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Similarity of Interval-Class Content between Pitch-Class Sets: The IcVSIM Relation

Eric J. Isaacson
Journal of Music Theory
Vol. 34, No. 1 (Spring, 1990), pp. 1-28
Stable URL: http://www.jstor.org/stable/843860
Page Count: 28
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Similarity of Interval-Class Content between Pitch-Class Sets: The IcVSIM Relation
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Abstract

Music theorists have studied intervallic properties of pitch-class sets for more than three decades. It is held that a function measuring the similarity of interval-class content between pc set-classes should: (1) provide a distinct value for every pair of sets; (2) be useful for sets of any size; and (3) provide a wide range of discrete values. On the basis of these criteria, measures of Teitelbaum, Forte, Morris, Rahn, Lewin, and Lord are found to be inadequate, and a new function, IcVSIM (for Interval-class Vector SIMilarity), is proposed. The function returns as its value the standard deviation of the entries in the Interval-difference Vector (IdV) of two sets. The IdV is formed by computing the difference between the terms of two ic-vectors. A value of 0.00 indicates maximum similarity with respect to interval-class content. Z-related sets and certain pairs of sets of different sizes are found to be maximally similar, while sets 6-35 (the whole-tone collection) and 8-28 (the octatonic collection) are more dissimilar than any other pair of sets of size 3 through 9, with an IcVSIM value of 3.58.

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