No Longer ‘Somewhat Arbitrary’ : Calculating Salience in GTTM-Style Reduction

Marsden, Alan Alexander and Tojo, Satoshi and Hirata, Keiji (2018) No Longer ‘Somewhat Arbitrary’ : Calculating Salience in GTTM-Style Reduction. In: DLfM '18 Proceedings of the 5th International Conference on Digital Libraries for Musicology :. ACM, New York, pp. 26-33. ISBN 9781450365222

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Abstract

Following earlier work on the formalisation of Lerdahl and Jackendoff’s Generative Theory of Tonal Music (GTTM), we present a measure of the salience of events in a reduction tree, based on calculations relating the duration of time-spans to the structure of the tree. This allows for the proper graphical rendition of a tree on the basis of its time-spans and topology alone. It also has the potential to contribute to the development of sophisticated digital library systems able to operate on music in a musically intelligent manner. We present results of an empirical study of branch heights in the figures in GTTM which shows that salience calculated according to our proposals correlates better with branch height than alternatives. We also discuss the possible musical significance of this measure of salience. Finally we compare some results using salience in the calculation of melodic similarity on the basis of reduction trees to earlier results using time-span. While the correlation between these measures and human ratings of the similarity of the melodies is poor, using salience shows a definite improvement. Overall, the results suggest that the proposed definition of salience gives a potentially useful measure of an event’s importance in a musical structure.