odd_harm]. 77 The purpose of the three banks is to allow the
chords to develop, change, and overlap through time. The duration is divided by two
[/ 2] for the first bank (since the oscillators will be working in pairs to form the total
duration). The trigger bang float object [t b f] 78 ensures the “float” (floating point number) enters the right hand side inlet of [pd fm_two_chord_pair_odd_harm] before the [bang) enters the left hand side inlet.
Figure 2.5 [pd oscillators]
The second bank further subdivides the duration by three [/ 3], and the third bank by two [/ 2]. For the second and third banks, the duration is sent to a float object
[f] (which stores the float entering via the right hand side inlet) and to a trigger bang float object [t b f]. The [t b f] seeds the [delay] via the right inlet, and follows with a bang to the left. A bang will be produced at the outlet of the [delay] after the elapse
77 The number of oscillators in each bank is related to the processing power of the computer. The number in Fig.2.5, 2+4+6, is the maximum number that my Compaq Evo N1000c can comfortably handle with 512MB of RAM. 78 [t b f] is an abbreviation for [trigger bang float].
32 of the seeded time, banging out the stored float in [f] to the right inlet of [pd fm_two_chord_pair_odd_harm] before banging the left inlet.
The function of [pd fm_two_chord_pair_odd_harm] (Figure 2.6) is to control two banks of six oscillators [pd mixout_x6] at the bottom of the canvas. The one at the right plays a six-part chord first and the one on the left follows with a complementary six-part chord.
Figure 2.6 [pd fm_two_chord_pair_odd_harm]
33 [pd fm_two_chord_pair_odd_harm] receives the number of harmonics via [r
range]. 79 [t f f] firstly sends the number to seed the six subtraction [-] objects, then
sends it to the right inlet of [pd random_x6].
The right [inlet] of [pd fm_two_chord_pair_odd_harm] receives the numerical
value of a “duration” and sends it to seed [random] before the left [inlet] receives a
[bang) to start. The “start” [inlet] bangs, in order, [random], [random 100], and [pd
random_x6].
[random] will output a random value less than the “duration” that seeded it (0
to n-1). [random 100] will output a value less than 100 (that is, between 0 and 99
inclusive), which will serve as the “amplitude” for the oscillators. These values are
sent straight to seed one of the [pd mixout_x6]s and to two [f ]s ready to seed the
other [pd mixout_x6].
Within the object [pd random_x6] there are six [random]s (see Figure 2.7), each producing six different random numbers when [random_x6] receives a bang.
Each random value produced by [pd random_x6] will therefore be less than half the received range (see Figure 2.6). Each of the outputs is then multiplied by 2 and incremented by 1 [* 2] [+ 1] in order to produce only odd harmonics. This procedure ensures there will be no “octave” relationships between the harmonics: they will all be odd. Each odd harmonic is sent to one of the [pd mixout_x6]s for immediate performance. It is also sent to [- ] [abs] 80 (seeded by the total number of harmonics) to produce a complementary value as a positive integer. This is stored in [f ] for delayed performance from the other [pd mixout_x6].
79 [r range] is an abbreviation for [receive range]. 80 [abs] for absolute.
34
Figure 2.7 [pd random_x6]
Each [pd mixout_x6] (Figure 2.8) is a bank of six oscillators, each one containing three [pd fund_fm_osc_on_off_L] objects and three [pd fund_fm_osc_on_off_R] objects.
Figure 2.8 [pd mixout_x6]
35 Each individual oscillator receives the fundamental pitch via [r fundamental] and a unique harmonic via the first six [inlet]s of [pd random_x6], which have been aligned on the [pd mixout_x6] canvas left-to-right. The seventh and eighth [inlet]s of
[pd random_x6] receive the amplitude and duration respectively and send them to the oscillators in [pd fund_fm_osc_on_off_L] or [pd fund_fm_osc_on_off_R]. The maximum amplitude for the system is 1, so the amplitude for each oscillator is divided by 1000 [/ 1000], which, in principle, allows for ten oscillators to be running at maximum volume without distortion due to clipping.
The two harmonic oscillators used in The paradox of Pythagoras , [pd
fund_fm_osc_on_off_L] (Figure 2.9) and [pd fund_fm_osc_on_off_R] (Figure 2.10),
are identical except that one oscillator is routed to the left audio output while the other
is routed to the right. The left hand side of the canvas is the patch for frequency
modulation and refers to the technique developed by John Chowning to generate
complex timbres. 81 The right hand side of the canvas controls the amplitude envelope of the sound.
81 See Chowning 1973 for the original paper and Chowning 1989 for subsequent research. The frequency modulation section of the canvas is an adaptation of Pd’s help file (Help. Pure Documentation…pd\doc\ 3.audio.examples\A07.freqency.mod.pd.), explained in Puckette (2003, 126- 129).
36
Figure 2.9 [pd fund_fm_osc_on_off_L]
37
Figure 2.10 [pd fund_fm_osc_on_off_R]
In Figures 2.9 and 2.10 the uppermost objects are the four inlets. In the following section, these will be referred to as the first, second, third and fourth inlets
38 and are numbered respectively in ascending order as they appear from left to right; the first of these is the left-most inlet while the fourth is the right-most.
The frequency of each oscillator is calculated harmonically by multiplying the fundamental frequency by the selected harmonic. Figure 2.9 shows how this is achieved in the left oscillator. The first [inlet] puts the value of the of the fundamental in the left inlet of the multiplication object [* ]; the second [inlet] sends the harmonic number to the right inlet of the same [* ] object. Multiplication of these values is performed when the first inlet of the [* ] object is triggered by the middle outlet of the [t b b f] object, which happens after the right inlet of the [* ] has read the right-most outlet of the [t b b f] object; this ensures that the selected harmonic is loaded into the [* ] object before multiplication is performed.
The third inlet temporarily stores the peak amplitude value of the oscillator in
[f ]. This value is loaded into the amplitude envelope generator (the lower-most
[line~] object) and triggered when the left-most output of [t b b f] sends a bang; that is, after the frequency of the oscillator has been selected. This ensures that any change in harmonic number initiates the envelope.
Finally, the right-most [inlet] sends the duration to the [line~] object 82 that affects the frequency modulation, as well as to the [t f f f] object that affects the amplitude.
The patch shown in Figure 2.9 also calculates the values for durations of attack, sustain and decay, the sum of which equals the total duration of the envelope.
The process begins by generating a random value less than the total duration to produce attack; it then generates a random value less than the remaining duration to
82 [line] changes the current value to a new value incrementally over the seeded time. [line~] does the same operation for signals.
39 produce sustain; finally, by subtracting both from the total duration, it produces decay.
Attack: when the total duration is received via the fourth [inlet] it seeds the
[random] object. This in turn produces a random duration less than the total duration
when it is triggered by a bang received via the second [inlet]; this is the attack time.
The attack time seeds the ramp generator [line~], which is subsequently given its
target amplitude value, previously received via the third [inlet] and stored in the [f ]
object. As a result the [line~] object generates a ramp envelope from 0 to the target
(amplitude) over the seeded duration; the outlet of the [line~] object is then sent to
control the right input of the signal multiplication object [*~].
Sustain is calculated in two steps: firstly, the difference between the total
duration and the attack is calculated; the attack value produced by the [random] object
is sent to the [t f f] object; this is initially sent to the right inlet of the [+ ] object where
it is stored as an offset for calculating the sum of attack and sustain times; it is
subsequently used to calculate the time remaining by subtracting attack time from
total duration (previously seeded by the fourth [inlet]); the [abs] object is used to
eliminate the possibility of calculating negative duration values. Secondly, a random
number less than this difference is calculated and added to the original attack
duration; when the [random] object is triggered by a bang from the middle outlet of [t
b b f] object its outlet sends random values to the inlet of the [t b f] object; initially
this seeds the [random] object by sending a value to its right inlet and subsequently
performs a calculation that sums the attack and sustain times; this is done by sending
a trigger to the left inlet of the [random] object which generates a random number
which subsequently performs addition when a value is sent to the left inlet of the [+ ]
object.
40 Decay: the difference between attack-plus-sustain and the total duration is
then calculated via [- ] (seeded by total duration) and [abs], and the result sent to seed
[f], in preparation for decay. Simultaneously, the sum of attack and sustain is sent to
a [delay] via [t b f] in order to seed the [delay] and then perform the calculation. The
result is that the [delay] bangs out after the sum of attack and sustain, which in turn
reads the duration stored in [f], which passes through a [t b f] object.
The float seeds the duration [line~] and the bang triggers a message box that sends the value “0” to the right inlet of the [line~] object; this ensures that a new envelope starting from zero is triggered for every pitch.
The total duration from the fourth [inlet] also seeds the duration of the [line~] in the FM section of the canvas. To establish a kind of structural relationship, and because a moderate effect was aesthetically desired, the frequency of the pitch is used as the modulation frequency. It passes through [t f b], which bangs a random number less than 1000 as the modulation index, which is passed to the signal multiplier object
[*~] via [line~]. The oscillator [osc~] converts the modulation frequency into a signal which is modified by the changing modulation index [*~] and sent to seed [+~] and add to the original frequency of the harmonic.
The whole effect, from the three banks of oscillators, is of two sets of two six- part chords, overlapping with four sets of two six-part chords, overlapping with six sets of two six-part chords, resulting in slow changes of pitch, texture and timbre.
41
2.3 Music of the spheres
Music of the spheres is a particular variant of The paradox of Pythagoras . Exploring
higher harmonics, and therefore “lower” fundamentals (already far below the range of
hearing), I arranged the patch using the duration of planets’ orbits around the sun as
the range of fundamentals from which to choose. Figure 2.11 shows the top canvas. 83
Figure 2.11 Music of the spheres top canvas
83 As for The paradox of Pythagoras , the names of the first two objects are truncated for the purposes of discussion. The full names are [pd fundamental_of_mercury_venus_earth_mars_jupiter_saturn_uranus_neptune_pluto] and [pd number_of_harmonics_9.53307e+010_2.43507e+011_3.95897e+011_7.44542e+011_4.69577e+012_1 .16606e+013_3.32804e+013_6.52428e+013_9.80559e+013]. Note that Pd’s method of notating the exponential is to use “e+”.
42
Earth’s fundamental was taken to be 365.26 days; Mercury’s fundamental,
87.96 Earth days; Venus’s, 224.68 Earth days; Mars’s, 686.98 Earth days; Jupiter’s,
11.862 Earth years; Saturn’s, 29.456 Earth years; Uranus’s, 84.07 Earth years;
Neptune’s, 164.81 Earth years; and Pluto’s, 247.7 Earth years.
[pd fundamental_of_mercury…] (Figure 2.12) calculates the fundamental frequencies. Mercury is 1.31583*10 -7 Hz; Venus, 5.15136*10 -8 Hz; Earth,
3.16872*10 -8 Hz; Mars, 1.68478*10 -8 Hz; Jupiter, 2.67132*10 -9 Hz; Saturn,
1.07575*10 -9 Hz; Uranus, 3.76915*10 -10 Hz; Neptune, 1.922165*10 -10 Hz; and Pluto,
1.27926*10 -10 Hz.
Figure 2.12 [pd fundamental_of_mercury…]
[pd number_of_harmonics_9.53307e+010…] (Figure 2.13) gives the choice of
number of harmonics. 84 [pd duration_1_2_5_10_15_20_30_40_50_60] and [pd
oscillators] are the same as in The paradox of Pythagoras .
84 As listed in the Pd object’s name, these are 9.53307*10 10 , 2.43507*10 11 , 3.95897*10 11 , 7.44542*10 11 , 4.69577*10 12 , 1.16606*10 13 , 3.32804*10 13 , 6.52428*10 13 , and 9.80559*10 13 .
43
Figure 2.13 [pd number_of_harmonics_9.53307e+010…]
The nine “movements” of Music of the spheres are included on the companion
CD to this volume. 85 The general effect of Music of the spheres is sometimes quite different from The paradox of Pythagoras . At these extreme low frequencies, the effects of frequency modulation may cease to be heard as changing timbres, instead allowing changing frequencies to be heard as gliding tones.
Having developed patches to “sculpt” sound into complementary panels, the next phase of the project was to extend aspects of The paradox of Pythagoras , especially the notion of higher harmonics based on a sub-audio fundamental and oscillators with variable amplitude envelopes, to compose pieces of some length and scale. Chapter 3 describes the compositions that comprise this next phase: the series of three works entitled Music of Grace .
85 As with the recordings of The paradox of Pythagoras , these nine recordings match the nine fundamentals to the “equivalent” nine options for harmonics.
44 Chapter 3
Music of Grace
Chapter 3 describes the three extended electronic works that comprise the series
Music of Grace . MP3 recordings of the pieces are included on the companion CD in the sleeve of this volume. Also included on the companion CD are the related appendices in soft copy. 86
3.1 The cat dances and the moon shines brightly
The cat dances and the moon shines brightly 87 extends and develops an extract from
Bach’s Befiehl du deine Wege , transposed down one tone. The extract is given below
in Figure 3.1 ( cf . the original in Figure 1.1). The MIDI note numbers, which are used
in the piece to determine the harmonic numbers, are shown for each pitch.
A table showing the actual pitches of the harmonics, together with the number
of cents deviation from equal temperament, is given in Appendix G. A version of
Figure 3.1, written at actual pitch, is given in Appendix H.
The number 62, the first and last numbers of the extract, is of structural
importance in this piece. 88
86 All appendices are provided in soft copy on the companion CD to this volume to allow for maximum flexibility when accessing the often lengthy materials. 87 This is the full text (without line breaks) of a poem by John Gracen Brown, entitled The Cat and the Moo n (Brown 2005, 5). 88 62 is also taken as being the lowest number for the right hand; number 60, first note second bar, is altered in the piece to facilitate this convention.
45
Figure 3.1 Extract from Befiehl used for The cat dances
The top canvas of The cat dances and the moon shines brightly (Figure 3.2) shows that the piece progresses through five “panels”. The [bang) between them signals to the observer the initiation of the next panel.
Figure 3.2 The cat dances and the moon shines brightly top canvas
46 There are in total 50 different individual patches in The cat dances and moon
shines brightly , too many for each one to be discussed individually here in the main
body of the thesis. These patches can be found in Appendix H. Additionally, the
complete composition structure of The cat dances , showing the placement of all
embedded sub-patches in relation to each other, is given in Appendix I. The intention
is that the two appended documents allow the description, detail and structure of the
work discussed here to be cross referenced and compared if the reader requires.
The piece has five sections, which I have termed “panels”. 89 The piece as a whole loosely reflects the “visions” 90 of movement and lunar light suggested by the title. Panel 1 presents chords based on the Bach extract, beginning tentatively, each note of the chord with the same overall duration, but with a different dynamic envelope which helps to change the balance and differentiate the component pitches.
The upper note of each chord is based on the right hand of the Bach extract, and the chord itself is derived from the calculation symmetrical axes between the number assigned to the top note, and the number 62 (the first and last notes of the extract). 91
Panel 2 continues with chords, inserting melodic components derived from the axes of each chord. The melodic inserts are based on axes between the notes in the chord and the number 62.
Panel 3 interpolates melodic descending passages between chords. The series of chords is put out of synchronisation and is periodically interrupted by descending runs, sometimes ending in a slow trill.
