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topology

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Journal Article
Journal of Music Theory (2015) 59 (1): 121–181.
Published: 01 April 2015
... by David Lewin and Ian Quinn but uses primarily the phases of Fourier components, unlike Lewin and Quinn, who focus more on the magnitudes. The space defined by phases of the third and fifth components closely resembles the Tonnetz and has a similar common-tone basis to its topology but is continuous...
Journal Article
Journal of Music Theory (2019) 63 (2): 167–207.
Published: 01 October 2019
... -, and OP -spaces of two- and three-note chords. The final section of the study shows that, although the discrete mod-7 versions of these lattices appear quite different from their continuous mod-12 counterparts, the topological space underlying each of these graphs depends solely on the number of notes...
Journal Article
Journal of Music Theory (2009) 53 (2): 227–254.
Published: 01 October 2009
... of Mathematics, Second Series 68 : 444 –49. Nakahara, Mikio. 2003 . Geometry, Topology, and Physics . New York: Taylor and Francis. Penrose, Roger. 2004 . The Road to Reality . New York: Knopf. Pynchon, Thomas. 2006 . Against the Day . New York: Penguin. Robinson, Derek. 1996 . A Course...
Journal Article
Journal of Music Theory (2012) 56 (1): 1–52.
Published: 01 April 2012
... the origin; the n-dimensional ball consists of all points less than or equal to a certain distance from the origin. (It is a “filled- in” sphere, the union of a sphere and its interior.) Topological equivalence can be understood as “equivalence to within stretching”: two shapes are topo- logically...
Journal Article
Journal of Music Theory (2002) 46 (1-2): 127–151.
Published: 01 October 2002
... on all sides” (105). Hyer then re-imagines Riemann’s space under the constraints of enharmonic and octave equivalence, and notes that in so doing Riemann’s “tabular representation of tonal rela- tions gives rise to remarkable algebraic and topological properties” (106). The result is the following...
Journal Article
Journal of Music Theory (2020) 64 (1): 105–121.
Published: 01 April 2020
... and lay out the steps of his linear mapping procedure, and chap- ters 4 6 present a staggeringly interconnected network of Wilson s tuning concepts through the topological lens of his keyboards. These latter three chapters form the book s theoretical core. Chapter 7 offers a brief conclusion that reflects...
Journal Article
Journal of Music Theory (2020) 64 (2): 241–281.
Published: 01 October 2020
...: University of Rochester Press. Douthett, Jack, Peter Steinbach, and Richard Hermann. 2018. Hypercubes and the Gener- alized Cohn Cycle. In Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological, and Applied Approaches to Understanding Musical Phenomena, edited by Mari- ana Montiel...
Journal Article
Journal of Music Theory (2007) 51 (2): 277–332.
Published: 01 October 2007
... { }O to its proximity to the maximum at 0, 2.4, 7.2 .17 Also note that the higher the harmonic the { }O greater the number of maxima and the steeper the slope away from these high points. Thus the topology for the first harmonic consists of a gradual...
Journal Article
Journal of Music Theory (2013) 57 (1): 47–85.
Published: 01 April 2013
.... 1988. “Cognitive Topology and Lexical Networks.” In Resolution: Perspectives from Psycholinguistics, Neuropsychology, and Artificial Intelligence, ed. Steven L. Small, Garrison W. Cottrell, and Michael K. Tanenhaus, 477–508. San...
Journal Article
Journal of Music Theory (2016) 60 (2): 213–262.
Published: 01 October 2016
..., the con- volution theorem. Figure 1 shows the one-dimensional phase spaces, which are equivalent to Quinn’s (2006–7) “Fourier balances.” All are topological circles, and every pitch class has a position in each of them. Phase space 1 is the (reflection of the) familiar pitch-class circle...
Journal Article
Journal of Music Theory (2012) 56 (2): 169–223.
Published: 01 October 2012
... Model and its Cognitive Implications. Ph.D. diss., Eastman School of Music, University of Rochester. 2009a. “HMM  analysis of Musical Structure: Identification of  hidden Variables through Topology-Sensitive Model Selection...
Journal Article
Journal of Music Theory (2020) 64 (1): 63–103.
Published: 01 April 2020
...) t3 and t6 sequences in violin-cello canon, mm. 18 26. (c) Implied t3 harmonic sequence, mm. 4 18. (b) (c) 77Julian Hook Generic Sequences 16 See, for instance, Cohn 2012 for many examples. 17 The arrowheads of opposite orientations are a common convention in topology for indicating boundaries...
Journal Article
Journal of Music Theory (2005) 49 (1): 1–43.
Published: 01 April 2005
... habit in music theory—are expressions of questionable theorizing. 20. Clough 1998 and Kochavi 1998 are particularly important in this connection. Kochavi 2002 expands richly on contextual transformations. Peck 2003 general- izes the issues involved from a topological...
Journal Article
Journal of Music Theory (2021) 65 (2): 325–374.
Published: 01 October 2021
... . 2020 . “ Generalized Tonnetze and Zeitnetze , and the Topology of Music Concepts .” Journal of Mathematics and Music 14 , no. 2 : 170 – 203 . Yust Jason . 2021 . “ Steve Reich's Signature Rhythm, and an Introduction to Rhythmic Qualities .” Music Theory Spectrum 43 , no. 1 : 74...
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Journal Article
Journal of Music Theory (2000) 44 (1): 171–229.
Published: 01 April 2000
... grouping. By summing the dis- continuities produced at different points, the system ultimately produces a segmentational topology that models musical flow. We consider the theory a tool for thinking in music—listening, per- forming, analyzing, and composing: it breaks music up into analyzable...
Journal Article
Journal of Music Theory (2014) 58 (2): 179–233.
Published: 01 October 2014
... and the whole-tone tube dances rendered in a similar way. (As discussed above, the whole-tone tube dance has a different topology as it fea- tures an additional symmetry.) We can observe that mutual positions of neigh- boring floors are different in the three tube dances...