The Geometry of Musical Chords
- 7 July 2006
- journal article
- other
- Published by American Association for the Advancement of Science (AAAS) in Science
- Vol. 313 (5783), 72-74
- https://doi.org/10.1126/science.1126287
Abstract
A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.Keywords
This publication has 14 references indexed in Scilit:
- Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual PrinciplesMusic Perception, 2001
- As Wonderful as Star Clusters: Instruments for Gazing at Tonality in Schubert19th-Century Music, 1999
- Voice-Leading SpacesMusic Theory Spectrum, 1998
- Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited TranspositionJournal of Music Theory, 1998
- Neo-Riemannian Operations, Parsimonious Trichords, and Their "Tonnetz" RepresentationsJournal of Music Theory, 1997
- Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic ProgressionsMusic Analysis, 1996
- Properties and Generability of Transpositionally Invariant SetsJournal of Music Theory, 1991
- Geometrical approximations to the structure of musical pitch.Psychological Review, 1982
- Meta-Variations, Part IV: Analytic Fallout (I)Perspectives of New Music, 1972
- ON A GENERALIZATION OF THE NOTION OF MANIFOLDProceedings of the National Academy of Sciences, 1956