89 After Donatoni (see chapter 1). 90 John Gracen Brown refers to these short poems as “visions”. See chapter 1. 91 The detail of these calculations, which convert symmetrical pairs of MIDI numbers into asymmetrical pairs of frequencies, is given in Appendix H.
47 Panel 4 transforms the chords into “arpeggios” that trigger other events
(according to whether arpeggiation is ascending and descending). A “melody” based
on the Bach extract is played, accompanied by arpeggios derived from the chords.
Panel 5 reads the Bach extract again and applies procedures that control the
duration of the melodic lines, add trills, and direct the two parts into contrary motion
before a final chord to finish.
3.2 The heavy dark trees line the streets of summer
The heavy dark trees line the streets of summer 92 is the second in the collection of pieces entitled Music of Grace . Like the first, discussed in the previous section, it too
extends and develops an extract from Bach’s Befiehl du deine Wege . The extract is
given below in Figure 3.3 ( cf . the original in Figure 1.1). Like the previous piece, this
extract is transposed down one tone from the original to begin on D. 93 The MIDI note
numbers, which are used for later calculations, are shown for each pitch. (A version
of Figure 3.3, written at actual pitch, is given in Appendix J.)
Figure 3.3 Extract/arrangement from Befiehl used for The heavy dark trees
92 This is the full text (without line breaks) of a poem by John Gracen Brown, entitled Streets on a Summer Night (Brown 2005, 5). 93 See Chapter 2 for the significance of the pitch D.
48
As a kind of homage to Franco Donatoni, the extract has been laid out in the approximate rhythm and voicing of the first three beats of the eighth bar of the second movement of Schönberg’s Fünf Klavierstücke , op.23 (1923), a musical fragment used by Donatoni as the genesis of his seminal work Etwas ruhiger im Ausdruck (1967) for clarinet, violin, cello and piano. My interest in, and appreciation for, Donatoni was rekindled in 2003 when Cornell University doctoral student Yotam Haber contacted me a number of times over a period of a year to discuss Donatoni’s composition technique and this piece in particular. 94 I therefore decided to apply processes not unlike Donatoni’s to the second piece of the Music of Grace series.
The left hand of the extract above is the first seven pitches of Befiehl ,
transposed down a tone (as noted above) plus two octaves for the first three notes, and
one octave for the last four notes. The right hand uses chords taken from the original
right hand part, with minor rhythmic adjustments.
The heavy dark trees line the streets of summer has five sections, again
labelled “panels” after Donatoni. It loosely reflects visions of repetitive periodicity
that move in and out of phase, as suggested by the title. The top canvas of The heavy
dark trees line the streets of summer (Figure 3.4) shows the five panels through which
the piece progresses.
94 A significant part of Haber’s research (Haber 2004) was to compare and critically evaluate analyses by myself (Barkl 1985) and Robert Piencikowski (1990).
49
Figure 3.4 The heavy dark trees line the streets of summer top canvas
A detailed discussion of the 257 different patches that comprise the piece is
given in Appendix J where every individual object in the piece is reproduced. It also
includes some more detailed discussion of differences between the various sub-
patches. Most significantly, however, this appendix may be reproduced as a collection
of screen prints that represent the entire piece. In order to assist the understanding of
how the patches are organised in the piece, the complete composition structure of The
heavy dark trees line the streets of summer , showing the placement of all embedded
sub-patches in relation to each other, is given in Appendix K. 95
95 Again, these appendices are intended to facilitate the reader’s cross referencing.
50 Panel 1 breaks up the original material, transposing and dissipating it. It is
transposed and altered rhythmically, and is accompanied by sustained chords. The
resultant musical material is stored in a series of arrays.
Panel 2 collates material to be played by taking it from the Panel 1 arrays and
writing it to a new array where it can be subsequently reread and played by Panels 3
and 4.
Panels 3 and 4 play concurrently: they read the arrays, perform
transformations on the material, and “coagulate” it by playing it in an overlapping
accelerando. At the same time, the material is modified and rewritten to the original
arrays, in effect, “recycling” it in a constant flux. There are eight tempos (or
“clocks”) ranging from 1-55 to 15-55 notes per bar. Panel 3 and Panel 4 are
accompanied by soft chords taken from the Befiehl extract.
Panel 5, like the final panel of Etwas ruhiger , reads the results and selects
material from the arrays. Its purpose is to take the “chaotic” values written to the
arrays and reconstitute something approaching the original extract.
The nine “mixout” objects are banks of oscillators. Each object has eight
oscillators, making 72 oscillators altogether.
3.3 The crystals in the cave absorb the light as if they have not seen it
in a million years
The third piece of the Music of Grace series is The crystals in the cave absorb the
light as if they have not seen it in a million years. 96 Like the first and second pieces,
the third extends and develops an extract from Bach’s Befiehl du deine Wege . The
extract is given below in Figure 3.5 ( cf . the original in Figure 1.1). In this case, the
96 This is the full text (without line breaks) of a poem by John Gracen Brown, entitled Cavern Crystals (Brown 2005, 5).
51 extract is a simplification of the 40 chords that Bach wrote, transposed to the key of D minor.97 The MIDI note numbers, which are used in the piece’s calculations, are shown for each pitch. (A version of Figure 3.5, written at actual pitch, is given in
Appendix L.)
Figure 3.5 Chords from Befiehl used for The crystals in the cave
The top canvas of The crystals in the cave (Figure 3.6) shows the panels through which the piece progresses.
97 See Chapter 2 for the significance of the pitch D.
52
Figure 3.6 The crystals in the cave top canvas
A discussion of all 718 individual patches in detail can be found in Appendix
L, where every different object in the piece is reproduced. 98 Additionally, the
complete patch structure of The crystals in the cave absorb the light as if they have
not seen it in a million years , showing the placement of all embedded sub-patches in
relation to each other, is given in Appendix M.
The nine “mixout” objects are banks of oscillators that operate in a similar
manner as those used in the previous piece. 99
The crystals in the cave absorb the light as if they have not seen it in a million
years loosely reflects visions of absorption, then reflection through multiple prisms, as suggested by the title. Panel 1 plays the 40 chords of the Befiehl extract, some decorated by slow trills. The durations of the chords are based on the intervals between the top notes.
98 As for the previous two pieces in the Music of Grace series, it is acknowledged that many of the patches are identical except for small details (such as assigning to which oscillator the frequency information is to be sent). However, as previously noted, the intention is to include full documentation in addition to explanation. It will also be noticed that, because many of the patches are similar, much less textual annotation is required. 99 See Appendix J for an explanation of the internal workings of these objects.
53 Panel 2 plays the 40 chords of the Befiehl extract, in order, each one
“answered” by the chord axes in a descending arpeggio.
Panel 3 lightens the texture of the previous two panels. Two notes from each
of the 40 chords are sustained, decorated by pitches taken from the chords’ axes.
Every time a sustained note changes, it is reinforced by the accompanying chord.
Panel 4 is built from ten sets of ascending arpeggios. In each set, four overlapping arpeggios, from four successive chords, rise fairly rapidly over a period of 3840 ms, answered by slower and softer arpeggios based on their axes.
3.4 Reflections on the compositional process
In composing Music of Grace I was conscious of the influence of “instrumental” thinking, especially in the initial phases. Most obviously, the primary or source material, being a Bach chorale, tended to maintain my thinking in terms of “notes”,
“chords” and “bars”, rather than, perhaps, a more “abstract” notion of “frequencies”,
“densities” and “durations”.
The cat dances (the first piece) is linear in its approach and unfolds in a
manner not unlike a traditional instrumental work. The heavy dark trees , by contrast, has an entirely different structure, evident in the way it writes data to arrays for later use. Moreover, in its later sections (Panel 3 and Panel 4) it reads-writes-reads in quick succession, using the computer more recursively.
These two pieces scaled the use of Pd up to a large number of patches: 50 different patches (or the equivalent of 1,032 pages of text code) for The cat dances and 257 different patches (or 595 pages of code) for The heavy dark trees . This aspect, or capability, was further extended in the third piece, The crystals in the cave , to 718 different patches (equivalent to 7,644 pages of text code), which would seem to indicate Pd’s capacity to “scale up” to a remarkable degree. Instead of using arrays,
54 in this case banks of similar objects were lined up to process or modify the musical material concurrently in real time. As such, it differs significantly, not only from the previous two works in Music of Grace , but also from a linear instrumental approach.
55 Chapter 4
Discussion and Conclusion
4.1 Discussion
The primary purpose of discussion so far in this thesis has been to understand the processes involved in composing the electronic pieces in this folio 100 where the
process of composition is discernable graphically in the form of Pure Data patches. 101
While this may be of value to the interested listener, musicologist or even composition student, the principal motivation for doing this has been to clarify my own understanding of the compositional processes taking place in my work by finding a suitable way in which to document them. There are many cases in my own previous work where I simply cannot recall the composition process or method. Although this may not be particularly significant in itself, the importance of this enquiry lies in the potential or capacity for artistic development, improvement and refinement. That is,
I, a composer, am much more likely to develop consistently if I am not struggling to remember the last thing I did. For me, therefore, the value of the documentation of composition process is one of memory and recall, irrespective of the genre in which I happen to work.
The question that arises at this point is whether Pd and the application of
Agus’s conventions have facilitated this outcome. The answer would appear to be a qualified “yes”, though the project has not been entirely trouble-free. On its own, visually examining a Pd patch, without testing it, will not always accurately predict its
100 See Appendix Q for details of performances of the works while this thesis was being prepared. 101 The “process of composition” refers here to the “entire” production process of composition, typical of much electroacoustic music, as distinct from the production of a score which describes the process of composition for the benefit of the next person in the production chain.
56 operation. In particular, the order in which connections are drawn from a single source will be, all other things being equal, the order in which the messages are sent.
This situation is easily clarified by the use of the [trigger] object, such as [t b b], where the right outlet bangs before the left. A consistent use of [trigger] may also confirm its corollary—that where feeds are sent to multiple objects from a single source, the precise order of data flow is immaterial.
Nonetheless, visually examining a complex dynamic patch 102 some time after
its construction can be challenging, not only to imagine all its events dynamically
changing, but to imagine how the outcome of the patch interacts with other patches
operating concurrently. Additionally, when describing the patches, it became clear
that even being able to follow the functional operation of a patch or group of patches
is not the same thing as discerning the musical effect or musical meaning of the
composition or even parts of the composition. For this, additional commentary at the
“interpretive” level (as distinct from the “descriptive” level) will always be necessary.
One of the comments from the “Pd discussion group” was that Agus’s
proposed conventions 103 were “common sense”. 104 To some degree this must be true, yet it does disregard the specific purpose of these conventions. As Agus clarifies in his email, the aim was to maintain a consistent and similar style when a number of people were working semi-independently on different aspects of a large, complex patch. More particularly, Agus and his group were working with (or at the very least incorporating) the text code of Pd. 105 For this reason, Agus recommended that only
functional objects should be “in-line”: non-functional objects should be offset and
102 Such as [pd clock_accel_15-55]. See Figure J.243. 103 See Appendix D. 104 See Appendix O “Email Re: Pd conventions ”. 105 See Appendix P “Pd code” for an example.
57 labelled “DEBUGGING” (see Figure 4.1). 106 The label facilitates the identification of the non-functional object in the code, and having the object offset allows its deletion at any time (for example, after testing) without compromising signal flow.
Figure 4.1 Debugging
Because I was not working with the code, this aspect of the conventions was
not important. Indeed, the number of monitoring, or “debugging”, objects in the
project made the use of the label itself oppressive, cluttering the patch when it was
obvious why, for example, a [bang) was there. 107 Similarly, in-line objects such as bangs and number boxes can be very useful when laying out a patch; and there are numerous instances of their use in this regard in this project. 108
A further recommendation by Agus was not well supported by the Pd
discussion group: the use of camelCase. 109 The convention of camelCase is useful in
106 In this context, “non functional” refers to objects used for monitoring purposes (such as using a [bang) to blink when a process has occurred, or a number box to show a value) whereas “functional” refers to objects essential to the operation of the patch (such as using a [bang) to initiate another object). 107 “DEBUGGING” labels were therefore deleted from the patches. 108 See again, for example, [pd clock_accel_15-55]. However, one proviso should be acknowledged here. Music requiring a rhythmic exactitude (with an accuracy down to the millisecond) needs to minimise the number of objects through which the signal passes. Needless to say, such accuracy was not required for this project. 109 See Appendix O. The term camelCase refers to a typographic convention used by computer programmers for creating labels using multiple words with white space removed; the first letter of the
58 that it keeps text together and minimises space. Unfortunately it is not useful for numbers; in this project I chose to use underscores to keep text and numbers consistently together.
Another recommendation by Agus was to avoid using the [send] object where possible. Specifically, from Agus’s point of view, tracking the use of [send]s by multiple developers in code is particularly difficult. However, even in graphic patches one can easily lose track of what is sent where. 110 In The cat dances and the
moon shines brightly I avoided [send]s altogether. The result was more “organic”, but
also possibly wasteful, with oscillators being used briefly and then left dormant.
Using [send]s in The paradox of Pythagoras facilitated a convenient GUI; and
using them in The heavy dark trees line the streets of summer and The crystals in the
cave absorb the light as if they have not seen it in a million years allowed the
efficiency of a bank of oscillators that could be called into service any time they were
required. The use of [send]s in these cases was limited and defined and did not lead
to any confusion on my part; indeed, their use seemed not only to suit these more
structured process-style compositions, but be consistent with Agus’s recommendation
for “global” sends and receives.
In summary, while Agus’s conventions were useful to acknowledge as a
benchmark and a viable starting point (particularly with regard to “common sense”
procedures such as signal flow) it became evident that differences between his project
and this project led to certain inevitable adjustments to respond to different purposes
and methods. As such, it seems unlikely that the wide diversity of users in the Pd
community would ever commit to a “definitive” set of programming conventions.
first word is spelt using lower case while subsequent words are spelt using an initial capital without spaces. 110 Cf. Barknecht, F. “Good Pd Programming Practice?” 21 March 2004, 22:35:14 CET.
59 One further comment by Agus may deserve attention: he makes the point in his email that “hearing scientists prefer to use something like Matlab 111 which can be pretty much guaranteed click-free”. 112 Indeed, despite attention to the control of the onset of pitches (the “attack” of the envelope), at certain times the program can be heard operating in the background. While Agus’s current research into hearing science may demand an artefact-free environment, to my ears these minor noises do not affect the integrity of the project. Indeed, because I regard the computer and its program as a “machine” or “instrument”, evidence of the workings of that machine, while it is clearly desirable that it be kept to a minimum, is no more or less undesirable than any inherent machine noise. 113
The electronic pieces in this folio display four different approaches. The
paradox of Pythagoras is virtually a single-patch piece, generating a sound
environment. The cat dances and the moon shines brightly , by contrast, is far more
“organic”, where patches and oscillators are used in a more linear conception as the
piece “develops” in time. The heavy dark trees line the streets of summer takes a
contrary approach, where banks of oscillators are set up for use as and when required
and the material is treated in a far more recursive manner, unlike the linearity of The
cat dances . The crystals in the cave absorb the light as if they have not seen it in a
million years combines and extends aspects of the two, using banks of like objects to
take a fresh look at the original material in a process oriented way.
