Milne, Andrew J.; Sethares, William A.; Laney, Robin and Sharp, David B.
(2011).
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| DOI (Digital Object Identifier) Link: | http://dx.doi.org/10.1080/17459737.2011.573678 |
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| Google Scholar: | Look up in Google Scholar |
Abstract
Models of the perceived distance between pairs of pitch collections are a core component of broader models of music cognition. Numerous distance measures have been proposed, including voice-leading [1], psychoacoustic [2–4], and pitch and interval class distances [5]; but, so far, there has been no attempt to bind these different measures into a single mathematical or conceptual framework, nor to incorporate the uncertain or probabilistic nature of pitch perception.
This paper embeds pitch collections in expectation tensors and shows how metrics between such tensors can model their perceived dissimilarity. Expectation tensors indicate the expected number of tones, ordered pairs of tones, ordered triples of tones, etc., that are heard as having any given pitch, dyad of pitches, triad of pitches, etc.. The pitches can be either absolute or relative (in which case the tensors are invariant with respect to transposition). Examples are given to show how the metrics accord with musical intuition.
| Item Type: | Journal Article |
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| Copyright Holders: | 2011 Taylor & Francis |
| ISSN: | 1745-9745 |
| Extra Information: | Author Posting. (c) Taylor & Francis, 2011.
This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Journal of Mathematics and Music, Volume 5 Issue 1, March 2011. doi:10.1080/17459737.2011.573678 |
| Keywords: | music cognition; tone; tonality; microtonality; pitch; salience; expectation; expectation tensor; metric |
| Academic Unit/Department: | Mathematics, Computing and Technology > Computing & Communications Mathematics, Computing and Technology > Engineering & Innovation |
| Interdisciplinary Research Centre: | Centre for Research in Computing (CRC) |
| Related URLs: | |
| Item ID: | 28353 |
| Depositing User: | Andrew Milne |
| Date Deposited: | 27 May 2011 11:12 |
| Last Modified: | 10 Dec 2012 22:35 |
| URI: | http://oro.open.ac.uk/id/eprint/28353 |
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