Klumpenhouwer Networks, Trichords, and Axial Isography

Stoecker, Philip

doi:10.1525/mts.2002.24.2.231

Cited by 15 publications

(5 citation statements)

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“…Perle had already published some of his theoretical results before Lewin's article (Perle 1964 and [1977] 1996). The music‐theory community acknowledged Perle's remarks about K‐nets, and some years later, the journal again dedicated a special issue to this topic (Headlam 2002, Lambert 2002, Lewin 2002 and Stoecker 2002). Other scholars explored these resemblances further with great subtlety (Foley 2002 and 2009).…”

Section: Entering the Transformational Debatementioning

confidence: 99%

From Dürer's Magic Square to Klumpenhouwer Tesseracts: On Melencolia (2013) by Philippe Manoury

Besada¹,

Guichaoua²,

Andreatta³

2022

Music Analysis

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Many Western art music composers have taken advantage of tabulated data for nourishing their creative practices, particularly since the early twentieth century. The arrival of atonality and serial techniques was crucial to this shift. Among the authors dealing with these kinds of tables, some have considered the singular mathematical properties of magic squares. This paper focuses on a particular case study in this sense: Philippe Manoury's Third String Quartet, entitled Melencolia. We mainly analyse mainly several strategies conceived by the French composer – through his own sketches – in order to manipulate pitches and pitch‐classes over time. For that purpose, we take advantage of Klumpenhouwer networks as a way to settle wide and dense isographic relationships. Our hyper‐K‐nets sometimes reach a total of 32 arrows that allow geometrical arrangements as tesseracts in which their different dimensions cluster related families of isographies. In doing so, we aim to provide an instructive example of how to contextualise K‐nets and isographies as powerful tools for the analysis of compositional practices.

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Section: Entering the Transformational Debatementioning

confidence: 99%

From Dürer's Magic Square to Klumpenhouwer Tesseracts: On Melencolia (2013) by Philippe Manoury

Besada¹,

Guichaoua²,

Andreatta³

2022

Music Analysis

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“…(For information about K-net, see Klumpenhouwer 1991 andLewin 1994. For a further elaboration of K-net, see Philip Stoecker 2002 andMichael Buchler 2007. In addition, since the topic of this paper focuses on the transformational model, for those who may be interested in a similar approach in analyzing atonal music, I provide some references listing the related researches conducted by current theorists: John Roeder 1984, 1989, Robert Morris 1995a, 1995b, Richard Cohn 1997, Shaun O'Donnell 1997, Ciro Scotto 2003, Michael Siciliano 2005, J. Daniel Jekins 2010, Justin Lundberg 2012, and Joe Argentino 2010and 2013 The prolongational model, which "has its roots in the theories of Heinrich Schenker" (Straus 1997, 237), uses graphical notations-such as slurs and stems-to identify structural pitches from the embellishing ones.…”

Section: The Law Of Atonal Voice Leadingmentioning

confidence: 99%

An Issue between Contemporary Theory and Modern Compositional Practice A Study of Joseph Straus's Laws of Atonal Voice Leading and Harmony using Webern's Opus 12/2 and Crawford's String Quartet Mvt. 3

2013

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In his recent research project, music theorist Joseph Straus extends the traditional notions of smooth voice leading and the quality of harmony in tonal music to describe atonal voice leading and harmony. To achieve this goal, Straus proposes a theory called fuzzy transformations to analyze atonal music. Based on his findings, he further concludes the law of atonal voice leading and that of atonal harmony, which state that compositions, especially those in "more conservative styles," do obey these two laws. To test the validity of Straus's laws, I use Crawford's String Quartet Mvt. 3 and Webern's song op. 12/2 as case studies, examining the potential strengths and inherent weaknesses in Straus's fuzzy transformations, and further pointing out a conflict between music theory and compositional practice.

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“…[8] Philip Stoecker has proposed a seemingly logical addition to the small range of isographies through a new isography he has called axial isography (Stoecker 2002). In the relation of positive axial isography, two 3-node (trichordal) K-nets share an identical I transformation, and the differences between the subscripts of the remaining I and T transformations are complementary (mod 12).…”

Section: Isography and Dual Transformationsmentioning

confidence: 99%

Thoughts on Klumpenhouwer Networks and Mathematical Models

Nolan

2007

MTO

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Klumpenhouwer Networks, Trichords, and Axial Isography

Cited by 15 publications

References 0 publications

From Dürer's Magic Square to Klumpenhouwer Tesseracts: On Melencolia (2013) by Philippe Manoury

From Dürer's Magic Square to Klumpenhouwer Tesseracts: On Melencolia (2013) by Philippe Manoury

An Issue between Contemporary Theory and Modern Compositional Practice A Study of Joseph Straus's Laws of Atonal Voice Leading and Harmony using Webern's Opus 12/2 and Crawford's String Quartet Mvt. 3

Thoughts on Klumpenhouwer Networks and Mathematical Models

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