Case Studies of Physical Models in Music Composition Chris Chafe Center for Computer Research in Music and Acoustics Stanford University [email protected] Abstract out on current practice and it is hoped that a read-through alongside a “hear-through” of accompanying sound ex- Physical modeling in computer music has been develop- amples will build the picture. Technical descriptions are ing for twenty-five years. An assortment of algorithms, beyond the scope of this paper, but may be found in a often in the form of "self-modeling" by musician / en- number of the references cited. gineers, has accumulated and become available to com- Hans Tutschku posers. These software instruments have become mate- Eikasia (1999) modal, Modalys rial for composition and unveiling the range of designs forms the focus of this report. To a large extent, schemes Eikasia is my first work with physical applied in the works cited are reminiscent of schemes modeling. In all my previous electroacous- which employed "real" instrumental material in 20c con- tic pieces, I used processed recorded sounds. temporary music. We can test for uniqueness in the phys- My research was to reach a sound complex- ical modeling approach and the likelihood that it is grist ity with pure synthesis comparable to natural for "composers to continue to do what composers do" as sounds. new material is added or swapped for old. I began with a palette of sounds mod- eled and organized by means of their phys- 1. Introduction ical representation in the computer. During the realization, I compared them to their real The world of techniques for computer sound generation origins, and from this starting point reached has become vast. For its part, the physical model class of a wide sounding scale: from abstraction to techniques was a foreseeable outcome of physics research realistic image[2]. encountering fast computers. Digital simulation spawned numerical experimentation as a tool in which models Paul Lansky are iterated over time to observe behavior (weather fore- Things She Carried (1996) waveguide, STK Flute casting and studies of jet engine turbulence are illus- Do you spend a lot of time trying to em- trative of this tool’s revolutionary impact on other do- ulate the sound of "real" instruments or is the mains). Castagne lists five physical modeling approaches sound that’s never been heard before usually in music[1]: 1) “traditional” wave equation, 2) mass or the magic ingredient? particle interaction, 3) waveguide, 4) modal, and 5) non- I am interested in being able to emulate linear source / filter “black boxes.” real instruments but mainly in the sense that One dozen brief descriptions representing practice I can get them to assume unreal proportions. with subclasses 2-5 have been collected from composers For example, I’ve been using Perry Cook’s to see if taken together they allude to something new. flute physical model for a few years, but Apologies are given upfront, that more is left out than is my favorite way of using it is to construct a included. In this vast world (with its continually chang- model of a flute which is about 20 feet long ing ecology of techniques), there are many musics, music and has a diameter of 3 feet. It produces makers and potential collections such as this one. Putting great sounds[3]. together these brief snapshots is necessarily limited to what is known and nearby. Claude Cadoz pico.. TERA (2001) mass interaction, GENESIS 2. From the music Recently, Cadoz proposed an innovative I have freely extracted essences from writings and corre- approach to composition based on the mass- spondence on composers’ use of physical models. Each interaction modular scheme. As Cadoz ex- refers to a piece of music. Together they provide a read- plains, one may obtain a succession of sound events rather [th]an isolated sound by as- modeling synthesis the audience can expe- sembling in a complex structure both high rience a real-time performance of a soprano frequency models and low frequency mod- saxophone with the virtual body of a singing els: the high frequency model will gener- bowl[5]. ate the sound, whereas as the low frequency model will be responsible for sound event S-Trance-S (2000) waveguide, bowed string generation. With his experimental piece pico..TERA, Cadoz demonstrated that it is ...the saxophone sound, the bowed string possible to extend dramatically this idea. sound, and the combined metasax/string pico..TERA is made of a single model with physical model sound are transformed into thousands of masses and tens of different a series of hybrid instruments that are per- "objects" (or models) interacting. The 5 min- formed live by the saxophone and transfused utes of music of this piece are then obtained into independent timbral screens... In trance, by executing this model without any