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\begin{document}
\sf
\paragraph{}
\paragraph{}
\begin{center}
{\Huge {\bf Musical Concept} \\[1mm]}
{\LARGE {\bf and} \\[1mm]}
{\Huge {\bf System Design} \\[1mm]}
{\LARGE {\bf of} \\[1mm]}
{\Huge {\bf ``Chaotic Grains''} \\[25mm]}
{\Large {\bf Yoichi Nagashima }}
{\Large {\sf Art \& Science Laboratory} \\[8mm]}
{\large {\bf Hamamatsu, Shizuoka 430, Japan}}
\end{center}
\paragraph{}
\paragraph{}
\paragraph{ABSTRACT}
\paragraph{}
{\bf
Musical automata and automatic composition are interesting themes in
computer music.
This report is about one approach called ``PEGASUS Project'', to research
musical environment for composition or perfomance, and about
experimental composing one piece.

The piece ``Chaotic Grains'' is composed in 1992-1993, and performed
Feb. 11th in Tokyo (Jujiya Hall).
One special software is produced with the concept of ''Chaos'' in this
composition, and some special hardware is produced/arranged for the piece.

All parameters are controlled individually by conductor or sequence
data in real time, and the results of the generation of chaos are different
from each other in every performances.
The characters of ``Chaos'' are changing and metamorphosing every time
in this piece, thus there is one kind of ``real-time composing''.
}
\newpage

\section{Background}

\subsection{Computer Music}
There are many field to research in ``Computer Music''.
For example, ``musical automata'' and ``automatic composition'' are
interesting themes for composers.
Many theories and models are discussed, many systems and softwares are
researched or developed by many researchers and composers in the
world \cite{degazio} \cite{beyls}.

Today, software engineering and computer technology are growing powerful,
so we have good environment for computing musical information
in real time, and the concept of ``real-time composing'' can be used
easily in compact system \cite{chadabe}.

\subsection{PEGASUS Project}
The research called PEGASUS Project (Performing Environment of
Granulation, Automata, Succession, and Unified-Synchronism) has
produced one compact system of real-time Granular Synthesis
\cite{nagasm1} \cite{nagasm2}, and the second step of this project
is aimed at ``automata and unified-synchronism''.

This project aims at not only producing any systems or the softwares,
but also trying experimental composition for application with the
concept in every developing steps.

This paper presents the ``MAKING'' of the piece called ``Chaotic Grains'',
which is composed in 1992-1993, and performed Feb. 11th
in Tokyo (``DENGAKU'' at Jujiya Hall) \footnote{Pianist : Ayano Fujiwara, 
Conductor : Yoichi Nagashima.}.
This piece is one result of the PEGASUS Project at current level,
and one special software is produced with the concept of ''Chaos''.

\subsection{Chaos in Music}

\subsubsection{Logistic Function}
There are many reports of ``Chaos'' applications for wide fields.
Chaos is easily generated with simple equation :
{\boldmath \[ X_{n} = \mu \cdot X_{n-1} \cdot (1 - X_{n-1}) \] }
and this equation is called ``Logistic Function''.

With the area {\boldmath \( 1 < \mu \leq 3 \)}, the value of
{\boldmath \( X_{n} \)} is only one, but with increasing in the area
{\boldmath \( 3 < \mu \)}, the value of {\boldmath \( X_{n} \)}
is separated into two, four, eight, ... and is going into ``chaos''
zone \cite{devaney}.

In this area, some kind of randomness is generated, but there is
special different from other ``noisy'' randomness.
The parameter {\boldmath \( \mu \)} is very important to control
the random character, and it is possible to control the ``chaos''
with the selecting the value of {\boldmath \( \mu \)}.

\subsubsection{CIM}
It is very interesting that the result state of chaos cannot be
determined in spite of its deterministic definition.
With experiment of chaos simulation, there is more interesting
character as if ``it lives''.
There are many points with finite values of {\boldmath \( X_{n} \)}
in ``chaos zone'' of {\boldmath \( \mu \)} (normally with infinite
values), and called ``Windows''.

The interesting interaction is occured on the edge of this Window.
The finite chaos vibration falls into perfect random state with
wide shift of the value of {\boldmath \( \mu \)}, but if the value
is slight shifted, the chaos vibration may be pushed back in some case.
This reaction is very critical and nervous, but interesting.

