Physical Model Synthesis in Music Composition

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. Then slightly varying slider positions, thus utiliz- I did a bunch of things with overblowing ing a technique reminiscent of the animation and unrealistic "breath" noise gains into the of a cartoon[12]. algorithms[10]. Juan Reyes Juraj Kojs Wadi Musa (2001) particle interaction, CLM maracas Garden of Dragon (2003) waveguide, corrugated tube Given the South American nature of the The Voice of the dragon is the name instrumentation, performers, sound texture given to a group of Japanese children and style, the model of the maracas was twirling flexible plastic tubes above their chosen as a contrasting synthesized sound... heads. The burst of tones that emerged polyrhythms are the result of combinations, from each musical pipe soared and dropped somewhat chaotic between durations, shake with rotational velocity. A corrugated plas- rate, seed quantity and resonances of the tic tube, in fact, produces pleasant sonorities shell. while rotating in a circular motion. The model of the maracas is a very flex- Singing corrugated tubes became popu- ible algorithm because it can help generate lar in early 70’s when a toy called hummer various timbres ranging from wooden mara- was introduced to the market. The hummer cas or plastic maracas with synthetic parts to is a corrugated plastic tube about one meter tambourines and wind chimes. It can pro- long... When whirled in the air, the tube produce other sounds like the afuche, the sekere, duces a series of pitches, starting from the the cabasa or exotic sounds / performances first harmonic to its overtones. such as throwing a maraca from one hand to This piece presents a communication be- the other. In the model, beans can be ordered tween the virtual and real singing pipes. The in different ways and can be manipulated di- Max/MSP physical model extends the possi- rectly by toggling filter states, probabilities bilities of the real tubes in several areas: vi- of collision, bean size and quantities[13]. brato, pitch and amplitude control, and noise Chris Burns to pitch ratio. The acoustic tubes control the Hero and Leander (2003) waveguide, Pd networks virtual choir of tubes using the fiddle~ pitch tracker of Max/MSP[11]. The sonic character of the feedback network is varied and idiosyncratic. Com- plex, swooping pitch contours with contin- uous micro-alterations of timbre are typical, while the continuously varying delay lengths the brilliant, resonant, exuberant tones of fa- produce shifting, inharmonic pitch relations. miliar instruments and finds what is hidden Depending on the gain settings, punctuating away in their attics and basements. He then noisy explosions may also be frequent. Be- recycles these found remnants into new com- cause the network disregards some of the tra- pounds, rather like splicing genes to create ditional tuning techniques for physical mod- new life-forms[16]. els (especially polarity inversion), it is likely to enter marginal and turbulent states. The Harry Partch system’s behavior is emergent; the output is The Bewitched (1955) musical, articulate, and often surprising. The unpredictable behavior of the desta- Harry Partch experimented with tones bilized feedback network, enhanced by the even lower than those produced by the algorithmic generation of many of its param- Bass Marimba and eventually arrived at the eters, is the primary feature...[14]. present Marimba Eroica. The instrument is fashioned from individually hung Sitka Torsten Belschner Spruce blocks placed over cave like res- SonoMorphis (1998) [interactive image and sound in- onators about the size of a piano. The wave stallation] waveguide, VL-1 length of the lowest bar is more than 50 feet, making the performance space an important As one of the installation’s aesthetic part of the instrument. Ideally, the performer goals is the bodily impression of the gen- should, in Partch’s words, cultivate the as- erated object on the user, a sound synthesis pect of a hero of the Trojan War, and in furi- technique was in demand, that is able to both ous passages, "convey the vision of Ben Hur render a visible object’s genuine sound thru in his chariot, charging around the last curve all its user-inferred alterations in shape and of the final lap"[17]. space in a plausible way, and to be abstract enough where needed to not duplicate a real- 3.1. Manipulated identity world artifact. The technique of choice is Similar quests are found wherein musical sources assume known as physical modeling which derives unreal proportions (Lansky’s flutes), or provide a range the emerging sound from the physical prop- of physical shapes (Schloss’ drums), supplant one instru- erties of an assumed object, i.e. its shape, ment with the body of another or explore hybrids (Burt- material, excitation mode etc. ner’s sax / bowl and sax / strings), or magnify certain ef- Based on associative relationship to the fects by pushing them beyond their usual amounts (Scav- genome’s textures, each acoustic represen- one’s sax overblowing and breath sound). All reference tation has first been assigned a set of mate- the known instrumentarium. Starting from existing iden- rial properties, causing its basic timbre. Sec- tities, they are the result of Frankenstein-luthiers work- ond, the genome’s shape is taken into ac- ing to inflate size, distort shape, hybridize identity, and count, controlling the representations’ ba- amplify particular timbral qualities. Such instrument de- sic modes of vibration and their reaction to signs could be said to result from splicing genes. But parameter-induced deformations. Third, the within a physically plausible space, leaving perceptual single graphic objects’ current spatial posi- schema intact. tions are mapped to the sound space, ren- dering their horizontal movement as well as 3.2. Abstract to concrete perceptual spaces their proximity to the user[15]. Escaping the plausible means disengaging available per- 3. Summary ceptual schema. Some have manipulated their models to provide a wide sounding scale: from abstraction to real- Key concepts in the descriptions above can be distilled in istic image (Tutschku), to describe the border between an comparison to practice outside the domain. abstract and concrete form of sound perception (Born- Helmut Lachenmann hoeft’s strings) and to provoke a communication between ...Zwei Gefühle... Musik mit Leonardo (1992) the virtual and real (Kojs’s singing pipes). Such designs play at edges within a model’s parameter space. Lachenmann does not use electronic In these abstract zones, models are allowed to enter sources, but instead reduces the sounds of marginal and turbulent states where the output is musi- conventional instruments to their most prim- cal, articulate, and often surprising (Burns), achieving itive constituents. He burrows in behind for example, chaotic combinations yielding polyrhythms (Reyes, maracas), or some very interesting and realistic [14] Burns, C. “Emergent Behavior from Idiosyncratic higher-order dynamic(s) (Stilson, engine). The most ab- Feedback Networks,” Proc. of the Int. Conf. on stract are comprised of networks of interacting modules, Computer Music, 2003. the composer’s design exploits sound sources in which the system’s behavior is emergent (Burns) and must be [15] Belschner, T.,SonoMorphis newly learned (though perhaps it retains traces of its [16] Clarkson, A. program notes "Helmut Lachenmann, physical origins). A Voyage to the Edge of Music"