external a medium passes under the control of some interaction nor post-treatment. external force. In "S-Trance-S" this takes Such a compositional process presents the form of the saxophone acting as a con- three major advantages. First, since low troller for the string physical model. As if in frequency models are slightly perturbed a dream or hallucination, different morpho- in a natural manner by retroaction from logical forms are generated as the energy of sound models, the sound events gener- the controller is transfused into the medium. ated do present convincing short-term evo- These hybrid forms then act as the ghost- lutions, expressiveness and musicality, such like extension of their archetypes, exploring as changes in a rhythm or in the timbre of states of metamorphoses[6]. successive musical events – somehow as a musician would do. Second, the process David Jaffe proves that physical modeling makes it pos- Racing Against Time (2003) SoundMAX, SynthCore sible to meld within a single paradigm both sound synthesis and computer-aided com- One innovation in “Racing Against position. Third, the compositional process Time” is the use of the Radio Drum to is deeply transformed: the "think physical" control physical models of automobiles, jet dictum... may be extended to the composi- planes and “weird strings.” The automobile tional scale.[1]. model... consists of a nonlinear dynamics model of engine spark plug firing, with the Andrew Schloss timing of a V8 engine. These impulses are Can You Hear the Shape of a Drum? (2004) modal, then filtered and modified by non-linear pro- drums cesses to simulate the exhaust system of a race car. The surface of the Radio Drum In 1966, esteemed mathematician Marc controls the throttle of the engine, while the Kac wrote an article called Can You Hear height above the surface controls the engine the Shape of A Drum? The article was load. The mapping of the throttle is in three a serious mathematical treatment of differ- overlapping horizontal strips so that it is easy ent boundary conditions of a vibrating mem- to simulate up and down-shifting. Other con- brane; the mathematics are extremely com- trols available to the performer include the plex but the idea can be thought of in sim- amount of engine “damage” (misfiring, etc.) ple physical terms: Does a shaman’s square- and the characteristics of the muffler[7]. shaped frame drum sound different from a (Tim Stilson, on the model itself) round one? I first encountered that article 30 What was always most interesting to years ago, and now I am finally able to act me... ...was that by playing with the dy- on it in my own artistic work [4]. namics of the filters in the [engine model’s] feedback, one could get some very interest- Matthew Burtner ing and realistic higher-order dynamic spark S-Morphe-S (2002) waveguide, singing bowl timings, which sounded like various one- cylinder 2-cycle engines I had heard while The acoustics of a soprano saxophone growing up (always sounding like they were and a singing bowl are molded into a sin- about to die), or like a Harley-Davidson en- gle instrument. Through the use of physical gine (i.e. various fun subharmonics of the main rpm, or even nicely chaotic timings, Achim Bornhoeft etc.)[8]. Virtual String (1997) waveguide lattice, stretched string Gary Scavone Pipe Dream (2003) waveguide, STK saxofony With it’s acoustic manifestations of non- existing objects "virtual string" musically describes the border between an abstract and Pipe Dream is... exploring subtle wind concrete form of sound perception. The soft- instrument overblowing effects. In this ware used for this piece ("vstring") offers a work, all sounds are generated using real- graphical interface to a physical model of a time computer-based saxophone-like physi- string. Although this was never intended to cal modeling algorithms implemented with be a compositional tool, the very intuitive the Synthesis ToolKit in C++. The algo- approach to the different parameters of the rithms are performed with a new MIDI wind model was my inspiration to make a piece controller called The Pipe. The controller with it. In vstring, several software sliders makes use of a variety of sensors, includ- control the string tension, stiffness or damp- ing buttons, potentiometers, and accelerom- ing, the type and position of the string’s ex- eters which respond to breath pressure, fin- citation and the frequency response and po- ger pressure and tilt[9]. I basically took sition of the virtual pickup placed upon it. 4 saxofony algorithms and assigned them As only one static configuration could be to separate channels for a quad setup. ...I saved in an audio file, every transition had to also mixed in 2 more saxofonies which were be accomplished with many successive and equally panned across all 4 channels.