I called this ``Chaotic Interaction Model (CIM)'', and using this value
range (interaction range) of {\boldmath \( \mu \)},
the CIM simulator is produced and experimented \cite{nagasm3}.

This edge area of chaos is considered for somewhat ``intelligent
system'' application \cite{aihara} \cite{isabelle} \cite{pecora},
and chaos system may be useful for composition \cite{bidlack}.

\section{Musical Concept}

\subsection{Scale and Tonality}
The notes in ``Chaotic Grains'' are selected by some scales with 12--equal
temperament.
``Chaos Generator'' software generates MIDI note messages,
and these notes are easily generated by MIDI synthesizer modules.

There are three scenes, and each scene has each tonality with scales : 
Diatonic, Whole Tone, and Pentatonic \footnote{See [Appendix] Score Notes.}.

\subsection{Chaos Event}
With ``Chaos Generator'' software, many chaotic MIDI events are generated.
In this piece, all chaotic notes are selected as ``Percussive Sound'',
because this software manages only the ``rising edge event'' of notes.
This simplification is no problem in this piece, and the contrast
between chaotic notes and back-grounded notes is emphasized.

``Chaos Generator'' ganerates each MIDI note event with short duration,
and every synthesizers are tuned up for frequently sound generation.

The main theme of this piece is ``metamorphosing chaotic character''.
With changing the chaotic parameters, each scales/renges/tonalities are
changed with the ``scene''.
And there is somewhat ``musical conversation'' of chaotic notes, synthesizer
sounds, granulation sound, and acoustic piano sound.

\subsection{Pianist}
Pianist part is independent with electronic systems.
Pianist generates ``natural'' acoustic sounds as an antithesis of
digital/electronic/synthesized sounds.

Pianist plays some cluster notes and the reaction of chaotic notes
with improvisation.
Only some rules are defined for selecting enabled scales, and pianist
may play every White Keys in ``Diatonic Scene'', may play every
Black Keys in ``Pentatnic Scene'', must play only 6 notes in
``Whole Tone Scene''.

\subsection{Performer/Conductor}
Besides the pianist, there is another performer on stage.
He/she conducts some cues, and performs real-time granulation
synthesizers.
In some scene he/she performs to send triggers for chaotic parts.

Almost part of ``Chaotic Grains'' are played with pre-recorded
MIDI sequences, but sometimes the sequencer stops for waiting
the conductor at some point, thus the duration of this piece
is not fixed exactly.

\section{System}

\subsection{Software}

\subsubsection{Chaos Generator}
As the part of this composition, one original software is produced.
The software, called ``Chaos Generator'' is programmed with C language,
compiled by MS-C (ver5.1), and runs on MS-DOS (NEC PC9801NS/T).

System clock cycle is about 16msec with VSYNC interrupt, and there are
8 channel parallel-running musical tasks and MIDI/Mouse/Console tasks.

Each channel contains : Channel, Volume, Panpot, Program, Timing, Duration,
Down, Note Ranges, Note Filters, and ``Myu'' parameters.
Parameters of ``Channel, Volume, Panpot, Program'' mean MIDI messages.
``Timing'' is the interval between MIDI trigger and starting point of
generating chaos.
``Duration'' is the interval between each chaotic events.
``Down'' is the rate of decreasing velocity, and chaotic events continue
eternally with this value ZERO.
``Note Ranges'' are highest and lowest edge of enabled note number
in generating chaotic note events.
``Note Filters'' are enabled 12-tones probability in generating chaotic
note events, and these parameters can be controlled for any tonalities
in real time.
``Myu parameters'' are the Logistic function parameter
{\boldmath \( \mu \)}, and the value is represented with 6 mantissa data.

Except only MIDI channel, all parameters can be controlled in real time,
not only with mouse/console but also MIDI special messages.
For example, the ``Note filters'' parameters are frequently changed
with sequenced MIDI data, so selected chaotic note events are
changed little by little.

The sample of this software will be uploaded into Data Library of
AI Forum in Nifty-Serve as ``Freeware''.

\subsubsection{System Control}
Performing control parameters are all included as special MIDI messages.
I defined MIDI 16 channel only for ``Control Channel'' in this piece,
and all control parameters are specially/irregularly/systematically
defined.