111 MATLAB ( mat rix lab oratory), created by The MathWorks , is a numerical computing environment that allows matrix manipulation, numerical analysis, implementation of algorithms, and the plotting of data. It does not imitate the modalities of a patchable analogue synthesiser like Pd does. 112 See Appendix O. 113 Analogies in the world of acoustic music may be guitar fret noise and breathing for singers and wind players.
60 4.2 Conclusion
The aim of the project was to compose a folio of electronic pieces that used Pd as a
“meta-compositional instrument”: that is, a vehicle for documenting the creative process in a graphical way, as a kind of analytical notation.
The pieces extended and explored creative aspects of my previous research into binary processes, symmetry, and complementary pairs, using sine tone frequencies based on the higher partials of sub-audio fundamentals.
Pd programming conventions, proposed by Trevor Agus, provided a standard benchmark with regard to “common sense” signal flow conventions, and were only adjusted when significant differences between working in code (Agus) and working graphically (in this project) were encountered.
Despite the “composition of the composition” being evident in the graphical layout of the patches, it became clear that further “interpretive” commentary was necessary to explain the artistic or musical purposes of different patches.
Nonetheless, it was shown that a composition in Pd can explicitly show its own construction and interrelation of compositional elements, providing a kind of descriptive analysis of the work. Moreover, Pd was shown to be suitable for relatively large scale, multi-sectional projects. Perhaps of most importance, however, was that Pd allowed me to realise the music of my imagination, leaving me free to approach the process of composition, including the composition of instrumental music, from a broader perspective and with a heightened appreciation.
61 Chapter 5
Epilogue: Here …
Mid-way through composing The crystals in the cave , which was discussed in chapter
3 and Appendix L, the opportunity presented itself to compose an instrumental chamber piece. Thus, as the electronic music composition project was drawing to a close, it overlapped with the process of composing instrumental music. In order to link the two together and highlight similarities and differences in the process of composition between the two media, I decided to use the same source material used in
The crystals in the cave for the instrumental piece. Chapter 5 describes the process of composing the chamber work entitled Here… It revisits instrumental composition in
the light of the electronic works composed using Pure Data and reviews some of the
special characteristics of instrumental writing. The composition of this piece acts as
an epilogue to the project since, after an intense period of composing purely electronic
music, it allowed a return to the issues identified at the beginning of the project.
5.1 Origins
Here … (for clarinet, piano and cello) is the result of an invitation to submit a short
piece for the 2008 Aurora Festival. The Festival included composer workshops with
academic staff from the Universities of Western Sydney, 114 Wollongong 115 and
California, San Diego, 116 and with the contemporary chamber group Charisma 117 at
the Joan Sutherland Performing Arts Centre in Penrith, NSW. (The MP3 recording
114 Professor Michael Atherton, Dr Diana Blom, Dr Bruce Crossman, Professor Roger Dean and Dr Garth Paine. 115 Dr Houston Dunleavy. 116 Professor Chinary Ung. 117 Roslyn Dunlop (clarinet), David Miller (piano) and Julia Ryder (cello).
62 provided on the companion CD is the live recording from the Festival concert. 118 )
Although initially reluctant to set aside time for this project (considering my other
commitments), I recognised that it was an excellent opportunity to investigate the
transfer or projection of some of the organisational thinking I had applied to Pd back
to instrumental (acoustic) music.
Here ... is the title of a rather bleak poem by John Gracen Brown. 119 My use of
the title is not so much to illustrate the poem as to highlight the “humanness” and
immediacy of the ensemble and its creation of the music in real time. The source
material for the piece is exactly the same as for The crystals in the cave ; that is, 40
chords taken from Bach’s Befiehl du deine Wege . These chords were transposed to
the key of D minor and laid out on a single clef (Figure 5.1).
118 18 April 2008. 119 Brown (2005: 6). Using just the title of the poem as the title of the piece, as distinct from the whole poem (as I did with the electronic works) was not fortuitous. My intention was to reflect the complementary nature of the instrumental piece to the electronic pieces. The complete poem is: “Here there is the cold wind, / The darkness of the night / And these lonely hills – without end.”
63
Figure 5.1 Extract from Befiehl used for Here…
5.2 Here …
Here … for clarinet, piano and cello comprises 11 panels.
Panel 1: bars 1-14;
Panel 2: bars 15-32;
Panel 3: bars 33-41;
Panel 4: bars 42-48;
Panel 5: bars 49-54;
Panel 6: bars 55-62;
Panel 7: bars 63-74;
64 Panel 8: bars 75-80;
Panel 9: bars 81-87;
Panel 10: bars 87-92;
Panel 11: bars 92-98.
The full score is reproduced in Appendix R.
5.2.1 Panel 1
The first panel of Here … (bars 1-14) contrasts the complementary textures of the piano chords with the clarinet and cello. The piano chords (always mf ) are derived from inversions of chords from the Befiehl extract. Instead of reading “up” the original chord (d ’-f’’ -a’-d’’ as it appears in Figure 5.1), the piano reads “down” to form the chord d-a-f’-d’’ . The left- and right-hand dyads are then “filled in” with notes that form the axes of symmetry for the dyad: f-gb for the left-hand and a ’-bb’ for the right-hand. The first phrase of the piano comprises the first five chords of the
Befiehl extract. The process comes to a halt upon the repetition of the first d, and the first chord of the piece is repeated (Figure 5.2).
65
Figure 5.2 Here… bars 1-2
The descending clarinet staccato semiquaver line reads the axes of the piano chords, beginning with the first chord right-hand (piano b b’-a’ becoming clarinet bb’’ -a’’ ) and ending with the fourth chord left-hand (piano a b-g becoming a b-g at the same pitch in the clarinet). The cello reads the fifth chord axes. The clarinet also includes two ( mf ) semiquavers that reinforce the cello’s entry: these two notes are the last two from the cello, forming a kind of harmonic reinforcement.
The piano continues with five chords. The first of the five is the same as the first chord of the piece, but with its position inverted so f is on the bottom and f ’’ is on the top. Chords 6-7-8 of the Befiehl extract follow before the initial chord of the second phrase is repeated (Figure 5.3).
66
Figure 5.3 Here… bars 3-4
Again the clarinet reads the axes of the piano chords as a descending figure
(chords 6-7 of the Befiehl extract) and the cello reads the axes of the last new chord
(chord 8 of the Befiehl extract), while the clarinet reinforces the cello’s entry by doubling the last two pitches. This time the articulation is different, contrasting the semitones with the other intervals through the use of slurs.
67 The number of new chords used in the second piano phrase (three in this case) is determined by the inversion of the first chord in the phrase. The top note of the first (and last) chord of the first piano phrase was d ’’ ; the top note of the first (and last) chord of the second piano phrase is f ’’ : an interval of three semitones.
Similarly, the next inversion of the first Befiehl chord has g b’’ as its top note: an interval of one semitone triggering just one new chord from the Befeihl extract for the third piano phrase. The single axis pitch of c ’’ (right-hand) and c (left-hand) generate a decorated response in the clarinet and cello.
The rest of the panel, to midway through bar 12, continues in the same manner, the first and last chords of each piano phrase repeating the first chord of the piece in higher and higher inversions, adding new chords from the Befiehl extract according to the intervallic change, with the clarinet and cello playing the chord axes with different contrasting articulations.
Midway through bar 12 the texture changes, preparing for a more “dramatic” conclusion to the first panel. The piano has, so far, used 33 chords from the Befiehl extract and now plays chords 34-40 as cascading arpeggios, without including dyad axes. These are played by the clarinet (piano top stave axes) and the cello (piano bottom stave axes), holding the last note as a trill until the piano completes its last arpeggio in bar 14 (Figure 5.4). The trill repeats as an “upbeat” to panel 2.
68
69
Figure 5.4 Here… bars 12-14
5.2.2 Panel 2
Panel 2 re-reads the initial piano chords in an arpeggiated form while contrasting
clarinet and piano inserts with accented reinforcement.
The range of the piano has been restricted. The right hand’s top note is d ’, and its range is within one octave; for the left hand, the lowest note is D and its range is also restricted to one octave. These range restrictions are also assigned to the clarinet and cello. The rationale for the restriction is the range of the first chord itself: in effect the first chord has been transposed down one octave and provides the boundary for all chords that follow. All piano notes from panel 1 are thus repositioned in panel 2 (Figure 5.5).
70
Figure 5.5 Here… bars 15-16
The piano right-hand reads notes from bar 1 until the first pitch-class repetition, in this case f, as does the left-hand, which stops before the repetition of D.
(This follows the rationale for the interruption of the first piano phrase in panel 1.)
Each hand resumes the process after waiting for exactly one beat (four semiquavers).
Because the right-hand’s phrase was seven semiquavers and the left-hand’s phrase was four semiquavers, the “open space” before the resumption of the process is just
71 one semiquaver. The clarinet and cello, having reinforced the piano entry at unison, insert a forte semiquaver into the space. The pitches are taken from the clarinet insert
in bars 1-2: the first note b b for the clarinet, and the last note of the insert G for the
cello.
Again, cello and clarinet reinforce the piano entries at unison and fill the space
between piano entries, two semiquavers this time, with pitches taken from each end of
the clarinet insert from bars 1-2 (the clarinet reading forwards and the cello reading
backwards).
The third piano phrase (bar 16) is extended to two sub-phrases; that is, the
repeated note is accented and the new sub-phrase continues immediately. This time,
the two sub-phrases trigger a rest of two beats between this and the next piano
phrase—a break that is again filled by forte clarinet and cello inserts taken from the
clarinet in bars 1-2.
The fourth piano phrase (bar 17) extends to three sub-phrases. The clarinet
and cello match this by using three repeated notes (rather than two) to reinforce each
accent. The rests at the end of the piano phrase are also extended to three beats
duration for each hand (filled by the clarinet insert from bar 3) (Figure 5.6).
72
Figure 5.6 Here… bars 21-22
The process continues through bars 18-22, the piano extending to five sub- phrases (generating equivalent repeated notes for reinforcement and longer rests between the piano phrases). The end of the process is triggered by the simultaneous completion of the reading of the fourth piano phrase from bars 4-5, and its consequent clarinet insert from bar 5 for the clarinet and cello.
At bar 23 the texture changes. The piano dynamic changes to forte and plays the complete fifth piano phrase from bars 5-6. The clarinet reinforces the right-hand
73 accents (still generated by repeated notes) and the cello uses the left-hand accents to create a sustained counter melody (Figure 5.7). Repeated notes in the cello are decorated with a mordent.
Figure 5.7 Here… bars 23-24
The clarinet and cello respond with material taken from the fifth clarinet insert
from bars 6-7 (the clarinet reading forwards and the cello retrograde), this time played
in doubled semiquavers, mimicking the initial clarinet and cello reinforcement in bar
15. The reading of the sixth piano phrase and clarinet insert from panel 1 follow in
74 the same manner. From the reading of the seventh piano phrase, however, the range begins to expand, the process continuing until the end of bar 32 and the completion of the reading of the tenth piano phrase from bar 12.
5.2.3 Panel 3
Panel 3, beginning at bar 33, features crescendo chords followed by decorated ascending clarinet figures (Figure 5.8).
Figure 5.8 Here… bars 33-34
75
Each long crescendo chord is taken from the second last chord of each piano
phrase in panel 1. The fortissimo chord is the last chord of each piano phrase. That
is, the first chord in bar 33 is taken from the fifth chord of bar 1, and the second chord
of bar 33 is taken from the sixth chord of bar 1. For each crescendo chord the clarinet
and cello double the highest and lowest piano notes; they then arpeggiate the chord as
an upbeat to the reinforcement of the fortissimo chord. The cello follows the changes in the piano, but the clarinet uses d ’’ as its constant upper limit.
The ascending clarinet figure plays the axes of the fortissimo piano chord: d-f gives d# ’-e’; g b-a gives g ’-ab’; a-f’ gives d b’’ ; f ’-a’ gives g ’’ ; and b b’-d’’ gives c ’’’ . Double axes are given as staccato semiquavers and single axes are given as quavers decorated with mordents alternating normal and inverted.
The process continues until the completion of the reading of the fifth piano phrase from panel 1. The final clarinet flourish reads the axes of the fortissimo chords
(1 descending, 2 ascending, 4 descending, 5 ascending), holding its upper fortissimo chord limit, d ’’’ (Figure 5.9).
76
Figure 5.9 Here… bars 39-40
5.2.4 Panel 4
At bar 42 the demisemiquavers of the clarinet flourish are transferred to the piano ( pp ) while the clarinet and cello play pianissimo descending phrases (Figure 5.10).
77
Figure 5.10 Here… bars 42-43
The piano reads from the first piano phrase of panel 1 (all six chords), right- hand followed by left-hand (marked by the slurs) in an overlapping descending manner. The direction changes (to ascending) when the piano begins reading the second phrase from panel 1 in bar 43 and this process continues until the completion of the reading of the fifth phrase in bar 48.
78 The clarinet and cello read the right- and left-hand chords of the piano (from
panel 1) respectively to form descending legato arpeggios. The beginning of each
new piano phrase (from panel 1) is marked by a decorative mordent, and preceded by
a rest that completes the crotchet beat. 120 The duration of each arpeggio note is determined by the interval to the next note: thus, for example, d ’’ -bb’ in the clarinet is 4 semitones and generates a duration of 4 semiquavers for d ’’ ; b b’ to a ’ is 1 semitone, generating a duration of 1 semiquaver for b b’. The duration last note of each original panel 1 phrase is always a semiquaver.
The process continues until the fifth phrase from panel 1 has been read by the
piano, and stops at bar 48, triggered by a rhythmic unison between clarinet and cello
upon their completion of the reading of the second piano phrase from panel 1 (bar 3).
The final piano chord in bar 48 is the last chord from the fifth piano phrase (bar 6).
5.2.5 Panel 5
At bar 49 the piano takes over the role of the clarinet and cello in the previous panel,
continuing with a reading of the third piano phrase from bars 3-4. Again, the change
from one original phrase to another is marked by alternating mordents preceded by a
rest that completes the beat (Figure 5.11).
120 A semiquaver rest is also inserted before each clarinet arpeggio as a notional breathing point.
79
Figure 5.11 Here… bars 49-50
The clarinet and cello, instead of duplicating or imitating the piano’s texture from panel 4, play two-octave demisemiquaver staccato arpeggios. The arpeggios are read from the third piano phrase of panel 1 (bars 3-4), the clarinet taking the right- hand and the cello taking the left-hand. The arpeggios coincide with every second piano pitch (right-hand relative to the clarinet and left-hand relative to the cello) and alternate their direction.
80 The process ends at bar 54 with the completion of the reading of the fifth piano phrase from bars 5-6 in the piano (the clarinet has completed the fifth chord and the cello the sixth chord). The final piano chord of the fifth phrase is repeated to initiate panel 6.
5.2.6 Panel 6
In panel 6 the lead is taken by the cello, which imitates the descending figures of the previous two panels while punctuations are provided by clarinet and piano. The cello line reads the six chords of the first piano phrase in bar 1. The clarinet and piano punctuations are taken from both the first and second piano phrases (Figure 5.12).
81
Figure 5.12 Here… bars 55-56
The durations for the cello are derived from the intervals. Intervals of one
semitone are given one semiquaver. All other intervals are doubled to augment the
line: that is, the interval from the initial a ’ to g b’ is three semitones, giving a duration of six semiquavers.
