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FORMAL SEMANTICS for MUSIC NOTATION CONTROL FLOW As an Example, Particle Behaviours Might Include: Distributed Behavioral Model,” in ACM 1

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FORMAL SEMANTICS for MUSIC NOTATION CONTROL FLOW As an Example, Particle Behaviours Might Include: Distributed Behavioral Model,” in ACM 1 order, to affect the trajectories of the emitted particles. [8] C. W. Reynolds, “Flocks, herds and schools: A FORMAL SEMANTICS FOR MUSIC NOTATION CONTROL FLOW As an example, particle behaviours might include: distributed behavioral model,” in ACM 1. Bounded spaces and edge effects (e.g. SIGGRAPH Computer Graphics, 1987, vol. 21, ‘bouncing’ trajectories) pp. 25–34. Zeyu Jin Roger Dannenberg 2. Interparticle attraction or repulsion [9] T. Blackwell and M. Young, “Self-organised Carnegie Mellon University Carnegie Mellon University 3. Randomized motion (e.g. drunken walks) music,” Organised Sound, vol. 9, no. 2, pp. 123– 4. Dynamical non-linear systems (e.g. Lorenz 136, 2004. School of Music, Pittsburgh, PA Computer Science Department, Pittsburgh, PA attractors, cellular automata) [10] Wilson, Scott, “Spatial Swarm Granulation.” [email protected] [email protected] 5. Flocking systems (boids, swarms) [Online]. Available: 6. Vortex and other ‘wind’ motions (may not be so http://eprints.bham.ac.uk/237/1/cr1690.pdf. effective in audio) [Accessed: 07-Feb-2013]. ABSTRACT Two other developments that would reap artistic [11] D. Smalley, “Spectromorphology: explaining benefits: sound-shapes,” Organised sound, vol. 2, no. 2, pp. Music notation includes a specification of control flow, 1. A non-linear method for creating grains instead 107–126, 1997. which governs the order in which the score is read us- of the current fixed ‘hop-size with variance’. [12] V. Pulkki, “Virtual sound source positioning using ing constructs such as repeats and endings. Music theory We imagine some kind of ‘swarm’ or ‘burst’ vector base amplitude panning,” Journal of the provides only an informal description of control flow no- algorithm could be applied to the creation times Audio Engineering Society, vol. 45, no. 6, 1997. tation and its interpretation, but interactive music systems of grains to further simulate environmental need unambiguous models of the relationships between effects the static score and its performance. A framework is in- 2. Quantization of the readhead to the nearest troduced to describe music control flow semantics using attack transient to avoid the traditional theories of formal languages and compilers. A formaliza- Figure 1: Control flow definition in Read’s book ‘smoothness’ of granular envelope attack portions in most granular synthesis algorithms tion of control flow answers several critical questions: Are Finally, we intend to implement a multi-voice version the control flow indications in a score valid? What do the a gap between often simplified theoretical ideals and ac- that will manage multiple soundfiles/buffers control flow indications mean? What is the mapping from tual practice, especially in modern works. In practice, we simultaneously, each buffer being fed to an performance location to static score location? Conven- find nested repeats, exceptions and special cases indicated independently moving emitter. This would allow for a tional notation is extended to handle practical problems, truly ‘symphonic’ approach to spatialized, trajectorial and an implementation, Live Score Display, is offered as by textual annotations, multiple endings, and symbols for granular synthesis. Such an approach would have strong a component for interactive music display. rearrangement. implications for a macrostructural use of spin/drift, by We encountered this gap between theory and practice in the implementation of music notation display software. taking into account the tensional and teleological aspects 1. INTRODUCTION of varying spatial motions, energies and articulations. We needed a formal (computable) way to relate notation Music notation has been evolving for centuries, creating to its performance, and we found conventional notions too The spindrift~ object and sample Max/MSP patch will a symbolic system to convey music information. Early limiting to express what we found in actual printed scores. be available for download from http://michaelnorris.info music notation contained only lines and notes, which are To address this problem, we developed new theoretical in late 2013. sufficient for communicating pitches and durations. It was foundations based upon models of formal language and later that bar lines and time signatures emerged, grouping compilation, and we applied these developments to the 8. REFERENCES music into measures and introducing the idea of beats.1 implementation of a flexible music display system. The notation for music control flow, like repeats and co- Music control flow is the reading order of measures [1] W. T. Reeves, “Particle systems—a technique for das, came even later. Control flow helps to identify repeat- affected by control symbols including the time signature, modeling a class of fuzzy objects,” in ACM ing structures of music and eliminates duplication in the