For example, Joy-Stick X-axis value is sent with [DF 00]--[DF 7F], and
Y-axis value is sent with [CF 00]--[CF 7F].
For real-time granular synthesizer, ``grain compression'' parameter is
sent with [AF 19 00]--[AF 19 1F], and ``average density'' parameter is
sent with [AF 1A 00]--[AF 1A 7F].
For Bar Counter machine, current bar number is sent with [AF 5F nn].

The start/stop command and MIDI external clocks are generated by the
Chaos Generator, and another simple sequencer is controlled by it as the
``slave'' machine.

\subsection{Hardware}

\subsubsection{Synthesizers}
Because of the policy for ``Simple and Compact System'', there is only one
8U--Rack on stage.
Normal Synthesizers are two [K4r] modules (2U + 2U), but they are arranged
for containing original synthesizers.
Other materials in this rack are 8 channel stereo mixer [MX8SR] (2U),
double half-rack Effectors [SE50][EMP100] (1U), and original MIDI
message display (1U).

[K4r] is set for ``mutli mode'', and all sounds are not specially
synthesized.
Because there are many good sound as default, only ``factory'' sounds are
used.
Specially synthesized sound of [K4r] is not important in this piece.

\subsubsection{Granular Synthesizer}
Original two granular synthesizers are built into one [K4r] \footnote{
The detail of this system is already reported \cite{nagasm1}.}.

In this piece, two control mode are both used : one is direct MIDI
controlled parameter from sequencer, the other is Joy-Stick assigned
parameter control.
This assigned parameters are real-time changed, so ``X = pitch, Y = panpot''
is set in some scene, and ``X = volume, Y = density'' can be set in other
scene.

\subsubsection{Sinusoid Synthesizer}
Original two sinusoid synthesizers are built into another [K4r].
These synthesizers can generate some strange and interesting sounds
only by sinusoid waveshapes.

Using PCM sampling and wave-table looping technique, each wave data
are not read out constant rate.
Thus, the sound does not have constant pitch or constant timble.
These sounds are used only as ``spice'' in the piece.

\subsubsection{Joy-Stick Controller}
Original Joy-Stick Controller is already produced \cite{nagasm2},
and re-arranged for this piece.

There are three modules in it : Joy-Stick (X-axis and Y-axis) sensor
and A/D conversion, MIDI stream input buffering, and MIDI output merger
of input data and Joy-Stick data.

\subsubsection{Monitor Display}
Original two Monitor Display for performance are produced.
One is 7-segment LED display box on the piano for pianist, the other
is LCD Panel with EL back-light display box for conductor.

These monitors display ``measure number'', because this piece is
very long, and it is important to follow ``where is this?''.
The measure information is sent as special MIDI message from sequencer,
and performers can easily detect the point.

\section{Composition}

\subsection{Part and Scene}
There are 12 parts for synthesizers, and 6 parts are double-defined
for ``sequenced'' and ``chaotic generated''.
Each part is assigned to MIDI channels with sequencer.
All data are set as input by console, not by MIDI real-time recording.

\subsection{Timbre and Sound}
Timbles for chaotic part are selected as ``instrumental sound'',
and back-grounded sounds are selected as ``artificial sound'',
because I hoped the audience to listen to the scales and notes.

\subsection{Rehearsal}
Some rehearsals of pianist and composer (another performer) was held.
At first, free discussion of images for this piece and common
definition for perfornmance was approached.

After pianist's experiment/training, studio rehearsal was held only once.
The computer/synthesizer part was tape-recorded with uncontrollable
style as KARAOKE, so the main theme was ``how to feel and play the piano''.

At final rehearsal in the hall, both performers and computer systems
had their first ensemble.

\section{Discussion and Conclusion}
I have discussions with some audiences about the performance.
Unfortunately most of them told me that they could not distinguish
chaotic (real-time composed) notes from sequenced (pre-recorded) notes.

There are some reasons and problems, my low-level composition
of couese, but I think it is important to synchronize visual information
with music.
For example, graphical media diaplaying chaotic generation will
give some impact or message to audience, and it may be easily
understood the structure of the music.
This theme will be researched.

This is start of the second step of PEGASUS project, and next target is
CIM application for real-time compositional system and
next experimental composition.

