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Journal Article
Journal of Music Theory (2007) 51 (2): 277–332.
Published: 01 October 2007
... by their spectra and located in a harmonic space of all possible chord spectra. Euclidean and angular distance metrics defined on chord spectra correlate strongly with common interval-based similarity measures such as IcVSIM and ANGLE. Thus, we can approximate these common measures of harmonic similarity...
Journal Article
Journal of Music Theory (2008) 52 (2): 251–272.
Published: 01 October 2008
...Dmitri Tymoczko In this article, I consider two ways to model distance (or inverse similarity) between chord types, one based on voice leading and the other on shared interval content. My goal is to provide a contrapuntal reinterpretation of Ian Quinn's work, which uses the Fourier transform...
Includes: Supplementary data
Journal Article
Journal of Music Theory (2011) 55 (2): 167–220.
Published: 01 October 2011
... Gottfried Herder’s rejection of Kant through Hegel, Friedrich Theodor and Robert Vischer, Karl Köstlin, and Johannes Volkelt. Eduard Hanslick, in arriving at his own destination, travels some distance on both paths, collecting along the way, on the one hand, Kant’s rigorous focus on the phenomenon...
Journal Article
Journal of Music Theory (2010) 54 (1): 37–60.
Published: 01 April 2010
... of time, however, the distance between Cavell's and the postmodernists' views concerning subjectivity and the role of the arts in defining it have become increasingly clear. In Cavell's scenario, a contemporary listener or critic confronted with the new music faces a sort of existentialist crisis: he...
Journal Article
Journal of Music Theory (2016) 60 (1): 23–50.
Published: 01 April 2016
... inclusive. This not only systematically eliminates the distortions and inconsistencies that crop up with respect to mixed cardinality csegs but also provides a considerably more nuanced metric for intervallic distances in contour space. Using analytical case studies juxtaposing the two notational systems...
Journal Article
Journal of Music Theory (2005) 49 (2): 333–357.
Published: 01 October 2005
... on transposition). Example 1 shows a segment of the chord progression from the second half of John Coltrane’s “Giant Steps.” In Example 1, notice that the ii– V–I cadential paradigm cycles at a distance of four semitones (interval class 4), creating brief tonicizations of E≤, G, B, and E≤. This technique...
Journal Article
Journal of Music Theory (2009) 53 (2): 227–254.
Published: 01 October 2009
....” American Mathematical Monthly 86 : 571 –74. Gollin, Edward. 2000 . “Representations of Space and Conceptions of Distance in Transformational Music Theories.” Ph.D. thesis, Harvard University. Hall, Rachel. 2009 . Review of two books by David Lewin. Journal of the American Musicological...
Journal Article
Journal of Music Theory (2014) 58 (2): 155–178.
Published: 01 October 2014
... Harold Morgenstern Sam . 1948 . A Dictionary of Musical Themes . New York : Crown . Bartlette Christopher . 2007 . “ A Study of Harmonic Distance and Its Role in Musical Performance .” Ph.D. diss. , University of Rochester . Bell Alan Jurafsky Daniel Fosler-Lussier...
Journal Article
Journal of Music Theory (2014) 58 (1): 79–101.
Published: 01 April 2014
... schools of thought with which his ideas share these boundaries. For example, while the book recognizes and respects three methods of measuring distance between chords (the reader may wish to look ahead to my Figure 1) and three conceptions of musical syntax, Cohn concentrates upon one of each...
Journal Article
Journal of Music Theory (2005) 49 (1): 45–108.
Published: 01 April 2005
... is the inversion, in pitch space, of the first—and say that the inversion that exchanges A5 and E3 also sends G4 onto F≥4. This transformational voice leading is not smooth, because the mappings involve an exchange of tones, traversing large distances, rather than the simple retention of tones...
Journal Article
Journal of Music Theory (2009) 53 (1): 1–56.
Published: 01 April 2009
... series—the set of mixed meters—serves as a way station between the extremes, resulting in a smooth “modulation” from pure duple to pure triple. Although this space includes any possible meter, its relatively small size proffers only three different “distance...
Journal Article
Journal of Music Theory (2015) 59 (1): 121–181.
Published: 01 April 2015
... it gives us access to a range of metaphors commonly used to explain and interpret harmony: distance, direction, position, paths, boundaries, regions, shape, and so on. From a mathematical perspective, these metaphors are all inherently topological. The most prominent current theoretical...
Journal Article
Journal of Music Theory (2008) 52 (2): 219–249.
Published: 01 October 2008
... metaphorical spaces inhabited by pitch-class sets. Maps conceive of distance between pitch-class sets in two different ways. The first type of map, generalized by Clifton Callender, Ian Quinn, and Dmitri Tymoczko (2008), is based upon voice-leading proximity; in these maps, the distance between sets...
Journal Article
Journal of Music Theory (2019) 63 (2): 167–207.
Published: 01 October 2019
.... These OPTIC relations are applied to the points of geometrical spaces, and the result is a set of complex structures, each with a unique topology.2 Points in the spaces represent various equivalence classes of chords, and the distances between points relate to the voice-leading proximity of such chord types...
Journal Article
Journal of Music Theory (2004) 48 (1): 99–141.
Published: 01 April 2004
... captures our histori- cally grounded idea of interval as distance or measurement, a simply tran- sitive group captures both the idea of interval as distance and of interval as transformation (GMIT 158–59). We begin by looking at the transfor- mational side of the dichotomy, the simply-transitive-group...
Journal Article
Journal of Music Theory (2001) 45 (1): 73–118.
Published: 01 April 2001
...). The number two may also have some symbolic significance in Gas- congne’s case: the canon is set at a time-interval of two tempora, and stacked at the highly unusual distance of the second.11 If it must be admit- ted that there is very little choice of interval available when stacking twelve voices...
Journal Article
Journal of Music Theory (2012) 56 (1): 1–52.
Published: 01 April 2012
... 27/1 : 1 – 49 . ———. 2008c . “ Set-Class Similarity, Voice Leading, and the Fourier Transform .” Journal of Music Theory 52/2 : 251 – 72 . ———. 2009b . “ Three Conceptions of Musical Distance .” In Mathematics and Computation in Music , ed. Chew Elaine Childs Adrian Chuan...
Journal Article
Journal of Music Theory (2019) 63 (2): 231–260.
Published: 01 October 2019
... of work has been the theorization of metric spaces. Like the circle of fifths, Cube Dance, and other familiar pitch spaces, metric spaces relate objects (i.e., meters) by distances.1 Perceived changes of meter (notated or not) in a phrase, part, or piece inscribe closer and more remote paths in metric...
Journal Article
Journal of Music Theory (2016) 60 (2): 213–262.
Published: 01 October 2016
... on the given component, and project each pitch class onto this axis, taking the distance from the origin (positive in the same direction as the phase, negative in the opposite direction), as illustrated in Figure 3. These distances define...
Journal Article
Journal of Music Theory (2017) 61 (2): 243–287.
Published: 01 October 2017
... and E minor). 3 As I show in this article, each relation preserves a different number♭ of common tones while maximizing tonal distance, for which reason the PSM framework is ideally suited to an atonal triadic style, as demonstrated in Schnittke’s music...