Proceedings of the 2002 Conference on New Instruments for Musical Expression (NIME-02), Dublin, Ireland, May 24-26, 2002
The Limitations of Mapping as a Structural Descriptive in Electronic Instruments
Joel Chadabe Electronic Music Foundation 116 North Lake Avenue Albany, New York 12206
USA
Abstract sound generator, through which a performing Mapping, which describes the way a per- musician can maintain control over the sound former's controls are connected to sound vari- generated by the instrument, has defined the ables, is a useful concept when applied to the mainstream concept of musical instrument for structure of electronic instruments modelled performing musicians even into the electronic after traditional acoustic instruments. But age. mapping is a less useful concept when applied to the structure of complex and interactive in- In an electronic instrument, controllers, sound struments in which algorithms generate control generators, and links are independent structural information. units that can be combined with great structural and functional flexibility. Electronic control-
lers can be based on a wide variety of tech- This paper relates the functioning and benefits nologies -- capacitance-sensitive devices, mer- of different types of electronic instruments to cury switches, stress sensors, video cameras, the structural principles on which they are resistive-ink pads, ultra-sound, radar, and infra- based. Structural models of various instru- red beams, to name a few -- according to what- ments will be discussed and musical examples ever physical gesture is found to be appropriate played. in controlling a particular sound. Electronic sound generators can produce a wide variety of Keywords synthesized, recorded, or recorded-and- mapping fly-by-wire algorithmic network in- transformed sounds. And most important, the teractivity instrument deterministic indetermin- link between controller and sound generator istic can be active, which is to say that the link can be a computer that can generate information, INTRODUCTION run algorithms, or act in any way as an inter- A traditional acoustic musical instrument typi- mediary between a performer's controls and the cally consists of three components: a controller variables of a sound generator. In short, any (to call it by an electronic instrumental term), a physical gesture can be interpreted in any way sound generator, and a link that connects the to control any sound. controller to the sound generator. In a violin, for example, the controller is the strings and Given, then, the flexibility with which gestural bow, the sound generator is the sound box, and controllers can be interpreted by software to the link is the bridge. In general, in an acoustic control sound generators, the questions are: instrument the controller excites resonances in How do we decide what kind of instrument to the sound generator via the link; and that close design? And how do we build that instrument? and tight relationship between controller and The goal of this paper is to describe the differ-
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ent ways an electronic instrument can function, to identify the benefits that different function- At the rightmost extreme, an indeterministic ing affords a performer, and to relate an elec- instrument outputs a substantial amount of un- tronic instrument's functioning to its structure predictable information relative to a per- former's controls. In working with such an in- FUNCTIONING AND BENEFITS strument, a performer shares control of the mu- sic with algorithms as virtual co-performers It is recognized wisdom to state that the goal of such that the instrument generates unpredict- technology is to benefit humans. It follows that able information to which the performer reacts, the design intent of any particular instrument the performer generates control information to should be based on the potential benefits of which the instrument reacts, and the performer that instrument's functioning to a particular and instrument seem to engage in a conversa- group of people with common creative goals. tion. Interaction means 'mutually influential'. Since the instrument is influenced by the per-
former's controls, and the performer is influ- The functioning of any particular electronic enced by the instrument's output, I have called musical instrument can be placed on a taxo- such instruments 'interactive instruments'. nomic line marked by deterministic function- The definition of interactive instrument is es- ing at, let's say, the left, and indeterministic pecially important because interactive instru- functioning at the right. At the leftmost ex- ments, which incidentally can not exist in non- treme of the line, a deterministic instrument is electronic technologies, provide a particular set defined by the complete predictability of its of benefits to a new musical constituency. The output relative to a performer's controls. Be- primary benefits of an interactive instrument cause such an instrument leaves a performer in are, first, that the performer is called upon to precise control of every detail of the output think and act like a creative person with intelli- sound and provides no information beyond that gence, imagination, and musical expressivity, supplied by the performer, such an instrument as against like an executor of someone else's is likely to require skill, talent, and a knowl- composition; and, second, that the level of mu- edge of music, and, consequently, benefit a sical skill required to 'play' the instrument is professional (or aspiring professional) musi- flexible. Interactive instruments embody all of cian more than an unskilled amateur. the nuance, power, and potential of determinis- tic instruments, but the way they function al- As we move along the taxonomic line towards lows for anyone, from the most skilled and the right, instruments contain increasing musically talented performers to the most un- amounts of unpredictable information. In the skilled members of the large public, to partici- functioning of a slightly indeterministic in- pate in a musical process. Since the instrument strument, a relatively small amount of unpre- provides cues for musical actions, thereby ob- dictable information can simulate a performer's viating the need for a musical score, and since talented assistants, automatically supplying the performance device need not require previ- creative details while the macro-music remains ously-learned musical skills, interactive in- completely under the performer's control. De- struments may be especially beneficial to inter- pending upon the amount of unpredictable de- ested amateurs. The concept of an interactive tail and the way it is triggered, such an instru- instrument may, in the near future, define a ment may become a powerful performance en- new way for the public to experience music. hancement for a professional.
