Page  282 ï~~A System for the Musical Investigation and Expression of Levels of Self-Similarity in an Arbitrary Data Stream David Rossiter Wai-Yin Ng rossiter~ie.cuhk.edu.hk wyng@ie.cuhk.edu.hk Department of Information Engineering Chinese University of Hong Kong Shatin, Hong-Kong Abstract This paper presents a system developed for the analysis and subsequent musical expression of data performance at an arbitrary number of levels of self-similarity within an arbitrary (linear) data sequence. The system employs two software components; the Csound audio generation software and a program to manage the data processing and file handling. System structure and operation is described, with an example based upon analysis of the Dow Jones financial stock market index data. 1 Introduction Over the past decade or two there has been a massive expansion of interest and research in the area of fractals (see, for example, Gleick, 1991). Fractal patterns have been seen in a vast variety of phenomenon. Fractals exhibit self-similarity in which the mathematical properties of the data are similar regardless of the level at which the data is being examined. Today, research continues with investigations into self-similar properties of data ranging from stress patterns of earthquakes at different depths (Beroza, 1995) to World Wide Web traffic (Crovella & Bestavros, 1995). Self-similar properties are similarly evident within pitch and music structures (i.e. Rosenboom, 1992) and have been directly embodied in musical compositions (i.e. see Econ, 1992). Analysis of levels of self-similarity (currently processed via graphical representations) may therefore be suitable for analysis in the sound domain, in which properties of sound and music may be used to reflect levels of self-similarity in patterns of data. In this paper a system is presented that has been developed to enable this form of analytical expression, which is termed sonification. The system can serve both scientists and artists who seek to express data in a musical form. The former may use the system as a tool for enhancing conventional data analysis techniques for investigating self-similarity in data streams, such as fourier analysis and chaotic modeling. The latter may use the system as a compositional tool to express heirarchical patterns of non-musical data in a musical form. 2 Implementation The system is currently implemented under a Unix environment. It employs two programs. One is the public domain Csound audio generation software. The other, called Audiostream, is a program developed for the task of managing the file handling and data processing tasks involved. Both pieces of software are written in the C programming language. This enables maximum ease of portability between different systems. Pre-compiled binaries of the Csound software are also available for most computer platforms. The Csound program currently requires two files for operation. One is the orchestra file in which the technical description of the sound-generating instrument(s) is provided, and the other is the score file, in which wavetables and directions concerning the timing and control of the instrument are given. Prior to operation, the user edits a configuration file with the required sonification parameters. This file is then loaded during the start-up procedure of the Audiostream program. In the file, the user may select a number of pre-designed Csound Rossiter & Ng 282 ICMC Proceedings 1996

Page  283 ï~~instruments for use in the sonification process. Each instrument has an associated score and orchestra file, but any invocation of the Csound software requires only one file of each type. The audiostream software therefore concatenates all the individual score files of the instruments selected into a single file, and pipes the contents to the Csound program. All of the associated orchestration files are also concatenated into a single file, and this is read by the Csound process. In addition to the choice of instruments, the configuration file also states the number of data windows to be analysed and their respective length, in addition to offset values and multipliers for fundamental frequency, duration, and amplitude. Data ranges may be distinct, overlapping or identical. During the main program execution the data stream to be processed is loaded by Audiostream, which performs a running mean evaluation of data windows based on the configuration details. Each data item within the file is processed in sequence. A mean value is determined for the data within each window. Mean data is then converted according to the configuration information and is formatted as appropriate in an ascii sequence for subsequently piping to the Csound software operating in real-time. Musical signals are then generated based upon the series of mean data. The complete process is illustrated in figure 1. 