3.3. Uniﬁed paradigm [17] Newband instrumentarium, "The Harry Partch instrument collection" The “think physical” dictum can achieve sound com- plexity with pure synthesis comparable to natural sounds (Tutschku) and derive an emerging sound... from an assumed object (Belschner). It is a way of imagining and designing music derived from experience, but with a path beyond. The most abstract systems are learned by ob- serving their response to stimuli and changing conditions. Prodding such a model is like prodding a new instrument, and the prodding itself (a physical or imagined physical act) can be composed or algorithmically organized. Cadoz extends this single paradigm [to] both sound synthesis and computer-aided composition. Contributors to this paper are many, some wittingly others not. Thanks go to all and especially to those who responded to my email canvassing.

4. References [1] Castagne, N. and Cadoz, C. “10 Criteria for evalu- ating physical modelling schemes for musical cre- ation,” Proc. of the 6th Int. Conference on Digital Audio Effects, 2003.

[2] Eikasia, program notes, trans. by the auth., 2003.

[3] Clark, P., interview with Paul Lansky, 1997

[4] Schloss, A., corres. with the auth., 2003.

[5] Burtner, M.,S-Morphe-S

[6] Burtner, M.,S-Trance-S

[7] Jaffe, D. program notes, 2003.

[8] Stilson, T. corres. with the auth., 2003.

[9] Scavone, G.,Pipe Dream

[10] Scavone, G. corres. with the auth., 2003

[11] Seraﬁn, S. and Kojs, J., "The Voice of the Dragon: a physical model of a rotating corrugated tube," Proc. of the 6th Int. Conf. on Digital Audio Effects, 2003.

[12] Bornhoeft, A. corres. with the auth., 2003.

[13] Reyes, J. Composing for the physical model of the maraca, 2002.