5.2.7 Panel 7
At bar 63, panel 7 begins reading from panel 1 again (but omitting the repetitions and inversions of the initial chord). The final d ’ in the cello from panel 6 initiates a feature of this pitch. All Ds from panel 1 are assigned to the clarinet and cello, and sustained until the end of the crotchet beat. When clarinet and cello’s Ds coincide, they are both trilled; if not, every second sustained D is decorated with a trill. The piano reads the remaining chord notes (Figure 5.13).
82
Figure 5.13 Here… bars 63-64
At bar 69, once the tenth piano phrase from panel 1 has been read, the music re-reads from bar 63, restricting the range and changing the texture. Rhythmically, each instrument cycles through triplets, quadruplets and quintuplets. The piano restricts its pitch to two notes per hand, and plays on every second subdivision of the
83 beat. Sustained Ds in the clarinet and cello are converted to two staccato Ds; other notes are left as is, but transposed to the new register Figure 5.14).
Figure 5.14 Here… bars 69-70
The process is interrupted at the end of the reading of the sixth piano phrase in
bar 67. From bar 72, the piano re-reads from bar 69, transposing the material up a
further octave and performing it in a melodic or linear fashion, rather than as two-note
84 dyads in each hand. The clarinet and cello also re-read from bar 69, this time omitting any pitches that are not preceded by a D (Figure 5.15).
Figure 5.15 Here… bars 72-73
5.2.8 Panel 8
At bar 75 the texture changes completely, with an ascending arpeggio flourish
followed by a pianissimo clarinet line edging its way to its top register (Figure 5.16).
85
Figure 5.16 Here… bars 75-76
The arpeggios are read from the first piano chord in bar 1. Each arpeggio is a different length so each instrument reaches its “target” at a different time. The clarinet line reads the chord notes, adding axes between them. Chord notes ascend and axes descend.
86 The process continues with the second and third chords from the first piano phrase, cello and then piano joining the clarinet in the ascending lines. In the final example, the piano doubles the clarinet with trills (Figure 5.17).
87
Figure 5.17 Here… bars 78-80
5.2.9 Panel 9
Panel 9 continues to contrast the piano material with clarinet and cello inserts. At bar
81 the piano reads the first piano phrase again, this time at original pitch. Axes are omitted from the first and last chords and only the inside parts are played from the remaining chords (Figure 5.18).
88
Figure 5.18 Here… bars 81-82
Clarinet and cello reinforce the first and last chords of each piano phrase by playing the second and third voice of the chord (the cello plays the second and third voice from the bottom). Each clarinet and cello reinforcement is preceded by a D grace note (d ’’’ for the clarinet and d for the cello).
89 The piano phrase is “answered” by clarinet and cello ppp arpeggios that read the last chord of the piano phrase (that is, the complete “original” piano chord, including axes). The arpeggios alternate descending with ascending, and alternate trilled with normal. The duration of each note of the arpeggio is determined by the number of chords in the preceding piano phrase, minus the first and last chord. That is, in the first piano phrase there are six chords (or four, not counting the first and last), giving a duration of four semitones (one crotchet) for each arpeggiated note. A total of four piano phrases from panel 1 are read in this manner.
5.2.10 Panel 10
Panel 10 begins on the third beat of bar 87 with the first chord of the fifth piano phrase played fortissimo . The upbeat to the chord is given by the clarinet, playing
d’’’ (the top note of the chord) preceded by a ’’ (the second voice of the chord)
(Figure 5.19).
90
Figure 5.19 Here… bars 87-88
The cello softly sustains the bottom note of the chord. The clarinet and piano answer the chord with arpeggiations of each subsequent new chord in the fifth piano phrase (omitting the last chord which repeats the first). The clarinet plays a different inversion of the piano’s right-hand, decorated with flutter-tongue. The process continues until the reading of the eighth phrase. In each case the fortissimo piano chord is preceded by the clarinet “upbeat”, fixed at the pitch of d ’’’ , and preceded by a grace note that successively reads “down” the first piano chord of the piece.
5.2.11 Panel 11
Panel 11, the final panel of the piece, begins on the second beat of bar 92 and reads the first nine piano phrases from panel 1 in rhythmic unison (omitting the inversions of the first chord) (Figure 5.20).
91
Figure 5.20 Here… bars 92-93
The clarinet and cello read the fourth voice of the right- and left-hand of the piano respectively, with sustained notes alternating trilled and normal. For the piano, left- and right-hands alternate between two and one note per hand, chosen from the remaining chord notes. Durations are determined by the intervals of the clarinet: a second generates a semiquaver’s duration; a fourth generates four semiquavers’ (a
92 crotchet) duration. At the end of every phrase an extra semiquaver rest is inserted into the clarinet part as a notional breathing place.
The process concludes with the reading of the chord from the tenth phrase and
a well-earned rest (Figure 5.21).
Figure 5.21 Here… bars 97-98
5.3 Discussion
Composing, and subsequently writing about, the acoustic instrumental work Here …, after an intense period of focusing solely on electronic music, served to highlight two features of this project.
Firstly, since I did not keep notes with regard to compositional procedures employed during the “white heat” of actually composing Here …, recalling them afterwards through looking at the score proved difficult. Indeed, certain specific triggering devices eluded me for two or three days before I was able to work them out, thus reinforcing the “meta-compositional” value of the Pd patches used in The
93 paradox of Pythagoras and Music of Grace , the two electronic works discussed in chapters 2 and 3.
The second feature was to revisit the differences in my personal approach to the two media (acoustic and electronic) and to discover that the responses I had to my initial MIDI studies were reinforced (see Chapter 1.4 MIDI Studies). Whilst, in a formal sense, Here … is not dissimilar to the Music of Grace series, the involvement
of human performers and acoustic instruments have once again significantly
influenced the parameters and general shape of the work. As a primary example of
this, throughout the piece the tempo is more-or-less as fast as possible; as such, the
tempo is effectively set by how fast the performers can play, rather than how fast the
listener can hear (that is, the perceptions of the listener). 121
In Panel 1, the articulations applied to the clarinet and cello at different times
highlight with slurs the semitones or non-semitones, a “proximity”, or lack of it, that
has a particular physical reality when orientated to the cellist’s fingerboard, and at the
end of Panel 1 the piano articulates its entire keyboard range. By comparison, for
computers and oscillators, such precise notions would be less meaningful: there is no
difference in “effort” between close and wide intervals and, with a range that extends
beyond the limits of human hearing, articulating the range of oscillators would
become an impractical exercise. 122
Panel 2 features coordinated accents between instruments—an exciting event for human performers, but not necessarily so for computers.
121 For example, two distinct notes are generally able to be heard (under experimental conditions) if their onsets are at least 3 milliseconds apart: closer than this and the two notes “smear” together. Frequency difference, timbre and general acoustic conditions may raise the time difference required to up to 50 milliseconds (Schubert 1979). 122 This is not to say that compositions are not written that do the equivalent for computers, pushing the processing power or other parameters of the technology to their limits, and using this concept as a creative tool for composition. The distinction is that this acoustic work deals with human parameters rather than overtly technological ones (to the extent that it does not even contain “extended” instrumental techniques). Indeed, equivalent “human” parameters have regularly been explored in a similar way in real-time human interaction (performance) with computers (Nelson 1989, Roads 1986).
94 Panel 3 features dynamic change, fast arpeggiation and definition of the
extremes of register, in particular the pitch-class D, which lies close to the top of the
conventional range of the clarinet and close to the bottom of the range of the cello. D
becomes more significant as a featured pitch because of this relative placement. Panel
4 contains a virtuosic piano line, while Panel 5 revisits coordination between the
instrumentalists, every piano note triggering arpeggiations in either the cello or
clarinet.
Panel 6 is the cellist’s solo, and an opportunity for expressive playing; Panel 7 advances ensemble coordination to rhythmic unison, trills adding not only colour, but
“life” to the sound, before featuring the contrast between tessitura, dynamic, synchronicity and non-synchronicity through Panels 8 to 11.
The aspects of composition summarised above are inherent to my approach to
the process of composing instrumental music. They apply not only to the “sound” of
the work, but to the “here-and-now” of the work’s realisation by human performers in
real time. In the light of the “freedoms” experienced in the process of composing the
electronic pieces for this folio, these are qualities I may now regard as “special”, even
precious, as a complementary part of my future compositional processes.
95
Bibliography
The following bibliography contains only those items that were consulted in the preparation of this thesis. 123 For reasons of clarity the bibliography is grouped into sections: Books and Dissertations, Chapters and Articles, Conference Proceedings,
Music Recordings, Music Scores, WWW Discussion List Messages, and WWW
Documents and Pages. All documents sourced from the web are held in either hard or soft copy.
Books and Dissertations
Aalst, J.A. van. Chinese Music . Peiping Press, 1933.
Apel, Willi (ed.). Harvard Dictionary of Music. London: Heinemann, 1976.
Ashton, Alan. “Electronics, Music and Computers.” PhD dissertation, University of Utah, 1971.
Barkl, Michael. “Franco Donatoni’s Etwas ruhiger im Ausdruck. ” MMus dissertation, University of New England, 1985.
Barkl, Michael. “Composition, Perception, and Analysis.” Unpublished MS, 1992: 120pp.
Barkl, Michael. “Vertigo: Riccardo Formosa’s Composition Technique.” PhD dissertation, Deakin University, 1994.
Brown, John Gracen. The Return . Martinsburg WV: self published, 2005.
Christensen, Thomas (ed.). The Cambridge History of Western Music Theory . Cambridge: CUP, 2002.
Cross, Lowell M. A Bibliography of Electronic Music . Toronto: University of Toronto Press, 1967.
123 Attempts at a comprehensive bibliography, even just for Pd, would be counter productive. Even by 1964 the bibliography for electronic music extended to over 120 pages (see Cross 1967).
