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Journal Article
Journal of Music Theory (2005) 49 (1): 45–108.
Published: 01 April 2005
...Joseph N. Straus VOICE LEADING IN SET-CLASS SPACE Joseph N. Straus Introduction to Transformational Voice Leading Figure 1 shows four pairs of chords and says something about the voice leading between Chord X and four...
Journal Article
Journal of Music Theory (2009) 53 (2): 163–190.
Published: 01 October 2009
... described in patents of 1829 and 1844. Like the later tonal spaces of the German dualist theorists, the concertina's button layouts were inspired by the work of eighteenth-century mathematician Leonhard Euler, who used a lattice to show relationships among pitches in just intonation. Wheatstone originally...
Journal Article
Journal of Music Theory (2015) 59 (1): 121–181.
Published: 01 April 2015
...Jason Yust This article introduces a type of harmonic geometry, Fourier phase space, and uses it to advance the understanding of Schubert’s tonal language and comment upon current topics in Schubert analysis. The space derives from the discrete Fourier transform on pitch-class sets developed...
Journal Article
Journal of Music Theory (2019) 63 (2): 231–260.
Published: 01 October 2019
...Stephen Guerra Pitch spaces such as the circle of fifths model change through time in a composition, recording, or improvisation. Metric spaces theorized over the past twenty years do the same for changes (notated or not) in meter. Trajectories in either space and their potentially reinforcing...
Image
Published: 01 October 2021
Figure 6. The rhythms of Figure 4 in the Cartesian space for the half-note periodicity. Figure 6. The rhythms of Figure 4 in the Cartesian space for the half-note periodicity. More
Journal Article
Journal of Music Theory (2008) 52 (2): 219–249.
Published: 01 October 2008
...Justin Hoffman Recent music-theoretical research has proposed two ways of mapping the pitch-class set universe. Fourier spaces, constructed by Quinn, relate sets to one another based upon their composition from members of interval cycles, reflecting what might be called “harmonic quality.” Voice...
Journal Article
Journal of Music Theory (2007) 51 (2): 277–332.
Published: 01 October 2007
...Clifton Callender This article generalizes Ian Quinn's recent harmonic characterization of pitch-class sets in equal tempered spaces to chords drawn from continuous pitch and pitch-class spaces. Using the Fourier transform, chords of any real-valued pitches or pitch classes are represented...
Journal Article
Journal of Music Theory (2015) 59 (2): 273–320.
Published: 01 October 2015
...José Oliveira Martins The article proposes that a construct I call the Dasian space provides an effective framework to interpret harmonic aspects of scale relations in twentieth-century polymodality, particularly in the music of Bartók. Based on Bartók's intuition that the pitch space modeled after...
Journal Article
Journal of Music Theory (2016) 60 (2): 181–212.
Published: 01 October 2016
... level, aligned-cycle families. To conclude, I reexamine a three-voice aligned cycle from the second movement of Berg's String Quartet, op. 3, and investigate cyclic progressions in Thomas Adès's Piano Quintet, Lieux retrouvés , and The Tempest . Aligned-Cycle Spaces...
Journal Article
Journal of Music Theory (2019) 63 (2): 167–207.
Published: 01 October 2019
...Leah Frederick This article constructs generic voice-leading spaces by combining geometric approaches to voice leading with diatonic set theory. Unlike the continuous mod-12 spaces developed by Callender, Quinn, and Tymoczko, these mod-7 spaces are fundamentally discrete. The mathematical...
Journal Article
Journal of Music Theory (2011) 55 (1): 43–88.
Published: 01 April 2011
...Joseph N. Straus This article creates transformational spaces for interpreting progressions of sets belonging to the same T/I equivalence class. Within these spaces, sets are placed in proximity based upon contextual inversion , specifically those contextual inversions that (like the familiar neo...
Includes: Supplementary data
Image
Published: 01 October 2021
Figure 24. Rhythm and canons in Cartesian spaces for the eighth (a) and fourth (b) coefficients. Figure 24. Rhythm and canons in Cartesian spaces for the eighth (a) and fourth (b) coefficients. More
Image
Published: 01 October 2021
Figure 12. (a) The spectrum of the basic rhythm of Phase Patterns (see Figure 10). (b) The phase space for coefficient 3 and different rotations of the rhythm in this space. Figure 12. (a) The spectrum of the basic rhythm of Phase Patterns (see Figure 10). (b) The phase space for coefficient More
Journal Article
Journal of Music Theory (2009) 53 (2): 227–254.
Published: 01 October 2009
... different directions—located at two different points in a geometrical space—are “the same” or not. Relevant examples include the surface of the earth and the geometrical spaces representing n-note chords. Section 2 argues that we should not require that every interval be defined at every point in a space...
Journal Article
Journal of Music Theory (2019) 63 (1): 35–70.
Published: 01 April 2019
... modifies the prototypical big-band arrangement by merging the solo section with the ensemble feature, resulting in a trademark “Solo-Recapitulation trajectory,” which creates a deep-level structure comprising three “Spaces.” “Space division criteria” capture how broad expectations for jazz performance...
Journal Article
Journal of Music Theory (2016) 60 (1): 23–50.
Published: 01 April 2016
... − 1, where n equals cardinality. This notation identifies pitches solely by their relative height, thereby eschewing any reference to specific interval size and effectively transforming pitches in pitch space into contour pitches in contour space. The variable end-point mechanism this procedure...
Journal Article
Journal of Music Theory (2009) 53 (1): 1–56.
Published: 01 April 2009
...Scott Murphy The metric cube is a kind of graph of meters proposed as a complement to the types of metric spaces that have already been put forth in music-theoretic scholarship, particularly by Richard Cohn. Whereas Cohn's most recent kind of metric space (2001) can compare meters only...
Journal Article
Journal of Music Theory (2006) 50 (2): 211–251.
Published: 01 October 2006
... simultaneously as a local, harmonic event and as a global, formal event. On the local level, it may either prolong one harmony or progress from one to another. On the global level, it can serve a variety of formal functions: highlighting salient cadences; opening a space for virtuosic display; and developing...
Journal Article
Journal of Music Theory (2016) 60 (2): 213–262.
Published: 01 October 2016
... proposes the use of phase spaces and Quinn's harmonic qualities in analysis of a wide variety of twentieth-century styles. The main focus is on how these ideas relate to scale-theoretic concepts and the repertoires to which they are applied, such as the music of Debussy, Satie, Stravinsky, Ravel...
Journal Article
Journal of Music Theory (2018) 62 (1): 1–39.
Published: 01 April 2018
... in generalized fretboard space. Musical examples in the essay involve guitar, mandolin, banjo, and ukulele, with extended analyses of pieces by Eddie Van Halen and Mark O’Connor. This investigation, with its blend of formalization and performance analysis, is framed by reflections on space, instruments...