Cross-Partitions as Harmony and Voice Leading in Twelve-Tone Music

Alegant, Brian

doi:10.1525/mts.2001.23.1.1

Cited by 15 publications

(6 citation statements)

References 44 publications

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“…Among some of the works that associate partitions and music in a more explicit way, we highlight the early studies of twelve-tone partitioning, in particular the source set approaches of Babbitt [13,14,15], Perle [129,130,131] and Martino [108], in addition to other studies in combinatoriality by Forte [56], Howe [85] and Gamer [65]. In the same direction, we also mention the works of Wintle [175], Bazelow and Brickle [20], Morris and Starr [117,124,161,162,163], Haimo and Johnson [77], and the further partitional or mosaic approaches of Mead [110,111], Kurth [97,98,99,100], Morris and Alegant [2,3,4,5,6,122,123]. Morris still uses partitions to shape some of his compositional designs, especially the Design VI [118, pp.…”

Section: Introductionmentioning

confidence: 90%

Partitional Harmony: The Partitioning of Pitch Spaces

Feitosa¹

2020

MusMat

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In this preliminary work, we seek to present a brief historical review of the use of partitions in music, to provide a concise introduction to the theory of partitions, and lastly, through an extensive bibliographic revision and a thoughtful theoretical reflection, to lay the foundations of what we call partitional harmony - a comprehensive harmonic conception which relates the theory of partitions to several fields of post-tonal music theory. At the end, some basic operations (pitch, transposition, inversion, and multiplication) are defined and an illustrative musical application is provided, followed by our research prospects.

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Section: Introductionmentioning

confidence: 90%

Partitional Harmony: The Partitioning of Pitch Spaces

Feitosa¹

2020

MusMat

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“…Networks with isomorphic graphs are called isographic (Klumpenhouwer, 1991). 1 The definition of space (a locus, as a set of data) and the transformations on it are relevant also for group theory. The tonnetz is also relevant in Tymoczko's and Hook's studies (Tymoczko, 2012;Hook, 2006).…”

Section: Tonnetzmentioning

confidence: 99%

“…Manipulations of the tonnetz in combinatorial terms might be suggested in the socalled "slot-machine" transformations, but, at the best of our knowledge, no physical realizations of these have been made. A "slot-machine" transformation is a metaphor to indicate a permutation, more than a rotation, according to Alegant (2001), in a crosspartition. The cross-partition is a way to arrange pitch classes with each column having numbers that represent the notes of a chord.…”

Section: Tonnetzmentioning

confidence: 99%

Musical combinatorics, tonnetz, and the CubeHarmonic

Mannone¹,

Kitamura²,

Huang³

et al. 2018

Zb Akad umetnosti

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In this paper, we give an overview of some applications of combinatorics and permutations in music through the centuries. The concepts of permutation and tonnetz (spatial representation of voice leading and modulation) can be joined together in a physical device, the CubeHarmonic, a musical version of the Rubik's cube. We finally describe a prototype of the CubeHarmonic that uses the magnetic tracking technology developed at the Tohoku University.

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“…Furthermore, in Cohn's approach, ordered pitch-class intervals can effectively cancel each other, so if one voice moves up a semitone and another moves down a semitone, Cohn considers the voice leading displacement to be 0; I think it should be 2. I follow Lewin 1998 andAlegant 2001 in measuring voice leading proximity according to the sum of the interval classes involved. In the measure employed here, total displacement values are not to be taken mod12.…”

Section: Smoothnessmentioning

confidence: 99%

Uniformity, Balance, and Smoothness in Atonal Voice Leading

Straus¹

2003

Music Theory Spectrum

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This paper offers a broadly applicable model for atonal voice leading, a model of pitch-class counterpoint to connect any two harmonies. Voice leadings are evaluated by three criteria: (1) uniformity: the extent to which the voices move by the same interval distance and thus approach traditional transposition; (2) balance: the extent to which the voices move by the same index number and thus approach traditional inversion; and (3) smoothness: the extent to which the voices travel the shortest possible distance. The most uniform, most balanced, or smoothest way of moving from one set to another in pitch-class space, or from one set class to another in a proposed voiceleading space, provides a standpoint from which to assess any specific compositional realization in pitch space.

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Cross-Partitions as Harmony and Voice Leading in Twelve-Tone Music

Cited by 15 publications

References 44 publications

Partitional Harmony: The Partitioning of Pitch Spaces

Partitional Harmony: The Partitioning of Pitch Spaces

Musical combinatorics, tonnetz, and the CubeHarmonic

Uniformity, Balance, and Smoothness in Atonal Voice Leading

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