96 Duckworth, William. Virtual Music: How the Web got Wired for Sound . NY & London: Routledge, 2005.
Emmerson, Simon (ed.). The Language of Electroacoustic Music . London: Macmillan, 1986.
Gozza, Paolo (ed.). Number to Sound: The Musical Way to the Scientific Revolution . The Western Ontario Series in Philosophy of Science, Vol.64, Dordrecht/Boston/London: Kluwer, 2000.
Haber, Yotam Moshe. “Aleatory and Serialism in Two Early Works of Franco Donatoni.” DMA Dissertation, Cornell University, 2004.
Helmholtz, Hermann von, Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik. Brunswick: 1863 (English translation by A. J. Ellis, On the Sensations of Tone , 1875/1954).
Holmes, Thom. Electronic and Experimental Music: Pioneers in Technology and Composition . NY and London: Routledge, 2002.
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Attachments (CD data)
Appendices A-R
Appendix A: Papers by Miller Puckette (4pp)
Appendix B: Pd Help and Tutorials (1p)
Appendix C: Pd Web Resources (2pp)
Appendix D: Pd Programming Conventions for Multiple Users of Large Pd Patches (7pp)
Appendix E: Pd Boxes (1p)
Appendix F: The paradox of Pythagoras : Patch Structure (4pp)
Appendix G: Pitch of Harmonics (7pp)
Appendix H: The cat dances and the moon shines brightly : Extract and Patches (58pp)
Appendix I: The cat dances and the moon shines brightly : Patch Structure (19pp)
Appendix J: The heavy dark trees line the streets of summer : Extract and Patches (173pp)
Appendix K: The heavy dark trees line the streets of summer : Patch Structure (11pp)
Appendix L: The crystals in the cave absorb the light as if they have not seen it in a million years : Extract and Patches (448pp)
Appendix M: The crystals in the cave absorb the light as if they have not seen it in a million years : Patch Structure (177pp)
Appendix N: Reverberation Patches (5pp)
Appendix O: Email: Re: Pd Conventions (2pp)
Appendix P: Pd Code (2pp)
Appendix Q: Performances (2pp)
Appendix R: Here… (49pp)
107
List of Appendix Figures
Appendix F: Page: Figure F.1 “Tree” diagram scheme F1
Appendix H: Figure H.1 Extract from Befiehl used for The cat dances —actual pitch H1 Figure H.2 The cat dances and the moon shines brightly top canvas H2 Panel 1: Figure H.3 [pd panel_1] H3 Figure H.4 [pd p_1a] H4 Figure H.5 [pd high_control_1-22] H5 Figure H.6 [pd rests] H6 Figure H.7 [pd high_1-22] H7 Figure H.8 [pd low_1-22] H8 Figure H.9 [pd axis_50] H9 Figure H.10 [pd mixout_x6_d] H11 Figure H.11 [pd osc_on_off_pair_H_L_d] H12 Figure H.12 [pd osc_on_off_L] H14 Figure H.13 [pd osc_on_off_/_R] H15 Figure H.14 [pd osc_on_off_pair_L_H_d] H16 Figure H.15 [pd osc_on_off_R] H17 Figure H.16 [pd osc_on_off_/_L] H18 Figure H.17 [pd no_of_voices_playing] H19 Figure H.18 [pd p_1b] H20 Figure H.19 [pd beat_accent] H21 Panel 2: Figure H.20 [pd panel_2] H22 Figure H.21 [pd p_2a] H23 Figure H.22 [pd axis_melody] H24 Figure H.23 [pd p_2b] H25 Figure H.24 [pd axis_melody_p2b] H26 Figure H.25 [pd beat_accent_2b] H27 Panel 3: Figure H.26 [pd panel_3] H27 Figure H.27 [pd p_3a] H29 Figure H.28 [pd high_3_1-7] H30 Figure H.29 [pd low_3_1-7] H31 Figure H.30 [pd descending_axes] H32 Figure H.31 [pd delay_semiquaver_bank] H33 Figure H.32 [pd delay_semiquaver_1] H34 Figure H.33 [pd delay_semiquaver] H35 Figure H.34 [pd repeat_down_12] H37 Figure H.35 [pd 38_26_trilled] H38 Figure H.36 [pd mixout_x2_d] H39 Figure H.37 [pd p_3b] H40 Figure H.38 [pd high_3_8-14] H41
108 Figure H.39 [pd low_3_8-14] H42 Figure H.40 [pd descending axes_3b] H43 Figure H.41 [pd p_3c] H44 Figure H.42 [pd high_3_15-22] H45 Figure H.43 [pd low_3_15-22] H46 Panel 4: Figure H.44 [pd panel_4] H47 Figure H.45 [pd high_melody] H48 Figure H.46 [pd 0_1_out] H50 Figure H.47 [pd ascending_descending_arpeggio_axes] H51 Figure H.48 [pd low_high_62_trigger] H52 Figure H.49 [pd high_melody_fast] H54 Panel 5: Figure H.50 [pd panel_5] H55 Figure H.51 [pd trills] H57
Appendix I: Figure I.1 “Tree” diagram scheme I1
Appendix J: Figure J.1 Extract/arrangement from Befiehl used for The heavy dark trees —actual pitch J1 Figure J.2 The heavy dark trees line the streets of summer top canvas J3 Figure J.3 [pd high_array] J4 Figure J.4 [pd high_1_2_3_4_5_6_7_8_9_10_11_12] J5 Figure J.5 [pd low_array] J7 Panel 1: Figure J.6 [pd panel_1] J8 Figure J.7 [pd p_1_chords_low] J10 Figure J.8 [pd p_1_chords_high] J11 Figure J.9 [pd low_0] J12 Figure J.10 [pd low_0_0] J13 Figure J.11 [pd delay_number] J16 Figure J.12 [pd low_0_1] J17 Figure J.13 Low rhythm at tempo=10000 ms J18 Figure J.14 [pd low_0_2] J19 Figure J.15 [pd low_0_3] J20 Figure J.16 [pd low_0_4] J20 Figure J.17 [pd low_0_5] J21 Figure J.18 [pd low_0_6] J21 Figure J.19 [pd low_1] J22 Figure J.20 Low rhythm at tempo=6000 ms J23 Figure J.21 [pd low_1_0] J24 Figure J.22 [pd low_1_1] J25 Figure J.23 [pd low_1_2] J26 Figure J.24 [pd low_1_3] J27 Figure J.25 [pd low_1_4] J27 Figure J.26 [pd low_1_5] J28 Figure J.27 [pd low_1_6] J28 Figure J.28 [pd low_2] J29
109 Figure J.29 Low rhythm at tempo=4285 ms J30 Figure J.30 [pd low_2_0] J31 Figure J.31 [pd low_2_1] J32 Figure J.32 [pd low_2_2] J32 Figure J.33 [pd low_2_3] J33 Figure J.34 [pd low_2_4] J33 Figure J.35 [pd low_2_5] J34 Figure J.36 [pd low_2_6] J34 Figure J.37 [pd low_3] J35 Figure J.38 [pd low_3_0] J36 Figure J.39 [pd low_3_1] J36 Figure J.40 [pd low_3_2] J37 Figure J.41 [pd low_3_3] J37 Figure J.42 [pd low_3_4] J38 Figure J.43 [pd low_3_5] J38 Figure J.44 [pd low_3_6] J39 Figure J.45 [pd low_4] J40 Figure J.46 [pd low_4_0] J41 Figure J.47 [pd low_4_1] J41 Figure J.48 [pd low_4_2] J42 Figure J.49 [pd low_4_3] J42 Figure J.50 [pd low_4_4] J43 Figure J.51 [pd low_4_5] J43 Figure J.52 [pd low_4_6] J44 Figure J.53 [pd low_5] J45 Figure J.54 [pd low_5_0] J46 Figure J.55 [pd low_5_1] J46 Figure J.56 [pd low_5_2] J47 Figure J.57 [pd low_5_3] J47 Figure J.58 [pd low_5_4] J48 Figure J.59 [pd low_5_5] J48 Figure J.60 [pd low_5_6] J49 Figure J.61 [pd low_6] J50 Figure J.62 [pd low_6_0] J51 Figure J.63 [pd low_6_1] J51 Figure J.64 [pd low_6_2] J52 Figure J.65 [pd low_6_3] J52 Figure J.66 [pd low_6_4] J53 Figure J.67 [pd low_6_5] J53 Figure J.68 [pd low_6_6] J54 Figure J.69 [pd high_0] J55 Figure J.70 High rhythm at tempo=10000 ms J56 Figure J.71 [pd high_0_0] J56 Figure J.72 [pd pairs] J57 Figure J.73 [pd high_0_1] J59 Figure J.74 [pd threes] J60 Figure J.75 [pd high_0_2] J61 Figure J.76 [pd high_0_3] J62 Figure J.77 [pd high_0_4] J63 Figure J.78 [pd high_1] J64
110 Figure J.79 High rhythm at tempo=6000 ms J64 Figure J.80 [pd high_1_0] J65 Figure J.81 [pd high_1_1] J65 Figure J.82 [pd high_1_2] J66 Figure J.83 [pd high_1_3] J66 Figure J.84 [pd high_1_4] J67 Figure J.85 [pd high_2] J68 Figure J.86 High rhythm at tempo=4285 ms J68 Figure J.87 [pd high_2_0] J69 Figure J.88 [pd high_2_1] J70 Figure J.89 [pd high_2_2] J70 Figure J.90 [pd high_2_3] J71 Figure J.91 [pd high_2_4] J71 Figure J.92 [pd high_3] J72 Figure J.93 [pd high_3_0] J73 Figure J.94 [pd high_3_1] J73 Figure J.95 [pd high_3_2] J74 Figure J.96 [pd high_3_3] J74 Figure J.97 [pd high_3_4] J75 Figure J.98 [pd high_4] J76 Figure J.99 [pd high_4_0] J77 Figure J.100 [pd high_4_1] J77 Figure J.101 [pd high_4_2] J78 Figure J.102 [pd high_4_3] J78 Figure J.103 [pd high_4_4] J79 Panel 2: Figure J.104 [pd panel_2] J80 Figure J.105 [pd low_to_low_p_1] J81 Figure J.106 [pd low_0_to_low_p_1] J81 Figure J.107 [pd low_0_0_to_low_p_1] J82 Figure J.108 [pd low_0_1_to_low_p_1] J83 Figure J.109 [pd low_0_2_to_low_p_1] J83 Figure J.110 [pd low_0_3_to_low_p_1] J84 Figure J.111 [pd low_0_4_to_low_p_1] J84 Figure J.112 [pd low_0_5_to_low_p_1] J84 Figure J.113 [pd low_0_6_to_low_p_1] J85 Figure J.114 [pd low_1_to_low_p_1] J85 Figure J.115 [pd low_1_0_to_low_p_1] J86 Figure J.116 [pd low_1_1_to_low_p_1] J86 Figure J.117 [pd low_1_2_to_low_p_1] J87 Figure J.118 [pd low_1_3_to_low_p_1] J87 Figure J.119 [pd low_1_4_to_low_p_1] J87 Figure J.120 [pd low_1_5_to_low_p_1] J88 Figure J.121 [pd low_1_6_to_low_p_1] J88 Figure J.122 [pd low_2_to_low_p_1] J89 Figure J.123 [pd low_2_0_to_low_p_1] J90 Figure J.124 [pd low_2_1_to_low_p_1] J90 Figure J.125 [pd low_2_2_to_low_p_1] J90 Figure J.126 [pd low_2_3_to_low_p_1] J91 Figure J.127 [pd low_2_4_to_low_p_1] J91
111 Figure J.128 [pd low_2_5_to_low_p_1] J91 Figure J.129 [pd low_2_6_to_low_p_1] J92 Figure J.130 [pd low_3_to_low_p_1] J92 Figure J.131 [pd low_3_0_to_low_p_1] J93 Figure J.132 [pd low_3_1_to_low_p_1] J93 Figure J.133 [pd low_3_2_to_low_p_1] J94 Figure J.134 [pd low_3_3_to_low_p_1] J94 Figure J.135 [pd low_3_4_to_low_p_1] J94 Figure J.136 [pd low_3_5_to_low_p_1] J95 Figure J.137 [pd low_3_6_to_low_p_1] J95 Figure J.138 [pd low_4_to_low_p_1] J96 Figure J.139 [pd low_4_0_to_low_p_1] J97 Figure J.140 [pd low_4_1_to_low_p_1] J97 Figure J.141 [pd low_4_2_to_low_p_1] J97 Figure J.142 [pd low_4_3_to_low_p_1] J98 Figure J.143 [pd low_4_4_to_low_p_1] J98 Figure J.144 [pd low_4_5_to_low_p_1] J98 Figure J.145 [pd low_4_6_to_low_p_1] J99 Figure J.146 [pd low_5_to_low_p_1] J99 Figure J.147 [pd low_5_0_to_low_p_1] J100 Figure J.148 [pd low_5_1_to_low_p_1] J100 Figure J.149 [pd low_5_2_to_low_p_1] J101 Figure J.150 [pd low_5_3_to_low_p_1] J101 Figure J.151 [pd low_5_4_to_low_p_1] J101 Figure J.152 [pd low_5_5_to_low_p_1] J102 Figure J.153 [pd low_5_6_to_low_p_1] J102 Figure J.154 [pd low_6_to_low_p_1] J103 Figure J.155 [pd low_6_0_to_low_p_1] J104 Figure J.156 [pd low_6_1_to_low_p_1] J104 Figure J.157 [pd low_6_2_to_low_p_1] J104 Figure J.158 [pd low_6_3_to_low_p_1] J105 Figure J.159 [pd low_6_4_to_low_p_1] J105 Figure J.160 [pd low_6_5_to_low_p_1] J105 Figure J.161 [pd low_6_6_to_low_p_1] J106 Figure J.162 [pd high_to_high_p_1] J106 Figure J.163 [pd high_0_to_high_p_1] J107 Figure J.164 [pd high_0_0_to_high_p_1] J108 Figure J.165 [pd high_0_1_to_high_p_1] J109 Figure J.166 [pd high_0_2_to_high_p_1] J109 Figure J.167 [pd high_0_3_to_high_p_1] J109 Figure J.168 [pd high_0_4_to_high_p_1] J110 Figure J.169 [pd high_1_to_high_p_1] J110 Figure J.170 [pd high_1_0_to_high_p_1] J111 Figure J.171 [pd high_1_1_to_high_p_1] J111 Figure J.172 [pd high_1_2_to_high_p_1] J112 Figure J.173 [pd high_1_3_to_high_p_1] J112 Figure J.174 [pd high_1_4_to_high_p_1] J112 Figure J.175 [pd high_2_to_high_p_1] J113 Figure J.176 [pd high_2_0_to_high_p_1] J114 Figure J.177 [pd high_2_1_to_high_p_1] J114
112 Figure J.178 [pd high_2_2_to_high_p_1] J114 Figure J.179 [pd high_2_3_to_high_p_1] J115 Figure J.180 [pd high_2_4_to_high_p_1] J115 Figure J.181 [pd high_3_to_high_p_1] J116 Figure J.182 [pd high_3_0_to_high_p_1] J116 Figure J.183 [pd high_3_1_to_high_p_1] J117 Figure J.184 [pd high_3_2_to_high_p_1] J117 Figure J.185 [pd high_3_3_to_high_p_1] J117 Figure J.186 [pd high_3_4_to_high_p_1] J118 Figure J.187 [pd high_4_to_high_p_1] J118 Figure J.188 [pd high_4_0_to_high_p_1] J119 Figure J.189 [pd high_4_1_to_high_p_1] J119 Figure J.190 [pd high_4_2_to_high_p_1] J120 Figure J.191 [pd high_4_3_to_high_p_1] J120 Figure J.192 [pd high_4_4_to_high_p_1] J120 Panel 3: Figure J.193 [pd panel_3] J121 Figure J.194 [pd p_3_chords_low] J122 Figure J.195 [pd accel_1-14] J123 Figure J.196 [pd clock_tabread_low_1-14] J124 Figure J.197 [pd clock_accel_1-14] J126 Figure J.198 [pd compare_2] J129 Figure J.199 [pd b_minus_a] J130 Figure J.200 [pd accel_2-14] J132 Figure J.201 [pd clock_tabread_low_2-14] J133 Figure J.202 [pd clock_accel_2-14] J134 Figure J.203 [pd accel_3-14] J135 Figure J.204 [pd clock_tabread_low_3-14] J136 Figure J.205 [pd clock_accel_3-14] J136 Figure J.206 [pd accel_4-14] J137 Figure J.207 [pd clock_tabread_low_4-14] J138 Figure J.208 [pd accel_4-14] J138 Figure J.209 [pd accel_5-14] J139 Figure J.210 [pd clock_tabread_low_5-14] J140 Figure J.211 [pd clock_accel_5-14] J140 Figure J.212 [pd accel_6-14] J141 Figure J.213 [pd clock_tabread_low_6-14] J142 Figure J.214 [pd clock_accel_6-14] J142 Figure J.215 [pd accel_7-14] J143 Figure J.216 [pd clock_tabread_low_7-14] J144 Figure J.217 [pd clock_accel_7-14] J144 Panel 4: Figure J.218 [pd panel_4] J145 Figure J.219 [pd p_4_chords_high] J146 Figure J.220 [pd accel_1-55] J147 Figure J.221 [pd clock_tabread_high_1-55] J148 Figure J.222 [pd clock_accel_1-55] J149 Figure J.223 [pd accel_3-55] J150 Figure J.224 [pd clock_tabread_high_3-55] J150 Figure J.225 [pd clock_accel_3-55] J151