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system -- but the more sensitive is the system There is, of course, infinite nuance in instru- because it can change in many different ways. ment design that may cause a particular in- strument to be more useful for professionals Clearly it is better to have a sensitive instru- than for amateurs. But as a general rule, the ment with many variables than a crude instru- most important requirement of an instrument ment with a few variables. Yet it is also clear for a professional performer is that the instru- that within the limits of a normal human body, ment demonstrates for the audience that the no performer can track and manually control a performer is necessary and is in fact controlling large number of independent variables at the the music; and this requirement assumes a same time. The connections between a per- strong degree of determinism at least in certain former's gestures and a large number of sound- aspects of the instrument's behavior. generating variables is, at a certain abstract level, what we mean by 'mapping'. But map-
ping, as the term seems to be generally under- But such requirements of obviousness do not stood, is a concept that applies to certain in- exist when the instrument's behavior need be strumental designs more appropriately than to understood only by its performer, as in the case others. Further, the nature of mapping cannot of an amateur performer-at-home. For the per- be understood without also understanding the former-at-home, the creativity in the instru- nature of power. ment's output can be in itself rewarding. In- deed, creative instruments may be of great in- A hierarchy can be imagined as a stack of terest even to professionals who wish to ex- boxes in which each box contains several plore new musical horizons. As Iannis Xenakis smaller boxes. One big box contains several wrote, "With the aid of electronic computers smaller boxes, each of which contains several the composer becomes a sort of pilot: he smaller boxes, each of which contains several presses the buttons, introduces coordinates, and smaller boxes, etc. The idea of a hierarchy is supervises the controls of a cosmic vessel sail- that larger things contain smaller things. In a ing in the space of sound, across sonic constel- hierarchy of controls, power can be measured lations ... now he can explore them all ... " by the number of controls a control contains. If [Xenakis, 1992, 1963] a performer's control gesture is translated into 100 controls that cause change in 100 vari-
ables, for example, it is more powerful than if TYPES OF STRUCTURE it istranslated into two controls that cause A variable is something that can be changed. If change in two variables. an instrument contains two variables, its output can be changed in only two ways. If it has 100 In theory, hierarchies are simple and determi- variables, its output can be changed in 100 nistic. In the ideal hierarchy, controls pass ways. The fewer the number of variables in a downwards from level to level, each descend- system, the more powerful is each variable: ing level articulating the highest control with changing one of two variables, for example, is greater resolution but without distortion, until changing half of the system. The greater the the controls reach their target variables. In a number of variables in a system, the weaker is deterministic instrument, mapping means the each variable -- changing one of 100 variables, routing of controls through descending levels for example, is changing only 1/100th of the to the variables. The goal, in the context of a
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deterministic musical instrument, is to make as electronic pianos, for example, but the cate- the performer powerful and keep the performer gory also includes complex and original in- in complete control. struments, where a performer, for example, might use a multitude of touchpads or other devices to control the variables of a probabilis- In a network structure, on the other hand, con- tic expression that automatically produce mi- trol is decentralized because, theoretically, all cro-events in the resulting music. of the nodes in a network can generate and re- ceive controls independently. Each connection between any single nodes or subgroups of As deterministic electronic instruments be- nodes can be seen as a single deterministic come more sensitive and contain greater num- structure, and since the controls are generated bers of independent variables, simple control and transmitted through a complexity of differ- hierarchies are likely to become less useful as ent relationships, their total effect is likely to control structures, and fly-by-wire systems that be less predictable than the controls produced include algorithmic controls are likely to be- by a hierarchy. come more normal. In aviation, 'fly-by-wire' describes a system in which a pilot tells a com- puter what the airplane should do and the com- In theory, networks are complex and indeter- puter