Next chance for presentation and demonstration or performance is
scheduled at IAKTA Workshop in Osaka, September 16th 1993.

\begin{thebibliography}{99}
{\footnotesize
{\bf
\bibitem{degazio} B.Degazio : 
Musical Aspects of Fractal Geometry.
Proceedings of International Computer Music Conference, pp.435--442, 1986.
\bibitem{beyls} P.Beyls : 
The Musical Universe of Cellular Automata.
Proceedings of International Computer Music Conference, pp.34--41, 1989.
\bibitem{chadabe} L.Chadabe : 
Interactive Composing.
Proceedings of International Computer Music Conference, pp.298--306, 1983.
\bibitem{nagasm1} Y.Nagashima : 
Neural Network Control for Real Time Granular Synthesis.
Proceedings of 6th Annual Conference of JSAI, vol.1, pp.381--384, 1992.
\bibitem{nagasm2} Y.Nagashima : 
Real-time Control System for ``Psuedo Granulation''.
Proceedings of International Computer Music Conference, pp404--405, 1992.
\bibitem{devaney} Robert L.Devany : 
An Introduction to Chaotic Dynamical Systems (Second Edition).
Addinson-Wesley Publishing Company, 1989.
\bibitem{nagasm3} Y.Nagashima : 
Chaotic Interaction Model for Hierarchical Structure in Music.
Proceedings of 46th Annual Conference of IPSJ, vol.2, pp.319--320, 1993.
\bibitem{aihara} K.Aihara, T Yoshikawa : 
Ordered and Chaotic Systems and Information Processing.
Journal of JSAI, vol.8, no.2, pp.179--183, 1993.
\bibitem{isabelle} S.Isabella, A.Oppenheim, G.Wornell : 
Effects of Convolution on Chaotic Signals.
Proceedings of 1992 IEEE ICASSP, vol.4, pp.133--136, 1992.
\bibitem{pecora} L.Pecora, T.Carroll : 
Effects of Convolution on Chaotic Signals.
Proceedings of 1992 IEEE ICASSP, vol.4, pp.137--140, 1992.
\bibitem{bidlack} R.Bidlack : 
Chaotic Systems as Simple (bit Complex) Compositional Algorithms.
Computer Music Journal, vol.16, no.3, pp.33--47, 1993.
}
}
\end{thebibliography}

\section*{Appendix (from the Score)}
\paragraph{}

\begin{screen}
\begin{flushleft}
{\LARGE {\bf 　Chaotic Grains}}
\end{flushleft}
\begin{center}
{\Large {\sf Computer Music for Piano and Live Electronics}}
\end{center}
\begin{center}
{\bf 　　　　　　　　　　　　　　　　　　　　　　　　　　　　by Yoichi Nagashima \\}
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1993
\end{center}
\end{screen}

\subsubsection*{Performers}
{\small
``Chaotic Grains'' is played by two members : the pianist, and the
conductor who is also the player of live electronics.
Conductor may operate the computer system with only start command.
}

\subsubsection*{Pianist}
{\small
Pianist plays the piano with the score, and the piano sound may be
amplified with necessity.

In this piece, the pianist has much freedom of playing/selecting
phrases with improvisation, because this piece is composed with
some kind of random (chaos) under the concept of {\bf real-time
Composing}.

There are some rules for selecting notes in the score, so the pianist
must not play the prohibited notes.
The rules are changing with the score, and some part is written by
confused scales in order to metamorphose the scene.
}

\subsubsection*{Conductor}
{\small
Conductor stands at the opposite side from the pianist on the stage,
and plays ``joy-stick controller'' with conducting.
The computer system may be placed beside the conductor, and the
screen of computer display is watched for detecting the sign of
the sequence.

Conductor sends some cue to the pianist, sends the start signal
for the next scene to the computer, and plays some phrases
with the cue of Chaos Generator.
}

\subsubsection*{Media}
{\small
``Chaotic Grains'' is played with four types of sounds : acoustic piano,
granular synthesis, chaotic-controlled synthesizers, and sequence-controlled
synthesizers.
The piano part is already described.
}

\subsubsection*{System Block Diagram}
{\small
There are two notebook computer, three intelligent MIDI interface box,
two synthesizer modules including built-in some special synthesizers,
and joy-stick controller for conducting the system.

