TY - JOUR

T1 - Schenkerian analysis by computer

T2 - a proof of concept

AU - Marsden, Alan

N1 - The final, definitive version of this article has been published in the Journal, Journal of New Music Research, 39 (3), 2010, © Informa Plc

PY - 2010/9

Y1 - 2010/9

N2 - A system for automatically deriving a Schenkerian reduction of an extract of tonal music is described. Schenkerian theory is formalised in a quasi-grammatical manner, expressing a reduction as a binary-tree structure. Computer software which operates in the manner of a chart parser using this grammar has been implemented, capable of deriving a matrix of reduction possibilities, in polynomial time, from a representation of the score. A full reduction of the extract can be discovered by selecting a tree from this matrix. The number of possible valid reductions for even short extracts is found to be extremely large, so criteria are required to distinguish good reductions from bad ones. To find such criteria, themes from five Mozart piano sonatas are analysed and samples of 'good' reductions (defined by reference to pre-existing analyses of these themes) are compared with randomly sampled reductions. Nine criteria are thereby derived, which can be applied in the process of parsing and selecting a reduction. The results are promising, but the process is still too computationally expensive--only extracts of a few bars in length can be reduced--and more extensive testing is required before the system can be properly claimed to perform automatic Schenkerian analysis.

AB - A system for automatically deriving a Schenkerian reduction of an extract of tonal music is described. Schenkerian theory is formalised in a quasi-grammatical manner, expressing a reduction as a binary-tree structure. Computer software which operates in the manner of a chart parser using this grammar has been implemented, capable of deriving a matrix of reduction possibilities, in polynomial time, from a representation of the score. A full reduction of the extract can be discovered by selecting a tree from this matrix. The number of possible valid reductions for even short extracts is found to be extremely large, so criteria are required to distinguish good reductions from bad ones. To find such criteria, themes from five Mozart piano sonatas are analysed and samples of 'good' reductions (defined by reference to pre-existing analyses of these themes) are compared with randomly sampled reductions. Nine criteria are thereby derived, which can be applied in the process of parsing and selecting a reduction. The results are promising, but the process is still too computationally expensive--only extracts of a few bars in length can be reduced--and more extensive testing is required before the system can be properly claimed to perform automatic Schenkerian analysis.

U2 - 10.1080/09298215.2010.503898

DO - 10.1080/09298215.2010.503898

M3 - Journal article

VL - 39

SP - 269

EP - 289

JO - Journal of New Music Research

JF - Journal of New Music Research

SN - 1744-5027

IS - 3

ER -