113 Figure J.226 [pd _accel_5-55] J152 Figure J.227 [pd _clock_tabread_high_5-55] J152 Figure J.228 [pd _clock_accel_5-55] J153 Figure J.229 [pd accel_7-55] J154 Figure J.230 [pd clock_tabread_high_7-55] J154 Figure J.231 [pd clock_accel_7-55] J155 Figure J.232 [pd accel_9-55] J156 Figure J.233 [pd clock_tabread_high_9-55] J156 Figure J.234 [pd clock_accel_9-55] J157 Figure J.235 [pd accel_11-55] J158 Figure J.236 [pd clock_tabread_high_11-55] J158 Figure J.237 [pd clock_accel_11-55] J159 Figure J.238 [pd accel_13-55] J160 Figure J.239 [pd clock_tabread_high_13-55] J160 Figure J.240 [pd clock_accel_13-55] J161 Figure J.241 [pd accel_15-55] J162 Figure J.242 [pd clock_tabread_high_15-55] J162 Figure J.243 [pd clock_accel_15-55] J163 Panel 5: Figure J.244 [pd panel_5] J164 Figure J.245 [pd p_5_low] J165 Figure J.246 [pd p_5_high] J166 Mixout objects: Figure J.247 [pd mixout_0] J167 Figure J.248 [pd mixout_x8] J168 Figure J.249 [pd osc_on_off_*_L] J169 Figure J.250 [pd osc_on_off_*_R] J170 Figure J.251 [pd mixout_1] J171 Figure J.252 [pd mixout_2] J171 Figure J.253 [pd mixout_3] J171 Figure J.254 [pd mixout_4] J172 Figure J.255 [pd mixout_5] J172 Figure J.256 [pd mixout_6] J172 Figure J.257 [pd mixout_7] J173 Figure J.258 [pd mixout_8] J173
Appendix K: Figure K.1 “Tree” diagram scheme K1
Appendix L: Figure L.1 Chords from Befiehl used for The crystals in the cave —actual pitch L2 Figure L.2 The crystals in the cave top canvas L3 Panel 1: Figure L.3 [pd panel_1] L4 Figure L.4 [pd chords_1-4] L5 Figure L.5 [pd chords_1-4_+_axes_+_trills] L6 Figure L.6 [pd 4_part_chord_1_+_axes] L7 Figure L.7 [pd axis] L8 Figure L.8 [pd 4_part_chord_2_+_axes] L9
114 Figure L.9 [pd 4_part_chord_3_+_axes] L10 Figure L.10 [pd 4_part_chord_4_+_axes] L10 Figure L.11 [pd interval_=_duration] L11 Figure L.12 [pd trill_480] L13 Figure L.13 [pd beat_1920_accent] L14 Figure L.14 [pd chords_5-8] L15 Figure L.15 [pd chords_5-8_+_axes_+_trills] L16 Figure L.16 [pd 4_part_chord_5_+_axis] L17 Figure L.17 [pd 4_part_chord_6_+_axis] L17 Figure L.18 [pd 4_part_chord_7_+_axis] L18 Figure L.19 [pd 4_part_chord_8_+_axis] L19 Figure L.20 [pd chords_9-12] L19 Figure L.21 [pd chords_9-12_+_axes_+_trills] L20 Figure L.22 [pd 4_part_chord_9_+_axes] L21 Figure L.23 [pd 4_part_chord_10_+_axes] L21 Figure L.24 [pd 4_part_chord_11_+_axes] L22 Figure L.25 [pd 4_part_chord_12_+_axes] L23 Figure L.26 [pd chords_13-16] L23 Figure L.27 [pd chords_13-16_+_axes_+_trills] L24 Figure L.28 [pd 4_part_chord_13_+_axes] L25 Figure L.29 [pd 4_part_chord_14_+_axes] L25 Figure L.30 [pd 4_part_chord_15_+_axes] L26 Figure L.31 [pd 4_part_chord_16_+_axes] L27 Figure L.32 [pd chords_17-20] L27 Figure L.33 [pd chords_17-20_+_axes_+_trills] L28 Figure L.34 [pd 4_part_chord_17_+_axes] L29 Figure L.35 [pd 4_part_chord_18_+_axes] L29 Figure L.36 [pd 4_part_chord_19_+_axes] L30 Figure L.37 [pd 4_part_chord_20_+_axes] L30 Figure L.38 [pd chords_21-24] L31 Figure L.39 [pd chords_21-24_+_axes_+_trills] L31 Figure L.40 [pd 4_part_chord_21_+_axes] L32 Figure L.41 [pd 4_part_chord_22_+_axes] L32 Figure L.42 [pd 4_part_chord_23_+_axes] L33 Figure L.43 [pd 4_part_chord_24_+_axes] L33 Figure L.44 [pd chords_25-28] L34 Figure L.45 [pd chords_25-28_+_axes_+_trills] L34 Figure L.46 [pd 4_part_chord_25_+_axes] L35 Figure L.47 [pd 4_part_chord_26_+_axes] L35 Figure L.48 [pd 4_part_chord_27_+_axes] L36 Figure L.49 [pd 4_part_chord_28_+_axes] L36 Figure L.50 [pd chords_29-32] L37 Figure L.51 [pd chords_29-32_+_axes_+_trills] L37 Figure L.52 [pd 4_part_chord_29_+_axes] L38 Figure L.53 [pd 4_part_chord_30_+_axes] L38 Figure L.54 [pd 4_part_chord_31_+_axes] L39 Figure L.55 [pd 4_part_chord_32_+_axes] L40 Figure L.56 [pd chords_33-36] L40 Figure L.57 [pd chords_33-36_+_axes_+_trills] L41 Figure L.58 [pd 4_part_chord_33_+_axes] L42
115 Figure L.59 [pd 4_part_chord_34_+_axes] L42 Figure L.60 [pd 4_part_chord_35_+_axes L43 Figure L.61 [pd 4_part_chord_36_+_axes] L43 Figure L.62 [pd chords_37-40] L44 Figure L.63 [pd chords_37-40_+_axes_+_trills] L44 Figure L.64 [pd 4_part_chord_37_+_axes] L45 Figure L.65 [pd 4_part_chord_38_+_axes] L45 Figure L.66 [pd 4_part_chord_39_+_axes] L46 Figure L.67 [pd 4_part_chord_40_+_axes] L46 Figure L.68 [pd panel_1a] L47 Figure L.69 [pd chords_1-4a] L48 Figure L.70 [pd chords_5-8a] L48 Figure L.71 [pd chords_9-12a] L49 Figure L.72 [pd chords_13-16a] L49 Figure L.73 [pd chords_17-20a] L49 Figure L.74 [pd chords_21-24a] L50 Figure L.75 [pd chords_25-28a] L50 Figure L.76 [pd chords_29-32a] L51 Figure L.77 [pd chords_33-36a] L51 Figure L.78 [pd chords_37-40a] L51 Figure L.79 [pd panel_1b] L52 Figure L.80 [pd chords_1-4b] L53 Figure L.81 [pd chords_5-8b] L53 Figure L.82 [pd chords_9-12b] L53 Figure L.83 [pd chords_13-16b] L54 Figure L.84 [pd chords_17-20b] L54 Figure L.85 [pd chords_21-24b] L55 Figure L.86 [pd chords_25-28b] L55 Figure L.87 [pd chords_29-32b] L56 Figure L.88 [pd chords_33-36b] L56 Figure L.89 [pd chords_37-40b] L56 Figure L.90 [pd panel_1c] L57 Figure L.91 [pd chords_1-4c] L58 Figure L.92 [pd chords_5-8c] L58 Figure L.93 [pd chords_9-12c] L58 Figure L.94 [pd chords_13-16c] L59 Figure L.95 [pd chords_17-20c] L59 Figure L.96 [pd chords_21-24c] L60 Figure L.97 [pd chords_25-28c] L60 Figure L.98 [pd chords_29-32c] L60 Figure L.99 [pd chords_33-36c] L61 Figure L.100 [pd chords_37-40c] L61 Panel 2: Figure L.101 [pd panel_2] L62 Figure L.102 [pd p2_1-4] L63 Figure L.103 [pd p2_chords_1-4] L64 Figure L.104 [pd p2_chords_1-4_+_axes] L65 Figure L.105 [pd chord_1_+_arp] L66 Figure L.106 [pd through->->->->->->->->->->] L66 Figure L.107 [pd interval_>_duration] L67
116 Figure L.108 [pd subdurations] L68 Figure L.109 [pd float_in_complements_out] L69 Figure L.110 [pd delay_x6_int_in_tbb_out] L70 Figure L.111 [pd chord_2_+_arp] L71 Figure L.112 [pd chord_3_+_arp] L71 Figure L.113 [pd chord_4_+_arp] L72 Figure L.114 [pd p2_chords_1-4a] L73 Figure L.115 [pd p2_chords_1-4b] L73 Figure L.116 [pd p2_chords_1-4c] L74 Figure L.117 [pd p2_5-8] L75 Figure L.118 [pd p2_chords_5-8] L75 Figure L.119 [pd chords_5-8_+_axes] L76 Figure L.120 [pd chord_5_+_arp] L76 Figure L.121 [pd chord_6_+_arp] L77 Figure L.122 [pd chord_7_+_arp] L78 Figure L.123 [pd chord_8_+_arp] L78 Figure L.124 [pd p2_chords_5-8a] L79 Figure L.125 [pd p2_chords_5-8b] L79 Figure L.126 [pd p2_chords_5-8c] L80 Figure L.127 [pd p2_9-12] L80 Figure L.128 [pd p2_chords_9-12] L81 Figure L.129 [pd p2_chords_9-12_+_axes] L82 Figure L.130 [pd chord_9_+_arp] L82 Figure L.131 [pd chord_10_+_arp] L83 Figure L.132 [pd chord_11_+_arp] L83 Figure L.133 [pd chord_12_+_arp] L84 Figure L.134 [pd p2_13-16] L84 Figure L.135 [pd p2_chords_13-16] L85 Figure L.136 [pd chords_13-16_+_axes] L86 Figure L.137 [pd chord_13_+_arp] L86 Figure L.138 [pd chord_14_+_arp] L87 Figure L.139 [pd chord_15_+_arp] L87 Figure L.140 [pd chord_16_+_arp] L88 Figure L.141 [pd p2_chords_13-16a] L89 Figure L.142 [pd p2_chords_13-16b] L89 Figure L.143 [pd p2_chords_13-16c] L90 Figure L.144 [pd p2_17-20] L90 Figure L.145 [pd p2_chords_17-20] L91 Figure L.146 [pd chords_17-20_+_axes] L91 Figure L.147 [pd chord_17_+_arp] L92 Figure L.148 [pd chord_18_+_arp] L92 Figure L.149 [pd chord_19_+_arp] L93 Figure L.150 [pd chord_20_+_ar L94 Figure L.151 [pd chords_17-20a] L94 Figure L.152 [pd chords_17-20b] L95 Figure L.153 [pd chords_17-20c] L95 Figure L.154 [pd p2_21-24] L96 Figure L.155 [pd p2_chords_21-24] L97 Figure L.156 [pd chords_21-24_+_axes] L97 Figure L.157 [pd chord_21_+_arp] L98
117 Figure L.158 [pd chord_22_+_arp] L98 Figure L.159 [pd chord_23_+_arp] L99 Figure L.160 [pd chord_24_+_arp] L100 Figure L.161 [pd p2_chords_21-24a] L100 Figure L.162 [pd p2_chords_21-24b] L101 Figure L.163 [pd p2_chords_21-24c] L101 Figure L.164 [pd p2_25-28] L102 Figure L.165 [pd p2_chords_25-28] L102 Figure L.166 [pd chords_25-28_+_axes] L103 Figure L.167 [pd chord_25_+_arp] L104 Figure L.168 [pd chord_26_+_arp] L104 Figure L.169 [pd chord_27_+_arp] L105 Figure L.170 [pd chord_28_+_arp] L105 Figure L.171 [pd p2_chords_25-28a] L106 Figure L.172 [pd p2_chords_25-28b] L106 Figure L.173 [pd p2_chords_25-28c] L107 Figure L.174 [pd p2_29-32] L107 Figure L.175 [pd p2_chords_29-32] L108 Figure L.176 [pd chords_29-32_+_axes] L108 Figure L.177 [pd chords_29-32_+_axes] L109 Figure L.178 [pd chord_29_+_arp] L109 Figure L.179 [pd chord_30_+_arp] L110 Figure L.180 [pd chord_31_+_arp] L111 Figure L.181 [pd chord_32_+_arp] L111 Figure L.182 [pd p2_chords_29-32a] L112 Figure L.183 [pd p2_chords_29-32b] L112 Figure L.184 [pd pd_chords_29-32c] L113 Figure L.185 [pd p2_33-36] L113 Figure L.186 [pd p2_chords_33-36] L114 Figure L.187 [pd chords_33-36_+_axes] L115 Figure L.188 [pd chord_33_+_arp] L115 Figure L.189 [pd chord_34_+_arp] L116 Figure L.190 [pd chord_35_+_arp] L116 Figure L.191 [pd p2_chords_33-36a] L117 Figure L.192 [pd p2_chords_33-36b] L117 Figure L.193 [pd p2_chords_33-36c] L118 Figure L.194 [pd p2_37-40] L118 Figure L.195 [pd p2_chords_37-40] L119 Figure L.196 [pd chords_37-40] L120 Figure L.197 [pd _chord_37_+_arp] L120 Figure L.198 [pd chord_38_+_arp] L121 Figure L.199 [pd chord 39_+_arp] L121 Figure L.200 [pd p2_chord_40_+_arp] L122 Figure L.201 [pd p2_chords_37-40a] L122 Figure L.202 [pd p2_chords_37-40b] L123 Figure L.203 [pd p2_chords_37-40c] L124 Panel 3: Figure L.204 [pd panel_3] L125 Figure L.205 [pd p3_1-10abc] L126 Figure L.206 [pd p3_1a] L127
118 Figure L.207 [pd 4_part_chord_1_+_axes_2] L128 Figure L.208 [pd axis_2] L129 Figure L.209 [pd p3_1bc] L130 Figure L.209 [pd p3_1bc] L131 Figure L.211 [pd 4_part_chord_2_+_axes_2] L132 Figure L.212 [pd interval_=_duration_3840] L133 Figure L.213 [pd axis_arp] L134 Figure L.214 [pd interval_=_duration_480] L135 Figure L.215 [pd axis_arp_a] L136 Figure L.216 [pd p3_2bc] L137 Figure L.217 [pd axis_arp_b] L138 Figure L.218 [pd axis_arp_c] L139 Figure L.219 [pd p3_3a] L140 Figure L.220 [pd 4_part_chord_3_+_axes_2] L140 Figure L.221 [pd p3_3bc] L141 Figure L.222 [pd p3_4a] L142 Figure L.223 [pd 4_part_chord_4_+_axes_2] L142 Figure L.224 [pd p3_4bc] L143 Figure L.225 [pd p3_5a] L144 Figure L.226 [pd 4_part_chord_5_+_axes_2] L144 Figure L.227 [pd p3_5bc] L145 Figure L.228 [pd p3_6a] L145 Figure L.229 [pd 4_part_chord_6_+_axes_2] L146 Figure L.210 [pd p3_6bc] L146 Figure L.211 [pd p3_7a] L147 Figure L.212 [pd 4_part_chord_7_+_axes_2] L147 Figure L.213 [pd p3_7bc] L148 Figure L.214 [pd p3_8a] L149 Figure L.215 [pd 4_part_chord_8_+_axes_2] L149 Figure L.216 [pd p3_8bc] L150 Figure L.217 [pd p3_9a] L151 Figure L.218 [pd 4_part_chord_9_+_axes_2] L151 Figure L.219 [pd p3_9bc] L152 Figure L.220 [pd p3_10a] L153 Figure L.221 [pd 4_part_chord_10_+_axes_2] L153 Figure L.222 [pd p3_10bc] L154 Figure L.223 [pd p3_11-20abc] L155 Figure L.224 [pd p3_11a] L156 Figure L.225 [pd 4_part_chord_11_+_axes_2] L156 Figure L.226 [pd p3_11bc] L157 Figure L.227 [pd p3_12a] L158 Figure L.228 [pd 4_part_chord_12_+_axes_2] L158 Figure L.229 [pd p3_12bc] L159 Figure L.230 [pd p3_13a] L160 Figure L.231 [pd 4_part_chord_13_+_axes_2] L160 Figure L.232 [pd p3_13bc] L161 Figure L.233 [pd p3_14a] L162 Figure L.234 [pd 4_part_chord_14_+_axes_2] L162 Figure L.235 [pd p3_14bc] L163 Figure L.236 [pd p3_15a] L164
