Quantifying Musical Merit

Abstract

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.