All audio outputs of synthesizers are connected to the stereo mixer, and
the final stereo output is sent to the P.A. system.
Some effectors may be connected with the mixer.

See the System Block Diagram below :
}

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\subsubsection*{Computer and Software}
{\small
One notebook computer is NEC PC9801N with intelligent MIDI interface.
The software is simple MIDI sequencer [Micro Musician 2] of MS-DOS,
containing 16 tracks, using external MIDI clock, and software THRU.
The file size of ``Chaotic Grains'' data is about 110Kbytes.

Another notebook computer is NEC PC9801NS/T with specialized
intelligent MIDI interface.
The ``Chaos Generator'' software is originally produced by the composer,
and this software is one part of this piece.
There are 8 parallel running musical tasks, each managing independent
chaotic operation.
With conductor control, this software also manages the MIDI system
clock and real-time messages, and send cues to many musical processes.
The detail of this software will be presented in some conferences : ISPJ
1993 spring, JMACS, etc.
}

\subsubsection*{Synthesizers and Joy-Stick Controller}
{\small
For producing chaos-generated and back-grounded sound, two Kawai
[K4r] modules are used.
Both synthesizers are set multi-timbre mode, and used as individual 4
channel MIDI sound modules.

Original two granular synthesizer modules are built into one K4r.
The parameters of granular synthesis are real-time controlled by
specialized MIDI commands : width of grain, average density of grains,
shape of grain, compress/expand modulation of grain, panpot, volume,
joy-stick control, etc.

Original two sinusoid synthesizer modules are built into another K4r.
The parameters of synthesis are real-time controlled by specialized
MIDI commands : looping points, pitch, panpot, volume, etc.

The Joy-Stick Controller is produced arranging the intelligent MIDI
interface applied with A/D converter.
This machine ganerates 2-D(X-axis,Y-axis) continuous control parameters
with specialized MIDI commands.
Conductor can send the control parameter for granular synthesis, and
can send cue to the system software with moving the stick.

The piano sound and the performance of pianist is somewhat Antithesis
of Live Electronics.
Thus, pianist may play with free feeling and may fight a battle against
the synthesized sounds or pre-recorded musical sequences.
}

\subsubsection*{Score}
{\small
The score of ``Chaotic Grains'' consists of 12 parts : conductor(1),
piano(2), MIDI/chaos synthesizers(7), granular synthesizers(1),
and sinusoid synthesizers(1).

``Beat'' and ``Tempo'' is not important in this piece, but
to adjust each part and to make somewhat ensemble, this score is written
with [12/2] beat notation with tempo [150].
This means about ``1 bar = 10 seconds'', and total duration of this
piece will be about 15 minutes (total 90 bars), but conductor can expand
the duration with delaying the cue of the next scene.
}

\subsubsection*{Scene}
{\small
There are three main blocks in this piece with each scale : Diatonic,
Whole tone, and Pentatonic, called ``scene''.
All sounds/notes are selected with these scales, so pianist must not
play inhibitive notes, but may play freely within the scale.

The Diatonic scene is constructed by C, D, E, F, G, A, B notes, thus
pianist can play {\bf everything} with white keys.
The Whole tone scene is constructed by C, D, E, F\#, G\#, A\# notes.
Pianist must be nervous to select these notes, but this feeling is
important in the scene.
The Pentatonic scene is constructed by C\#, D\#, F\#, G\#, A\# notes,
thus pianist can play {\bf everything} with black keys.
}

\subsubsection*{Performance}
{\small
For the pianist, there are only three points to fix the attention on
the conductor for adjusting the Tutti timing.
Then, pianist can listen to the whole sounds with relaxed feeling
in other everywhere.

It is important for pianist to imporvise every phrases triggered
with other parts.
Because other electronic parts are not played just same style prcisely,
and this random character is one of the concept of this piece.
Pianist must not play the piano part score of ``Chaotic Grains''
 : these notation means not ``to be played this note'', but ``to be
played {\bf like this}''.

Nevertheless the score shows one note, pianist may play chords.
Nevertheless the score shows low range notes, pianist may play highest
notes.
Nevertheless the score shows long duration notes, pianist may play
very short notes when the musical feeling is commanded.
}

\end{document}