A Pitch‐Class Set Space Odyssey, Told by Way of a Hexachord‐Induced System of Genera
Identifieur interne : 000040 ( Main/Exploration ); précédent : 000039; suivant : 000041A Pitch‐Class Set Space Odyssey, Told by Way of a Hexachord‐Induced System of Genera
Auteurs : Bernard GatesSource :
- Music Analysis [ 0262-5245 ] ; 2013-03.
English descriptors
- Teeft :
- Allen forte, Atonal, Atonal music, Atte tenkanen, Bernard gates, Bernard gates music analysis, Bernard gates table, Bichromatic, Bichromatic genus, Blackwell, Blackwell publishing, Callender, Cardinality, Cartography, Central node, Chord quality, Chromatic, Chromatic genera, Combination cycle cell, Combination cycles, Combination interval, Combination interval cycles, Cyclic, Cyclic sets, Diatonic, Distant points, Equatorial, Eriksson, Forte, Fourier, Fourier spaces, General equaltempered harmony, General harmony, Generalized spaces, Generic, Generic hexachord family, Genus, Genus membership, Genus nodes, Genus prototypes, Hanson, Harmonic materials, Hexachord, Hexachord families, Hexachordal, Hexachords, Hexatonic, Hierarchical taxonomy, Histogram, Horizontal planes, Ibid, Inclusional, Inclusional growth chains, Interface, Intergeneric, Interval, Interval class, Interval classes, Intervallic, Intrageneric, Intuitive genera, Limit case, Maximally, Maxpoint, Modern music, Music analysis, Music theory, Natural categories, Node, Octatonic, Octatonic scale, Other cardinalities, Other genera, Other hexachords, Otics, Para, Pentachords, Pitch organisation, Point structure, Prime form, Prime forms, Progenitor, Progression, Prototype, Prototypical, Prototypical hexachord, Prototypical hexachords, Quality space, Quinn, Relational, Relative saturation, Richard cohn, Round table, Same cardinality, Same number, Same time, Samplaski, Scaling, Similarity, Similarity measures, Similarity relations, Single genus, Space odyssey, Spatial model, Straus, Subset, Supragenus, Tenkanen, Tetrachords, Transformational symmetries, Transpositional, Trichordal, Trichordal intervallic cells, Trichords, Tymoczko, Vector analysis, Weak joiners.
Abstract
The notion that pitch‐class sets might occupy some form of multi‐dimensional space has engaged a number of theorists over the years. The ‘space odyssey’ in this article delves into several new issues, such as a methodology for the creation of a comprehensive array of bonded inclusional growth chains, the formation of a diatonic‐to‐chromatic, M5‐induced spectrum of symmetrically arranged set classes and a simple method for establishing levels of affinity between set classes. These investigations lead to the advancement of a sixfold system of genera and to hierarchical distributions of all set classes, furnishing a distinct shape or profile to the whole set‐class universe and to each of the genera. A productive way of producing a three‐dimensional model incorporating all set classes presents itself if four foci, the ‘bichromatic’ 6–7 (0,1,2,6,7,8), hexatonic 6–20 (0,1,4,5,8,9), octatonic 6–30 (0,1,3,6,7,9) and whole‐tone 6–35 (0,2,4,6,8,10), are granted their own spatial ‘homes’ at distant points on an M‐invariant axis placed perpendicular to a diatonic 6–32 (0,2,4,5,7,9) to chromatic 6–1 (0,1,2,3,4,5) axis. A transparent globe would seem to be the most suitable vehicle for the representation of this arrangement, where the chromatic and diatonic foci take the ‘north’ and ‘south’ poles and the other four take their positions around the ‘equator’.
Url:
DOI: 10.1111/j.1468-2249.2012.00340.x
Affiliations:
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The ‘space odyssey’ in this article delves into several new issues, such as a methodology for the creation of a comprehensive array of bonded inclusional growth chains, the formation of a diatonic‐to‐chromatic, M5‐induced spectrum of symmetrically arranged set classes and a simple method for establishing levels of affinity between set classes. These investigations lead to the advancement of a sixfold system of genera and to hierarchical distributions of all set classes, furnishing a distinct shape or profile to the whole set‐class universe and to each of the genera. A productive way of producing a three‐dimensional model incorporating all set classes presents itself if four foci, the ‘bichromatic’ 6–7 (0,1,2,6,7,8), hexatonic 6–20 (0,1,4,5,8,9), octatonic 6–30 (0,1,3,6,7,9) and whole‐tone 6–35 (0,2,4,6,8,10), are granted their own spatial ‘homes’ at distant points on an M‐invariant axis placed perpendicular to a diatonic 6–32 (0,2,4,5,7,9) to chromatic 6–1 (0,1,2,3,4,5) axis. A transparent globe would seem to be the most suitable vehicle for the representation of this arrangement, where the chromatic and diatonic foci take the ‘north’ and ‘south’ poles and the other four take their positions around the ‘equator’.</div></front></TEI><affiliations><list></list><tree><noCountry><name sortKey="Gates, Bernard" sort="Gates, Bernard" uniqKey="Gates B" first="Bernard" last="Gates">Bernard Gates</name></noCountry></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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