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Metrics for pitch collections

Milne, Andrew J.; Sethares, William A.; Laney, Robin and Sharp, David B. (2010). Metrics for pitch collections. In: Proceedings of the International Conference of Music Perception and Cognition 2010 (ICMPC 11), 23-27 Aug 2010, Seattle, USA.

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Abstract

Models of the perceived distance between pairs of pitch collections are a core component of broader models of the perception of tonality as a whole. Numerous different distance measures have been proposed, including voice-leading, psychoacoustic, and pitch and interval class distances; but, so far, there has been no attempt to bind these different measures into a single mathematical framework, nor to incorporate the uncertain or probabilistic nature of pitch perception (whereby tones with similar frequencies may, or may not, be heard as having the same pitch).

To achieve these aims, we embed pitch collections in novel multi-way expectation arrays, and show how metrics between such arrays can model the perceived dissimilarity of the pitch collections they embed. By modeling the uncertainties of human pitch perception, expectation arrays indicate the expected number of tones, ordered pairs of tones, ordered triples of tones and so forth, that are heard as having any given pitch, dyad of pitches, triad of pitches, and so forth. The pitches can be either absolute or relative (in which case the arrays are invariant with respect to transposition).

We provide a number of examples that show how the metrics accord well with musical intuition, and suggest some ways in which this work may be developed.

Item Type: Conference Item
Copyright Holders: 2010 Andrew Milne
Academic Unit/Department: Mathematics, Computing and Technology > Computing & Communications
Mathematics, Computing and Technology > Engineering & Innovation
Interdisciplinary Research Centre: Centre for Research in Computing (CRC)
Item ID: 21508
Depositing User: Andrew Milne
Date Deposited: 13 Jul 2010 11:08
Last Modified: 25 Oct 2012 15:27
URI: http://oro.open.ac.uk/id/eprint/21508
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