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Soft Computing

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04.11.2015 | Focus

A quantum-like semantic analysis of ambiguity in music

verfasst von: Maria Luisa Dalla Chiara, Roberto Giuntini, Antonino Riccardo Luciani, Eleonora Negri

Erschienen in: Soft Computing | Ausgabe 6/2017

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Abstract

Is it possible and interesting to analyze ambiguity in music by means of logical methods? We give a positive answer to this question in the framework of an abstract semantics suggested by the theory of quantum information. The concepts of quantum superposition and of entanglement are used for a formal representation of musical thoughts, which are dealt with as a kind of holistic intensional meanings. We discuss, in particular, the following subjects: (1) the abstract concept of musical theme. (2) The critical relationship between text and music in the case of Lieder. (3) The semantic role of Leitmotive in Wagner’ s operas.

Vorheriger Artikel Quantum music

Nächster Artikel Do spins have directions?

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For technical details, see Dalla Chiara et al. (2010, 2015). Some basic intuitive ideas of the quantum computational semantics are close to the “quantum theory of concepts” that has been studied, for instance, in Aerts and Gabora (2005a, b); Aerts and Sozzo 2014). The technical developments of the two approaches are, however, different.

See Dalla Chiara et al. (2012).

In a bright little brook/ there shot in merry haste/ a capricious trout:/ past it shot like an arrow.

In einem Bächlein helle, da schoss in froher Eil, die launische Forelle, vorüber wie ein Pfeil.

A. Schönberg,“Das Verhältniss zum Text”, Der Blaue Reiter, München, 1912. English translation of the author in Style and Idea, Philosophical Library, New York, 1950.

Know’st thou the land where the lemons flower, / ’Mid shady leaves the golden oranges glow, / A gentle breeze blows from a blue heaven, / The tranquil myrtle and the bay trees thrive?/ Know’st thou it? / Thither, oh my love, / I long to go with thee! / Know’st thou the house? On pillars rests its roof, / The hall is bright, the chambers dimly glow, / And statues stand and gaze down on me; / Poor child, what have they done to thee? / Know’st thou it? /Thither, oh my protector, / I long to go with thee! / Know’st thou the mountain and its cloudy path? / In the mist a mule picks its way, / In caves the dragon’s ancient brood doth dwell; / The rocks will tumble, and after them the flood. / Know’st thou it?/ Our way leads thither,/ Father, let us go!

Aerts D, Gabora L (2005a) A theory of concepts and their combinations I: the structure of the sets of contexts and properties. Kybernetics 34:167–191CrossRefMATH

Aerts D, Gabora L (2005b) A theory of concepts and their combinations II: a Hilbert space representation. Kybernetics 34:192–221CrossRefMATH

Aerts D, Sozzo S (2014) Quantum entanglement in conceptual combinations. Int J Theor Phys 53:3587–3603CrossRefMATH

Barenboim D (2008) Music quickens time, Verso, London

Dalla Chiara ML, Giuntini R, Ledda A, Leporini R, Sergioli G (2010) Entanglement as a semantic resource. Found Phys 40:1494–1518MathSciNetCrossRefMATH

Dalla Chiara ML, Giuntini R, Luciani AR, Negri E (2012) From quantum information to musical semantics, (illustrated by C. Seravalli). College Publications, London

Dalla Chiara ML, Giuntini R, Leporini R, Sergioli G (2015) A first-order epistemic quantum computational semantics with relativistic-like epistemic effects. Fuzzy Sets Syst (to appear)

Titel: A quantum-like semantic analysis of ambiguity in music
verfasst von: Maria Luisa Dalla Chiara
Roberto Giuntini
Antonino Riccardo Luciani
Eleonora Negri
Publikationsdatum: 04.11.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 6/2017
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-015-1895-y

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