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Tonnetz

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Journal Article
Journal of Music Theory (2020) 64 (1): 63–103.
Published: 01 April 2020
... chromatic transposition operators, and may be mapped in a generic Tonnetz analogous to the Tonnetz diagrams of neo-Riemannian theory. A complete classification of generic sequences with two-chord transposition blocks is derived from the paths described by the sequences in the Tonnetz . While it is tempting...
Journal Article
Journal of Music Theory (2012) 56 (1): 1–52.
Published: 01 April 2012
...-leading structure—including a three-note octahedral Tonnetz and tetrahedral models of four-note diatonic and chromatic chords. Dmitri Tymoczko is a composer and music theorist who teaches at Princeton University. His book A Geometry of Music was published in 2011, and his album Beat Therapy...
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 (2002) 46 (1-2): 127–151.
Published: 01 October 2002
... relationships. 128 2. Mapping PC Space Recent work in neo-Riemannian tonal theory has produced sophisti- cated representations of tonal space. Starting with the graphic arrays or tonnetze developed by Riemann and Oettingen, a number of theorists have developed spatial...
Journal Article
Journal of Music Theory (2011) 55 (1): 43–88.
Published: 01 April 2011
..., is often observed within compositional spaces known as Tonnetze.8 While the neo-Riemannian enterprise has concen- trated almost exclusively on tonally indeterminate relations among triads in the chromatic music of the nineteenth century, several theorists have raised the possibility...
Includes: Supplementary data
Journal Article
Journal of Music Theory (2014) 58 (1): 79–101.
Published: 01 April 2014
... . ———. 1996 . “ Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions .” Music Analysis 15 : 9 – 40 . ———. 1997 . “ Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations .” Journal of Music Theory 41 : 1 – 66...
Journal Article
Journal of Music Theory (2017) 61 (1): 111–140.
Published: 01 April 2017
... a hexagonal Tonnetz to visually portray key variations, start- ing with an overview of one particular path that Hauptmann’s linear rows, in the hands of two of his students, Louis Köhler and Otto Bähr, followed toward the Tonnetz. By way of demonstration, I...
Journal Article
Journal of Music Theory (2014) 58 (2): 235–256.
Published: 01 October 2014
..., composed in profusion by all the major composers after 1840, had to rely on the Tonnetz and associated transformations for acts of musical cognition, they would have proved as inac- cessible, in pitch terms, as some later repertoires have proved to be. Since...
Journal Article
Journal of Music Theory (2014) 58 (2): 179–233.
Published: 01 October 2014
... . ———. 1997 . “ Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations .” Journal of Music Theory 41/1 : 1 – 66 . ———. 1998 . “ Square Dances with Cubes .” Journal of Music Theory 42/2 : 283 – 96 . ———. 2012 . Audacious Euphony: Chromatic Harmony and the Triad’s...
Journal Article
Journal of Music Theory (2022) 66 (1): 135–145.
Published: 01 April 2022
... preferred method to handle LPR-composite labeling is to use the Tonnetz , particularly Cohn's ( 2012 ) three-axis version. The student learns L , P , and R as edge flips—and perhaps also N , S , and F as vertex flips—around the minor-third, perfect-fifth, and major-third axes, respectively. 5...
FIGURES
Journal Article
Journal of Music Theory (2007) 51 (2): 187–210.
Published: 01 October 2007
... between keys), and all third relations—diatonic or chromatic—help subvert a conven- tional tonic-dominant polarity (thereby putting the two keys on a relatively equal footing). Figure 4 uses a Tonnetz to demonstrate the common tone links 17  Lewis even compares the double-tonic...
Journal Article
Journal of Music Theory (2005) 49 (2): 301–332.
Published: 01 October 2005
...Steven Strunk © 2008 by Yale University 2008 Cohn, Richard. 1997 . “Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations.” Journal of Music Theory 41 : 1 –66. ———. 2004 . “Uncanny Resemblances: Tonal Signification in the Freudian Age.” Journal...
Journal Article
Journal of Music Theory (2004) 48 (2): 219–294.
Published: 01 October 2004
... Trichords, and their `Tonnetz' representations. Journal of Music Theory 41 : 1 -66. Douthett, Jack and Peter Steinbach. 1998 . “Parsimonious Graphs: a Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42 : 241 -263. Edstrom, Brent...
Journal Article
Journal of Music Theory (2015) 59 (2): 191–234.
Published: 01 October 2015
... of perfect fourths at three chromatically adjacent transposition levels and thus conveys the opera- tion [012] * 5. Following Brown 2003 and 2009, the melody’s two hexachords can each be visualized as 2 × 3 regions of an ic1/ic5 Tonnetz; if we assign ic1 and ic5 to its horizontal and vertical...
Journal Article
Journal of Music Theory (2019) 63 (2): 167–207.
Published: 01 October 2019
...; and Tymoczko 2004. Voice leading in mod-7 space has also been studied from the perspective of the diatonic Tonnetz; see Brower 2008 and Cohn 2012: chap. 8. 2 The OPTIC relations are thoroughly discussed in Callen- der, Quinn, and Tymoczko 2008. Brief definitions of each appear in this article in Table 2...
Journal Article
Journal of Music Theory (2000) 44 (2): 323–379.
Published: 01 October 2000
... pathways and regions within the fully expanded chromatic space of the Tonnetz, it is possible to understand the evolution of tonal convention as reflecting the ex- ploration over many centuries of tonality’s potential for metaphorical expression. By the end of the nineteenth century, the expressive...
Journal Article
Journal of Music Theory (2018) 62 (2): 165–204.
Published: 01 October 2018
... of Rochester Press . Cohn Richard . 1996 . “ Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions .” Music Analysis 15 / 1 : 9 – 40 . Cohn Richard . 1997 . “ Neo-Riemannian Operations, Parsimonious Trichords, and Their ‘Tonnetz...
Journal Article
Journal of Music Theory (2017) 61 (2): 243–287.
Published: 01 October 2017
...-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations ”. Journal of Music Theory 41 / 1 : 1 – 66 . Cohn Richard . 1998 . “ Square Dances with Cubes .” Journal of Music Theory 42 / 2 : 283 – 96 . Cohn Richard . 1999 . “ As Wonderful as Star Clusters...
Journal Article
Journal of Music Theory (2009) 53 (2): 163–190.
Published: 01 October 2009
... Oettingen und sein Orthotonophonium im Kontext.” Tartu ülikooli muusikadirektor 200: 12. http://hdl.handle.net/10062/5574 . Gollin, Edward. 2006 . “Some Further Notes on the History of the Tonnetz.” Theoria 13 : 99 –111. Hall, Rachel. 2006. “Playing Musical Tiles.” In Proceedings of the 2006...
Journal Article
Journal of Music Theory (2004) 48 (1): 69–98.
Published: 01 April 2004
... Space in Twentieth-Century Music .” Ph.D. diss., Yale University. Carpenter, Patricia. 1983 . “Grundgestalt as Tonal Function.” Music Theory Spectrum 5 : 15 -38. Cohn, Richard. 1997 . “Neo-Riemannian Operations, Parsimonious Trichords, and their Tonnetz Representations.” Journal of Music...