119 Figure L.237 [pd 4_part_chord_15_+_axes_2] L164 Figure L.238 [pd p3_15bc] L165 Figure L.239 [pd p3_16a] L166 Figure L.240 [pd 4_part_chord_16_+_axes_2] L166 Figure L.241 [pd p3_16bc] L167 Figure L.242 [pd p3_17a] L168 Figure L.243 [pd 4_part_chord_17_+_axes_2] L168 Figure L.244 [pd p3_17bc] L169 Figure L.245 [pd p3_18a] L170 Figure L.246 [pd 4_part_chord_18_+_axes_2] L170 Figure L.247 [pd p3_18bc] L171 Figure L.248 [pd p3_19a] L172 Figure L.249 [pd 4_part_chord_19_+_axes_2] L172 Figure L.250 [pd p3_19bc] L173 Figure L.251 [pd p3_20a] L174 Figure L.252 [pd 4_part_chord_20_+_axes_2] L174 Figure L.253 [pd p3_20bc] L175 Figure L.254 [pd p3_21-20abc] L176 Figure L.255 [pd p3_21a] L177 Figure L.256 [pd 4_part_chord_21_+_axes_2] L177 Figure L.257 [pd p3_21bc] L178 Figure L.258 [pd p3_22a] L179 Figure L.259 [pd 4_part_chord_22_+_axes_2] L179 Figure L.260 [pd p3_22bc] L180 Figure L.261 [pd p3_23a] L181 Figure L.262 [pd 4_part_chord_23_+_axes_2] L181 Figure L.263 [pd p3_23bc] L182 Figure L.264 [pd p3_24a] L183 Figure L.265 [pd 4_part_chord_24_+_axes_2] L183 Figure L.266 [pd p3_24bc] L184 Figure L.267 [pd p3_25a] L185 Figure L.268 [pd 4_part_chord_25_+_axes_2] L185 Figure L.269 [pd p3_25bc] L186 Figure L.270 [pd p3_26a] L187 Figure L.271 [pd 4_part_chord_26_+_axes_2] L187 Figure L.272 [pd p3_26bc] L188 Figure L.273 [pd p3_27a] L189 Figure L.274 [pd 4_part_chord_27_+_axes_2] L189 Figure L.275 [pd p6_27bc] L190 Figure L.276 [pd p3_28a] L191 Figure L.277 [pd 4_part_chord_28_+_axes_2] L191 Figure L.278 [pd p3_28bc] L192 Figure L.279 [pd p3_29a] L193 Figure L.280 [pd 4_part_chord_29_+_axes_2] L193 Figure L.281 [pd p3_29bc] L194 Figure L.282 [pd p3_30a] L195 Figure L.283 [pd 4_part_chord_30_+_axes_2] L195 Figure L.284 [pd p3_30bc] L196 Figure L.285 [pd p3_31-40abc] L197 Figure L.286 [pd p3_31a] L198
120 Figure L.287 [pd 4_part_chord_31_+_axes_2] L198 Figure L.288 [pd p3_31bc] L199 Figure L.289 [pd p3_32a] L200 Figure L.290 [pd 4_part_chord_32_+_axes_2] L200 Figure L.291 [pd p3_32bc] L201 Figure L.292 [pd p3_33a] L202 Figure L.293 [pd 4_part_chord_33_+_axes_2] L202 Figure L.294 [pd p3_33bc] L203 Figure L.295 [pd p3_34a] L204 Figure L.296 [pd 4_part_chord_34_+_axes_2] L204 Figure L.297 [pd p3_34bc] L205 Figure L.298 [pd p3_35a] L206 Figure L.299 [pd 4_part_chord_35_+_axes_2] L206 Figure L.300 [pd p3_35bc] L207 Figure L.301 [pd p3_36a] L208 Figure L.302 [pd 4_part_chord_36_+_axes_2] L208 Figure L.303 [pd p3_36bc] L209 Figure L.304 [pd p3_37a] L210 Figure L.305 [pd 4_part_chord_37_+_axes_2] L210 Figure L.306 [pd p3_37bc] L211 Figure L.307 [pd p3_38a] L212 Figure L.308 [pd 4_part_chord_38_+_axes_2] L212 Figure L.309 [pd p3_38bc] L213 Figure L.310 [pd p3_39a] L214 Figure L.311 [pd 4_part_chord_39_+_axes_2] L214 Figure L.312 [pd p3_39bc] L215 Figure L.313 [pd p3_40a] L216 Figure L.314 [pd 4_part_chord_40_+_axes_2] L216 Figure L.315 [pd p3_40bc] L217 Panel 4: Figure L.316 [pd panel_4] L218 Figure L.317 [pd p4_1-8] L219 Figure L.318 [pd p4_chords_1-4_+0_arp] L220 Figure L.319 [pd chord_1_+0_arp] L221 Figure L.320 [pd integer_store_x4] L222 Figure L.321 [pd subdurations_x4] L223 Figure L.322 [pd delay_line_x4_int_in_tbf_out] L223 Figure L.323 [pd chord_2_+0_arp] L224 Figure L.324 [pd chord_3_+0_arp] L225 Figure L.325 [pd chord_4_+0_arp] L226 Figure L.326 [pd p4_chords_1-4_+12_arp] L226 Figure L.327 [pd chord_1_+12_arp] L227 Figure L.328 [pd transposition_+12_x4] L228 Figure L.329 [pd chord_2_+12_arp] L228 Figure L.330 [pd chord_3_+12_arp] L229 Figure L.331 [pd chord_4_+12_arp] L229 Figure L.332 [pd p4_chords_1-4_+24_arp] L230 Figure L.333 [pd chord_1_+24_arp] L231 Figure L.334 [pd transposition_+24_x4] L231 Figure L.335 [pd chord_2_+24_arp] L232
121 Figure L.336 [pd chord_3_+24_arp] L232 Figure L.337 [pd chord_4_+24_arp] L233 Figure L.338 [pd p4_chords_1-4_+36_arp_axes_+48] L234 Figure L.339 [pd chord_1_+36_arp] L235 Figure L.340 [pd transposition_+36_x4] L235 Figure L.341 [pd chord_2_+36_arp] L236 Figure L.342 [pd chord_3_+36_arp] L236 Figure L.343 [pd chord_4_+36_arp] L237 Figure L.344 [pd axes_1_+48_arp] L238 Figure L.345 [pd transposition_+48_x6] L239 Figure L.346 [pd delay_line_x6_int_in_tbf_out] L239 Figure L.347 [pd integer_store_x6] L240 Figure L.348 [pd axes_2_+48_arp] L240 Figure L.349 [pd axes_3_+48_arp] L241 Figure L.350 [pd axes_4_+48_arp] L242 Figure L.351 [pd p4_chords_5-8_+0_arp] L242 Figure L.352 [pd chord_5_+0_arp] L243 Figure L.353 [pd chord_6_+0_arp] L244 Figure L.354 [pd chord_7_+0_arp] L244 Figure L.355 [pd chord_8_+0_arp] L245 Figure L.356 [pd chords_5-8_+12_arp] L246 Figure L.357 [pd chord_5_+12_arp] L247 Figure L.358 [pd chord_6_+12_arp] L247 Figure L.359 [pd chord_7_+12_arp] L248 Figure L.360 [pd chord_8_+12_arp] L248 Figure L.361 [pd chords_5-8_+24_arp] L249 Figure L.362 [pd chord_5_+24_arp] L250 Figure L.363 [pd chord_6_+24_arp] L250 Figure L.364 [pd chord_7_+24_arp] L251 Figure L.365 [pd chord_8_+24_arp] L251 Figure L.366 [pd chords_5-8_+36_arp_axes_+48] L252 Figure L.367 [pd chord_5_+36_arp] L253 Figure L.368 [pd chord_6_+36_arp] L253 Figure L.369 [pd chord_7_+36_arp] L254 Figure L.370 [pd chord_8_+36_arp] L254 Figure L.371 [pd axes_5_+48_arp] L255 Figure L.372 [pd axes_6_+48_arp] L256 Figure L.373 [pd axes_7_+48_arp] L256 Figure L.374 [pd axes_8_+48_arp] L257 Figure L.375 [pd p4_9-16] L258 Figure L.375 [pd p4_chords_9-12_+0_arp] L259 Figure L.376 [pd chord_9_+0_arp] L260 Figure L.377 [pd chord_10_+0_arp] L261 Figure L.378 [pd chord_11_+0_arp] L262 Figure L.379 [pd chord_12_+0_arp] L262 Figure L.380 [pd p4_chords_9-12_+12_arp] L263 Figure L.381 [pd chord_9_+12_arp] L264 Figure L.382 [pd chord_10_+12_arp] L265 Figure L.383 [pd chord_11_+12_arp] L265 Figure L.384 [pd chord_12_+12_arp] L266
122 Figure L.385 [pd p4_chords_9-12_+24_arp] L267 Figure L.386 [pd chord_9_+24_arp] L268 Figure L.387 [pd chord_10_+24_arp] L268 Figure L.388 [pd chord_11_+24_arp] L269 Figure L.389 [pd chord_12_+24_arp] L270 Figure L.390 [pd p4_chords_9-12_+36_arp_axes_+48+36] L270 Figure L.391 [pd chord_9_+36_arp] L271 Figure L.392 [pd chord_10_+36_arp] L272 Figure L.393 [pd chord_11_+36_arp] L272 Figure L.394 [pd chord_12_+36_arp] L273 Figure L.395 [pd axis_9_+48_arp] L274 Figure L.396 [pd axis_10_+48_arp] L274 Figure L.397 [pd axis_11_+48_arp] L275 Figure L.398 [pd axis_12_+48_arp] L276 Figure L.399 [pd axes_9_+36_arp] L277 Figure L.400 [pd transposition_+36_x6] L277 Figure L.401 [pd axes_10_+36_arp] L278 Figure L.402 [pd axes_11_+36_arp] L279 Figure L.403 [pd axes_12_+36_arp] L279 Figure L.404 [pd p4_chords_13-16_+_0_arp] L280 Figure L.405 [pd chord_13_+0_arp] L280 Figure L.406 [pd chord_14_+0_arp] L281 Figure L.407 [pd chord_15_+0_arp] L282 Figure L.408 [pd chord_16_+0_arp] L282 Figure L.409 [pd p4_chords_13-16_+12_arp] L283 Figure L.410 [pd chord_13_+12_arp] L283 Figure L.411 [pd chord_14_+12_arp] L284 Figure L.412 [pd chord_15_+12_arp] L284 Figure L.413 [pd chord_16_+12_arp] L285 Figure L.414 [pd p4_chords_13-16_+24_arp] L285 Figure L.415 [pd chord_13_+24_arp] L286 Figure L.416 [pd chord_14_+24_arp] L287 Figure L.417 [pd chord_15_+24_arp] L287 Figure L.418 [pd chord_16_+24_arp] L288 Figure L.419 [pd p4_chords_13-16_+36_arp_axes_+48+36] L288 Figure L.420 [pd chord_13_+36_arp] L289 Figure L.421 [pd chord_14_+36_arp] L290 Figure L.422 [pd chord_15_+36_arp] L290 Figure L.423 [pd chord_16_+36_arp] L291 Figure L.424 [pd axes_13_+48_arp] L292 Figure L.425 [pd axes_14_+48_arp] L292 Figure L.426 [pd axes_15_+48_arp] L293 Figure L.427 [pd axes_16_+48_arp] L293 Figure L.428 [pd axes_13_+36_arp] L294 Figure L.429 [pd axes_14_+36_arp] L294 Figure L.430 [pd axes_15_+36_arp] L295 Figure L.431 [pd axes_16_+36_arp] L295 Figure L.432 [pd p4_17-24] L296 Figure L.433 [pd p4_chords_17-24_+0_arp] L297 Figure L.434 [pd chord_17_+0_arp] L297
123 Figure L.435 [pd chord_18_+0_arp] L298 Figure L.436 [pd chord_19_+0_arp] L299 Figure L.437 [pd chord_20_+0_arp] L299 Figure L.438 [pd p4_chords_17-20_+12_arp] L300 Figure L.439 [pd chord_17_+12_arp] L300 Figure L.440 [pd chord_18_+12_arp] L301 Figure L.441 [pd chord_19_+12_arp] L301 Figure L.442 [pd chord_20_+12_arp] L302 Figure L.443 [pd chords_17-20_+24_arp] L302 Figure L.444 [pd chord_17_+24_arp] L303 Figure L.445 [pd chord_18_+24_arp] L303 Figure L.446 [pd chord_19_+24_arp] L304 Figure L.447 [pd chord_20_+24_arp] L304 Figure L.448 [pd chords_17-20_+36_arp_axes_+48+36+24] L305 Figure L.449 [pd chord_17_+36_arp L305 Figure L.450 [pd chord_18_+36_arp] L306 Figure L.451 [pd chord_19_+36_arp] L306 Figure L.452 [pd chord_20_+36_arp] L307 Figure L.453 [pd axes_17_+48_arp] L308 Figure L.454 [pd axes_18_+48_arp] L308 Figure L.455 [pd axes_19_+48_arp] L309 Figure L.456 [pd axes_20_+48_arp] L309 Figure L.457 [pd axes_17_+36_arp] L310 Figure L.458 [pd axes_18_+36_arp] L310 Figure L.459 [pd axes_19_+36_arp] L311 Figure L.460 [pd axes_20_+36_arp] L311 Figure L.461 [pd axes_17_+24_arp] L312 Figure L.462 [pd axes_18_+24_arp] L313 Figure L.463 [pd axes_19_+24_arp] L313 Figure L.464 [pd axes_20_+24_arp] L314 Figure L.465 [pd transposition_+24_x6] L314 Figure L.466 [pd p4_chords_21-24_+0_arp] L315 Figure L.467 [pd chord_21_+0_arp] L315 Figure L.468 [pd chord_22_+0_arp] L316 Figure L.469 [pd chord_23_+0_arp] L316 Figure L.470 [pd chord_24_+0_arp] L317 Figure L.471 [pd chords_21-24_+12_arp] L317 Figure L.472 [pd chord_21_+12_arp] L318 Figure L.473 [pd chord_22_+12_arp] L318 Figure L.474 [pd chord_23_+12_arp] L319 Figure L.475 [pd chord_24_+12_arp] L319 Figure L.476 [pd chords_21-24_+24_arp] L320 Figure L.477 [pd chord_21_+24_arp] L320 Figure L.478 [pd chord_22_+24_arp] L321 Figure L.479 [pd chord_23_+24_arp] L321 Figure L.480 [pd chord_24_+24_arp] L322 Figure L.481 [pd chords_21-24_+36_arp_axes_+48+36+24] L322 Figure L.482 [pd chord_21_+36_arp] L323 Figure L.483 [pd chord_22_+36_arp] L323 Figure L.484 [pd chord_23_+36_arp] L324