flies the plane. The advantages of such ministic. The ideal network is creative rather systems include the computer's ability to ex- than obedient and generates unpredictable in- pand simple but powerful instructions into co- formation. Yet each connection need not be ordinated controls for multitudes of variables, equally important in the performance of the to redefine controls in different contexts, and whole. In the design of an interactive instru- to maintain goal-orientation while introducing ment, a performer's control is likely to be enough unpredictability to keep the instrument placed in a more important and visible position interesting. A fly-by-wire system might be than other controls. In such a situation, map- viewed as a series of if-then algorithms, each ping may partially explain the performer's con- algorithm triggered by a performer's action in a trols because one can map the causes-and- particular context and able to react dynamically effects of each connection within a network. in changing arbitrary relationships between But mapping any one line of cause-to-effect controls. does not describe the operation of the instru- ment as a whole. As interactive instruments become more com- mon, they will be realized in a variety of dif- ferent ways. Yet one of the important questions THE LIMITATIONS OF MAPPING will remain: How does the indeterministic Mapping describes the way a control is con- functioning of an interactive instrument derive nected to a variable. But as instruments be- from its structure? Different composers have come more complex to include large amounts answered that question in different ways. In of data, context sensitivity, and music as well Voyager, for example, George Lewis created a as sound-generating capabilities, the concept of 'virtual improvising orchestra' that analyzed a mapping becomes more abstract and does not musician's performance in real time and gener- describe the more complex realities of elec- ated a complex response that contained unpre- tronic instruments. Deterministic instruments dictable information to which the musician include simple and derivative instruments such continued to react. [Lewis, 2000] Robert Rowe
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invented a virtual listener that sensed, ana- between gestural control and sound variable. lyzed, and responded to a player's inputs. The primary benefit for the amateur performer- [Rowe, 1993] Where both Lewis and Rowe at-home, which is that the instrument provides emulated the processes of an independent im- information to which the performer can react, provisor that analyzed and responded to the requires a network structure. To the extent that sound produced by a physical performer, my an automatic mechanism generates informa- own approach has been to share control of the tion, even while remaining obedient to a per- music with a virtual composer. In Solo, for ex- former's commands, it becomes more difficult ample, I used modified theremins to 'conduct' to conceptualize a performer's control gestures tempo and timbre while the notes of the mel- as mapped onto an output. Mapping, in short, ody were generated algorithmically. [Chadabe, is not the best way to conceptualize the struc- 1980] In Many Times ..., a more recent compo- tures of the most important and beneficial sition, a performer's input at any moment types of instruments. shares control of sound-processing algorithms and spatialization with many independent ran- REFERENCES dom number generators. In every case of the interactive instrument, whether based on analy- sis or independent algorithm, controls for the Iannis Xenakis. Formalized Music. Pendragon music and sound variables originate simultane- Press, Stuyvesant, New York. 1992. First pub- ously and asynchronously in different contexts lished in French as Musiques Formelles. Edi- and from different sources; and because the tions Richard-Masse, Paris. 1963. relative importance of each control may vary according to function and in time, the cause- effect relationships within such an instrument, George Lewis, "Too Many Notes: Computers, too complex to be usefully described in terms Complexity and Culture in Voyager" in Leo- of mapping, are most usefully described as a nardo Music Journal. Volume 10, 2000. Pages network. 33-39.
CONCLUSION Robert Rowe. Interactive Music Systems. MIT Press, Cambridge, Massachusetts. 1993. The mapping model, based on the deterministic functioning of traditional acoustic instruments, is limited in describing the most innovative and Joel Chadabe, "Solo: A Specific Example of potentially beneficial approaches in electronic Realtime Performance" in Computer Music – instrument design. The primary benefit of an Report on an International Project. Canadian electronic instrument for a professional per- Commission for UNESCO, Ottawa, 1980. former, which is that it extends the performer's capabilities in interesting, creative, and com- plex ways, requires an intermediary mechanism
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