measures, repeats, endings, etc. It can also be viewed for- SIGGRAPH Computer Graphics, 1983, vol. 17, printed score. In the Classical period, control flow nota- mally as a function f that maps the performed beat k to a pp. 359–375. tion is closely tied to music forms such as binary, ternary location of a score, <m,b>, a measure and beat pair. f (k) [2] D. Gabor, “Acoustical quanta and the theory of and sonata and is more of a musical architecture than a describes the reading order of the score. In principle, we hearing,” Nature, vol. 159, no. 4044, pp. 591–594, means of saving space.2 Conventional practice for control can rewrite the score in the order f (1), f (2), . to cre- 1947. flow notation is well established. The literature [6, 15] has ate an equivalent score with no control flow (other than [3] I. Xenakis, Formalized Music [Teils., engl.]: reading sequentially). We call this the “flattened score” thought and mathematics in composition. Indiana formalized the notation in all kinds of ways and there is or “performance score.” Audio recordings and MIDI se- University Press, 1971. little conflict among definitions. However, traditional mu- quences are both in the order of the flattened representa- [4] C. Roads, Microsound. MIT press, 2004. sic theory has not explored the possibilities of expanded tion of the corresponding score. [5] T. Wishart, Audible design: a plain and easy or enriched representations for control flow, and there is Existing music theory devotes little attention to con- introduction to practical sound composition. 1 Far beyond formalizing the notion of beats, music notation led to trol flow, and in fact, there does not seem to be even a Orpheus the Pantomime, 1994. the “discovery” of time as an independent dimension that did not de- [6] D. Kim-Boyle, “Sound Spatialization with Particle pend upon physical actions. In particular the musical rest is the first standard term for the concept of control flow. To define Systems,” in Proceedings of the 8th International direct representation of “nothingness” existing over time, or of time it- the meaning of control flow symbols, the conventional Conference on Digital Audio Effects (DAFX-05), self. Composers developed this concept centuries before the scientific practice is to use words and visuals to illustrate the read- 2005, pp. 65–8. revolution, Kepler, Newton, graphs with a time axes, etc. [3] ing order. For example, Read uses arrows to mark the true 2For example, “In practically all the sonatas of the earlier period the [7] D. Kim-Boyle, “Spectral and Granular exposition is repeated, as is indicated by the repeat-sign at its end, which reading order (see Figure 1) [15]. This approach defines Spatialization with Boids,” in SEAMUS National is also helpful for the reader in finding the end of the exposition ...” [2] both the syntax and meaning. Conference, Ames, Iowa, 2007. 308 | 2013 ICMC idea | SHORT PAPERS 309 | 2013 ICMC idea | SHORT PAPERS However, the visual definition is incomplete; there are cases where we are not sure which production to use. One such case is nested repeats where there are two ways of grouping the right repeat with the left repeat. In common practice music, we often restrict the number of levels of repeats to be 1, which excludes the nested repeat prob- lem. In more modern and flexible music practice, there are nested structures, text annotations [8] and repetitions conditioned on actual time [17]. There lacks an unam- Figure 4: Symbolizing the score: this score is converted biguous way to formalize the syntax and the meaning of to the following list of strings to represent control flow: such notation. While nested repeats are relatively simple (block, 0, 4) Fine : (block, 4, 4) : : (block, 8, 4) [ to formalize, we argue that the general problem of formal- (block, 12, 4) ] : [ (block, 16, 4) ] DC.Fine izing control flow is non-obvious, interesting, and useful. In this paper, we present a new framework for formal- izing control flow notation based on formal grammar and 5. MODEL FOR EXTENDED MUSIC PRACTICE compilation. One core feature of this framework is that it can be easily designed by humans and applied automati- The framework for defining music notation control flow cally by computer. As an example, we show a formal def- takes three steps: First, abstract the score into symbols; inition of control flow notation that unifies conventional next, define the syntax for a well-formed score based on music notation and some of the most frequent notations Figure 2: Control flow notation and the corresponding formal grammars; finally, define the meaning of each gram- used in modern music practice. We evaluate the ambiguity reading order in common music practice Figure 3: Control flow notation in modern music practice mar using meta expressions. From this, we obtain the and completeness of this definition within our framework. mapping function f (k). Finally, we show the implementation of this method and Book [8]. The six examples6 contain four typical notations its application. sentation. This work also draws attention to arrangement in which performance order is specified as a list of sec- in modern music practice: 5.1.
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