124 Figure L.485 [pd chord_24_+36_arp] L324 Figure L.486 [pd axes_21_+48_arp] L325 Figure L.487 [pd axes_22_+48_arp] L325 Figure L.488 [pd axes_23_+48_arp] L326 Figure L.489 [pd axes_24_+48_arp] L326 Figure L.490 [pd axes_21_+36_arp] L327 Figure L.491 [pd axes_22_+36_arp] L327 Figure L.492 [pd axes_23_+36_arp] L328 Figure L.493 [pd axes_24_+36_arp] L328 Figure L.494 [pd axes_21_+24_arp] L329 Figure L.495 [pd axes_22_+24_arp] L329 Figure L.496 [pd axes_23_+24_arp] L330 Figure L.497 [pd axes_24_+24_arp] L330 Figure L.498 [pd p4_25-32] L331 Figure L.499 [pd p4_chords_25-28_+0_arp] L332 Figure L.500 [pd chord_25_+0_arp] L332 Figure L.501 [pd chord_26_+0_arp] L333 Figure L.502 [pd chord_27_+0_arp] L334 Figure L.503 [pd chord_28_+0_arp] L334 Figure L.504 [pd p4_chords_25-28_+12_arp] L335 Figure L.505 [pd chord_25_+12_arp] L335 Figure L.506 [pd chord_26_+12_arp] L336 Figure L.507 [pd chord_27_+12_arp] L336 Figure L.508 [pd chord_28_+12_arp] L337 Figure L.509 [pd p4_chords_25-28_+24_arp] L337 Figure L.510 [pd chord_25_+24_arp] L338 Figure L.511 [pd chord_26_+24_arp] L338 Figure L.512 [pd chord_27_+24_arp] L339 Figure L.513 [pd chord_28_+24_arp] L339 Figure L.514 [pd p4_chords_25-28_+36_arp_axes_+48+36+24+12] L340 Figure L.515 [pd chord_25_+36_arp] L340 Figure L.516 [pd chord_26_+36_arp] L341 Figure L.517 [pd chord_27_+36_arp] L341 Figure L.518 [pd chord_28_+36_arp] L342 Figure L.519 [pd axes_25_+48_arp] L343 Figure L.520 [pd axes_26_+48_arp] L343 Figure L.521 [pd axes_27_+48_arp] L344 Figure L.522 [pd axes_28_+48_arp] L344 Figure L.523 [pd axes_25_+36_arp] L345 Figure L.524 [pd axes_26_+36_arp] L345 Figure L.525 [pd axes_27_+36_arp] L346 Figure L.526 [pd axes_28_+36_arp] L346 Figure L.527 [pd axes_25_+24_arp] L347 Figure L.528 [pd axes_26_+24_arp] L347 Figure L.529 [pd axes_27_+24_arp] L348 Figure L.530 [pd axes_28_+24_arp] L348 Figure L.531 [pd axes_25_+12_arp] L349 Figure L.532 [pd transposition_+12_x6] L350 Figure L.533 [pd axes_26_+12_arp] L350 Figure L.534 [pd axes_27_+12_arp] L351
125 Figure L.535 [pd axes_28_+12_arp] L351 Figure L.536 [pd p4_chords_29-32_+0_arp] L352 Figure L.537 [pd chord_29_+0_arp] L352 Figure L.538 [pd chord_30_+0_arp] L353 Figure L.539 [pd chord_31_+0_arp] L353 Figure L.540 [pd chord_32_+0_arp] L354 Figure L.541 [pd p4_chords_29-32_+12_arp] L354 Figure L.542 [pd chord_29_+12_arp] L355 Figure L.543 [pd chord_30_+12_arp] L355 Figure L.544 [pd chord_31_+12_arp] L356 Figure L.545 [pd chord_32_+12_arp] L356 Figure L.546 [pd p4_chords_29-32_+24_arp] L357 Figure L.547 [pd chord_29_+24_arp] L357 Figure L.548 [pd chord_30_+24_arp] L358 Figure L.549 [pd chord_31_+24_arp] L358 Figure L.550 [pd chord_32_+24_arp] L359 Figure L.551 [pd p4_chords_29-32_+36_arp_axes_+48+36+24+12] L359 Figure L.552 [pd chord_29_+36_arp] L360 Figure L.553 [pd chord_30_+36_arp] L360 Figure L.554 [pd chord_31_+36_arp] L361 Figure L.555 [pd chord_32_+36_arp] L361 Figure L.556 [pd axes_29_+48_arp] L362 Figure L.557 [pd axes_30_+48_arp] L363 Figure L.558 [pd axes_31_+48_arp] L363 Figure L.559 [pd axes_32_+48_arp] L364 Figure L.560 [pd axes_29_+36_arp] L364 Figure L.561 [pd axes_30_+36_arp] L365 Figure L.562 [pd axes_31_+36_arp] L365 Figure L.563 [pd axes_32_+36_arp] L366 Figure L.564 [pd axes_29_+24_arp] L366 Figure L.565 [pd axes_30_+24_arp] L367 Figure L.566 [pd axes_31_+24_arp] L367 Figure L.567 [pd axes_32_+24_arp] L368 Figure L.568 [pd axes_29_+12_arp] L368 Figure L.569 [pd axes_30_+12_arp] L369 Figure L.570 [pd axes_31_+12_arp] L369 Figure L.571 [pd axes_32_+12_arp] L370 Figure L.572 [pd p4_33-40] L371 Figure L.573 [pd p4_chords_33-36_+0_arp] L372 Figure L.574 [pd chord_33_+0_arp] L372 Figure L.575 [pd chord_34_+0_arp] L373 Figure L.576 [pd chord_35_+0_arp] L374 Figure L.577 [pd chord_36_+0_arp] L374 Figure L.578 [pd p4_chords_33-36_+12_arp] L375 Figure L.579 [pd chord_33_+12_arp] L375 Figure L.580 [pd chord_34_+12_arp] L376 Figure L.581 [pd chord_35_+12_arp] L376 Figure L.582 [pd chord_36_+12_arp] L377 Figure L.583 [pd p4_chords_33-36_+24_arp] L377 Figure L.584 [pd chord_33_+24_arp] L378
126 Figure L.585 [pd chord_34_+24_arp] L378 Figure L.586 [pd chord_35_+24_arp] L379 Figure L.587 [pd chord_36_+24_arp] L379 Figure L.588 [pd p4_chords_33-36_+36_arp_axes_+48+36+24+12+0] L380 Figure L.589 [pd chord_33_+36_arp] L380 Figure L.590 [pd chord_34_+36_arp] L381 Figure L.591 [pd chord_35_+36_arp] L381 Figure L.592 [pd chord_36_+36_arp] L382 Figure L.593 [pd axes_33_+48_arp] L383 Figure L.594 [pd axes_34_+48_arp] L383 Figure L.595 [pd axes_35_+48_arp] L384 Figure L.596 [pd axes_36_+48_arp] L384 Figure L.597 [pd axes_33_+36_arp] L385 Figure L.598 [pd axes_34_+36_arp] L385 Figure L.599 [pd axes_35_+36_arp] L386 Figure L.600 [pd axes_36_+36_arp] L386 Figure L.601 [pd axes_33_+24_arp] L387 Figure L.602 [pd axes_34_+24_arp] L387 Figure L.603 [pd axes_35_+24_arp] L388 Figure L.604 [pd axes_36_+24_arp] L388 Figure L.605 [pd axes_33_+12_arp] L389 Figure L.606 [pd axes_34_+12_arp] L389 Figure L.607 [pd axes_35_+12_arp] L390 Figure L.608 [pd axes_36_+12_arp] L390 Figure L.609 [pd axes_33_+0_arp] L391 Figure L.610 [pd axes_34_+0_arp] L392 Figure L.611 [pd axes_35_+0_arp] L392 Figure L.612 [pd axes_36_+0_arp] L393 Figure L.613 [pd p4_chords_37-40_+0_arp] L393 Figure L.614 [pd chord_37_+0_arp] L394 Figure L.615 [pd chord_38_+0_arp] L394 Figure L.616 [pd chord_39_+0_arp] L395 Figure L.617 [pd chord_40_+0_arp] L395 Figure L.618 [pd p4_chords_37-40_+12_arp] L396 Figure L.619 [pd chord_37_+12_arp] L396 Figure L.620 [pd chord_38_+12_arp] L397 Figure L.621 [pd chord_39_+12_arp] L397 Figure L.622 [pd chord_40_+12_arp] L398 Figure L.623 [pd p4_chords_37-40_+24_arp] L398 Figure L.624 [pd chord_37_+24_arp] L399 Figure L.625 [pd chord_38_+24_arp] L399 Figure L.626 [pd chord_39_+24_arp] L400 Figure L.627 [pd chord_40_+24_arp] L400 Figure L.628 [pd p4_chords_37-40_+36_arp_axes_+48+36+24+12+0] L401 Figure L.629 [pd chord_37_+36_arp] L401 Figure L.630 [pd chord_38_+36_arp] L402 Figure L.631 [pd chord_39_+36_arp] L402 Figure L.632 [pd chord_40_+36_arp] L403 Figure L.633 [pd axes_37_+48_arp] L404 Figure L.634 [pd axes_38_+48_arp] L404
127 Figure L.635 [pd axes_39_+48_arp] L405 Figure L.636 [pd axes_40_+48_arp] L405 Figure L.637 [pd axes_37_+36_arp] L406 Figure L.638 [pd axes_38_+36_arp] L406 Figure L.639 [pd axes_39_+36_arp] L407 Figure L.640 [pd axes_40_+36_arp] L407 Figure L.641 [pd axes_37_+24_arp] L408 Figure L.642 [pd axes_38_+24_arp] L408 Figure L.643 [pd axes_39_+24_arp] L409 Figure L.644 [pd axes_40_+24_arp] L409 Figure L.645 [pd axes_37_+12_arp] L410 Figure L.646 [pd axes_38_+12_arp] L410 Figure L.647 [pd axes_39_+12_arp] L411 Figure L.648 [pd axes_40_+12_arp] L411 Figure L.649 [pd axes_37_+0_arp] L412 Figure L.650 [pd axes_38_+0_arp] L412 Figure L.651 [pd axes_39_+0_arp] L413 Figure L.652 [pd axes_40_+0_arp] L413 Figure L.653 [pd p4_1-8a] L414 Figure L.654 [pd p4_chords1-4_+48_arp] L415 Figure L.655 [pd chord_1_+48_arp] L415 Figure L.656 [pd transposition_+48_x4] L416 Figure L.657 [pd chord_2_+48_arp] L416 Figure L.658 [pd chord_3_+48_arp] L417 Figure L.659 [pd chord_4_+48_arp] L417 Figure L.660 [pd p4_chords1-4_+60_arp] L418 Figure L.661 [pd chord_1_+60_arp] L418 Figure L.662 [pd transposition_+60_x4] L419 Figure L.663 [pd chord_2_+60_arp] L419 Figure L.664 [pd chord_3_+60_arp] L420 Figure L.665 [pd chord_4_+60_arp] L420 Figure L.666 [pd p4_chords1-4_+72_arp] L421 Figure L.667 [pd chord_1_+72_arp] L421 Figure L.668 [pd transposition_+72_x4] L422 Figure L.669 [pd chord_2_+72_arp] L422 Figure L.670 [pd chord_3_+72_arp] L423 Figure L.671 [pd chord_4_+72_arp] L423 Figure L.672 [pd p4_chords1-4_+84_arp] L424 Figure L.673 [pd chord_1_+84_arp] L424 Figure L.674 [pd transposition_+84_x4] L425 Figure L.675 [pd chord_2_+84_arp] L425 Figure L.676 [pd chord_3_+84_arp] L426 Figure L.677 [pd chord_4_+84_arp] L426 Figure L.678 [pd p4_chords5-8_+96_arp] L427 Figure L.679 [pd chord_5_+96_arp] L427 Figure L.680 [pd transposition_+96_x4] L428 Figure L.681 [pd chord_6_+96_arp] L428 Figure L.682 [pd chord_7_+96_arp] L429 Figure L.683 [pd chord_8_+96_arp] L429 Figure L.684 [pd p4_chords5-8_+108_arp] L430
128 Figure L.685 [pd chord_5_+108_arp] L430 Figure L.686 [pd transposition_+108_x4] L431 Figure L.687 [pd chord_6_+108_arp] L431 Figure L.688 [pd chord_7_+108_arp] L432 Figure L.689 [pd chord_8_+108_arp] L432 Figure L.690 [pd p4_chords5-8_+120_arp] L433 Figure L.691 [pd chord_5_+120_arp] L433 Figure L.692 [pd transposition_+120_x4] L434 Figure L.693 [pd chord_6_+120_arp] L434 Figure L.694 [pd chord_7_+120_arp] L435 Figure L.695 [pd chord_8_+120_arp] L435 Figure L.696 [pd p4_chords5-8_+132_arp] L436 Figure L.697 [pd chord_5_+132_arp] L436 Figure L.698 [pd transposition_+132_x4] L437 Figure L.699 [pd chord_6_+132_arp] L437 Figure L.700 [pd chord_7_+132_arp] L438 Figure L.701 [pd chord_8_+132_arp] L438 Mixout objects: Figure L.702 [pd mixout_0] L439 Figure L.703 [pd mixout_x8_0] L440 Figure L.704 [pd mixout_1] L440 Figure L.705 [pd mixout_x8_1] L441 Figure L.706 [pd mixout_2] L441 Figure L.707 [pd mixout_x8_2] L442 Figure L.708 [pd mixout_3] L442 Figure L.709 [pd mixout_x8_3] L443 Figure L.710 [pd mixout_4] L443 Figure L.711 [pd mixout_x8_4] L444 Figure L.712 [pd mixout_5] L444 Figure L.713 [pd mixout_x8_5] L445 Figure L.714 [pd mixout_6] L445 Figure L.715 [pd mixout_x8_6] L446 Figure L.716 [pd mixout_7] L446 Figure L.717 [pd mixout_x8_7] L447 Figure L.718 [pd mixout_8] L447 Figure L.719 [pd mixout_x8_8] L448
Appendix M: Figure M.1 “Tree” diagram scheme M1
Appendix N: Figure N.1 [pd reverb_sound] object N1 Figure N.2 [pd reverb_sound] N2 Figure N.3 [pd reverb_1] N3 Figure N.4 [pd reverb-echo echo-del_1 5.43216] N4 Figure N.5 [pd reverb-echo echo-del_2 8.45346] N4 Figure N.6 [pd reverb-echo echo-del_3 13.4367] N4 Figure N.7 [pd reverb-echo echo-del_4 21.5463] N5 Figure N.8 [pd reverb-echo echo-del_5 34.3876] N5 Figure N.9 [pd reverb-echo echo-del_6 55.5437] N5
129
Appendix O: Figure O.1 Email Re: Pd conventions O2
Appendix P: Figure P.1 Page l of code for The cat dances and the moon shines brightly P1
Appendix R: Figure R.1 Here… for clarinet, piano and cello R1
130
List of Appendix Tables
Appendix F: TABLE 1 The paradox of Pythagoras patch structure F2
Appendix G: TABLE 2 Pitch of harmonics given in cents G1 TABLE 3 Pitch of sub-harmonics given in cents G5
Appendix I: TABLE 4 The cat dances and the moon shines brightly patch structure I2
Appendix K: TABLE 5 The heavy dark trees line the streets of summer patch structure K2
Appendix M: TABLE 6 The crystals in the cave absorb the light as if they have not seen it in a million years patch structure M2
131
MP3 Recordings
The paradox of Pythagoras movements 1 to 27 (2:28:31)
1. 2 harmonics (0:59)
2. 4 harmonics (1:58)
3. 8 harmonics (3:04)
4. 16 harmonics (4:01)
5. 32 harmonics (4:41)
6. 64 harmonics (5:46)
7. 128 harmonics (7:07)
8. 256 harmonics (7:56)
9. 512 harmonics (7:28)
10. 1,024 harmonics (8:08)
11. 2,048 harmonics (9:12)
12. 4,096 harmonics (10:05)
13. 8,192 harmonics (9:54)
14. 16,384 harmonics (8:20)
15. 32,768 harmonics (8:18)
16. 65,536 harmonics (7:39)
17. 131,072 harmonics (9:31)
18. 262,144 harmonics (8:52)
19. 524,288 harmonics (8:27)
20. 1,048,576 harmonics (9:35)
21. 2,097,152 harmonics (8:39)
22. 4,194,304 harmonics (9:38)
132 23. 8,388,606 harmonics (10:00)
24. 16,777,216 harmonics (9:56)
25. 33,554,432 harmonics (9:50)
26. 67,108,864 harmonics (9:28)
27. 134,217,728 harmonics (9:59)
Music of the spheres , movements 1 to 9 (37:06).
1. Mercury (3:52)
2. Venus (3:56)
3. Earth (3:58)
4. Mars (3:52)
5. Jupiter (3:41)
6. Saturn (4:00)
7. Uranus (4:41)
8. Neptune (4:37)
9. Pluto (4:29)
Music of Grace , movements 1 to 3 (1:08:22).
1. The cat dances and the moon shines brightly (17:10)
2. The heavy dark trees line the streets of summer (20:56)
3. The crystals in the cave absorb the light as if they have not seen it in a million
years (30:16)
Here… (6:04).
1. Here… ‘Charisma’: Ros Dunlop (clarinet), David Miller (piano), Julia Ryder
(cello) (6:04)
133