3 Performance issues The system may be effectively used to musically express an incoming stream of data in real-time. or non-real-time. However, this is dependant on the timing of the incoming data and the workload on the underlying hardware. Through the use of the Csound system a range of instruments may be precisely designed with regard to an appropriate balance between real-time performance and processor capability. Instruments may be selected from those already available in the public domain. A configuration of instruments may be selected according to the particular requirements of the user. For example, an analyst seeking to explore patterns of data at different levels may choose instruments of acoustically similar but distinct properties by employing a selection of different instruments from the same orchestral class. An example from the chordophone classification group of in struments is the combination of double bass, guitar, and violin for the expression of a three-part analysis. 4 An illustration In this illustration, data has been taken from the world of finance. Analytical techniques used in this field have expanded over recent years (Solomon, 1996) and a sonified analysis may serve it well. The data used is the end-of-day closing Dow Jones index data over approximately a 6 year period, during which the infamous 'wall street crash' occured (October 19, 1987, when the Dow plunged more than 500 points to a value of 1738). In figure 2 the original index data is shown in addition to the output of three moving average data window analyses of the data at different levels of scale (and with different degrees of offset for the sake of clarity). Data offset values have been applied to each of the three analytical data streams. Parameters of the first analysis are selected to exhibit trends in data across a relatively small time frame, 50 days. The second involves an analysis across a 100 day period; the third across a 400 day period. The vertical axis shown may be mapped uniquely to each instrument. Standard sonification parameters include fundamental frequency, amplitude and output duration. A greater level of expression may be achieved via the appropriate design of new Csound sonification instruments so that any aspect of acoustical information may be exploited. The contrast between the essentially upward trend derived from the longest window and the original data indicates the differing conclusions that may be drawn according to the level at which the data is examined. By adjustment of the configuration parameters, the data may be presented in many alternative forms. For example, by adjusting the time offset and multiplier parameters self-similar levels may be consecutively expressed one after the other. This is illustrated in figure 3. Further treatment could include layering for simultaneous expression by a selection of similar or different instruments, or some form of combination. 5 Conclusions The structure and operation of a system for the acoustical investigation of levels of self-similarity has been presented. As it stands the system may be usefully employed in this context, although it would benefit from a number of enhancements. The ability to concentrate on a small subset of the data and to interactively alter parameters in order to determine the most suitable configuration are primary considerations for future development. ICMC Proceedings 1996 283 Rossiter & Ng

Page  284 ï~~References Beroza, 1995 Beroza, G.C. (1995) Seismic source modeling. Reviews of Geophysics, Vol. 33, supplement Crovella & Bestavros, 1995 Crovella, M.E. & Bestavros, A. (1995) Explaining World Wide Web Traffic Self-Similarity. Boston University, CS Dept. Technical Report TR-95-015 Econ, 1987 (1987) Holding a new mirror to nature. The Economist, 6 November Gleick, 1987 Gleick, J. Chaos - Making a new science. (1987) Abacus: London Rosenboom, 1992 Rosenboom, D. (1992) ASA 124th Meeting: New Orleans, USA Solomon, 1996 Solomon, S.D. (1996) A new market for CSE: An engineer goes to Wall Street. IEEE Computational Science & Engineering. Vol. 3, No. 1. Data window Otipal data Data window C.' Data window 5: Time Figure 2 Three window output streams with original data Figure 3 Three window output streams expressed as conseuctive time sequences (with line of best fit) File system Files associated Files associated Files associated with instrument 1 with instrument 2 with instrument N I. I., I.. m.D I m m.. I..0... * 1l acoe r ScoreÂ~ Score Â~ " Scorecore i = file 1 "+- file 2:+ "fileN Ufile. eiN ". Wave:.. tables"::: -... - I. ' " ' Master, IOrchestral Orchestra Orchestra Orchestra.+ Orchestra:+ file1 ':file2: fl fileN:'........ - 1lSonification instruments * Configuration, file Dt ie Data stream --n[rn-r stream Schoiceof.... -.............. p, Par...t os t-u pSo d MUpdaterdata in moving ui mappings for owindowuramespCround Pc Pipexe- se m escore aetbe fundamencyl;. Determine mean values parameter Generate Â~information feqeny,--- feld' sonification Â~ ampitude Im mForma Csound score Sdirectly to duration and 11o fields' according to configo Unix. coie f.-o..............."' pipeWit1 instwn t.amnplitude, Â~... -.. Â~,duration fr................timbre) Part of start-up procedure Main operation 'Audiostream ' program ' Csound' program Process execution systemt - Rendered sound Audio hardware Figure 1 System structure and operation Rossiter & Ng 284 ICMC Proceedings 1996