A Framework for Investigation of Schenkerian Reduction of Music by Computers (10/04/08)
The automatic analysis of structure in a musical score (which can be compared to the parsing of a text) has been a topic of research in computational musicology for forty years. A recurring theme has been the automatic derivation of Schenkerian analyses, or other kinds of reductional analyses such as those of Lerdahl & Jackendoff, particularly since this kind of analysis is well supported by music theory and gives a rich account of musical structure from which a wealth of other information can be drawn. There are two recurrent problems, though. Firstly the solution space is extremely large. Secondly, while the rules which define what makes a valid reduction are relatively clear, the criteria by which good reductions are distinguished from bad ones are far from clear. This presentation will describe an approach and associated software which, to some degree, circumvents the first problem by seeking to create not an actual reduction but a matrix of possible local reductions from which actual reductions can be derived. The matrix is still very large, but of order O(n^2) compared to O(n!) for the space of all possible reductions (where n is the length of the piece to analyse). This allows systematic sampling from the universe of possible reductions for a fragment of music (only short examples can realistically be studied) and so comparison between 'good' analyses (taken from teaching materials and music-analytical publications) and 'bad' analyses (from the sample of possibilities) with the objective of finding criteria of goodness applicable in a selective reduction procedure.