JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. The MIT Press and Leonardo are collaborating with JSTOR to digitize, preserve and extend access to Leonardo. I n my previous Leonardo article, "AutomatedComposition in Retrospect: 1956-1986", I described a variety of approaches that have been used over the past 30 years to generate musical compositions using computer programs [1]. One approach I mentioned only in passing was the Markov process, which I judged at the time to be only of peripheral interest to users of composing programs. Since then, several developments have shown me that the enthusiasm toward Markov processes is much greater than I had estimated. Undoubtedly the strongest indication of misjudgement on my part has been the phenomenal response to M and Jam Factory over the past 2 years-the first time any effort at automated composition has met with the slightest commercial success-but these important programs are only part of a general resurgence of interest in Markov chains over the past decade. Several new approaches toward Markov chains have come to my attention since I wrote my retrospective, and I even found myself personally involved with them in 1986 when John Myhill hired me to implement some Markov processes that could gradually evolve over the course of a musical work he was composing [2]. I choose to integrate the present survey of musical applications with a tutorial because there are some significant theoretical ramifications associated with Markov chains. As with all mathematical formalisms, the intrinsic logic behind Markov processes remains valid no matter what real-world meaning the symbols (in this case the 'states' of the chain) might have. Indeed, the matrix representation devised by mathematicians to describe how Markov chains behave lends a deceptive simplicity; Markov processes can be shown to include many seemingly more complex methodologies as special cases. Although the mathematics is too formidable to elaborate in a tutorial of this nature, a few examples will suffice to demonstrate how one can deduce the behavior of a chain from its matrix [3]. The meanings associated with each state of the chain depend, of course, on the application, and for examples of how Markov chains can be applied to music it will generally be best to go directly to the sources.A constructive evaluation of a compositional procedure ultimately must take into account the music produced; however, different procedures have their different strengths and weaknesses. A composer can estimate the appropriateness of such a procedure by considering his or her musical objectives and by determining how effective the procedure is at realizing these objectives. The last section of this article enumerates a number of objectives tha...
This paper surveys techniques for merit-based decision-making in automated composition and analysis. The paper has two parts, respectively covering the "tactics" and "strategy" of decision-making processes.Part I deals with functions used to assess a candidate's merit (or demerit) quantitatively. The "discrimination" or precision associated with a merit function determines whether it is suitable only for "black and white" judgments of acceptability or if it also can be used for "shades of grey" judgments of preference. Differences between absolute merit (magnitudes) and relative merit (distances) are briefly discussed. The bulk of Part 1 explores ways of reconciling several evaluative factors into a simple numerical measure: logical, additive, geometric, multiplicative, prioritized, and uniform. The introduction of a randomness is advised as a way of distinguishing candidates when their merit assessments would otherwise teeter at the knife edge.Part II discusses how merit functions may be used to guide a decision-making process to an acceptable, preferable, or even optimal solution. Distinction is drawn between "algorithmic" and "heuristic" procedures. Background is provided on heuristic reasoning, as first described by Polya. Newell, Shaw, and Simon's use of heuristics to guide a decision-making process efficiently toward an acceptable solution is contrasted with Ebcioglu's use of heuristics to obtain better-than-acceptable results. A survey of compositional and analytic applications compares relative strengths and weaknesses of different strategies including rote, random, "rule-based" or purely heuristic (e.g. sorting, conditional probability, the "Blackboard" model, Chomsky grammars), generate-and-test, heuristically guided search, and exhaustive search.
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