The unfolding of tonality in the music of Béla Bartók

Music Analysis

Volumn 17, Issue 1, 1998, Pages 21-38

  Cooper, David ^a  

^a NONE

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[No Author keywords available]

Indexed keywords

EID: 61949193714     PISSN: 02625245     EISSN: None     Source Type: Journal    
DOI: 10.2307/854369     Document Type: Review

References (21)

1. George Perle, 'Symmetrical Formations in the String Quartets of Béla Bartók', Music Review, 16 (November 1955), pp. 300-312;
2. Twelve-Tone Tonality (Berkeley: University of California Press, 1977);
3. Serial Composition and Atonality (Berkeley: University of California Press, 1981).
4. Elliott Antokoletz, The Music of Béla Bartók (Berkeley: University of California Press, 1984).
5. Paul Wilson, The Music of Béla Bartók (New Haven: Yale University Press, 1992).
6. B. Suchoff (ed.), Béla Bartók Essays (London: Faber, 1971), pp. 367-71.
7. The word 'folding' is used by analogy with the culinary term. It is a term which also interested the French philosopher Gilles Deleuze - see for instance The Fold: Leibniz and the Baroque, trans. T. Conley (London: The Athlone Press, 1993).
8. Wilson, The Music of Béla Bartók, p. 28.
9. The term 'artefact' has been adopted from the field of cell biology, where it indicates apparent cellular features observed through the microscope which are actually the result of the method of preparation rather than components of the tissue. Two types of artefact are found: intrinsic ones which are distortions of cellular features (cell biology) or musical primitives (OMR), and extrinsic ones which are formed from extraneous matter caused by the reaction of fixative with other chemicals used for tissue preparation (cell biology), or ink blots and other imperfections (OMR). See J. R. Baker, Cytological Technique (London: Chapman and Hall, 1966), p. 25.
10. This refined algorithm makes use of the properties of tonal music determined by the algorithm described in this article, and the accidentals determined by the process of OMR to deduce the key signature. See D. Cooper, K. C. Ng and R. D. Boyle, 'An Extension of the MIDI File Format: Expressive MIDI - expMIDI', in E. Selfridge-Field (ed.), Beyond MIDI: The Handbook of Musical Codes (Boston: MIT Press, 1997) for a discussions of the means by which notational data can be included within standard MIDI Files.
11. Technical details of the algorithm are given in K. C. Ng, R. D. Boyle and D. Cooper, 'Automatic Detection of Tonality using Note Distribution', Journal of New Music Research, 25/iv (December 1996), pp. 369-81.
12. D. Butler, 'On Pitch-Set Properties and Perceptual Attributes of the Minor Mode', in M. R. Jones and S. Holleran (eds.), Cognitive Bases of Musical Communication (Washington: American Psychological Association, 1992), pp. 161-9.
13. C. L. Krumhansl, Cognitive Foundations of Musical Pitch, (New York: Oxford University Press, 1990).
14. For convenience, pitches 0, 3 and 7 are described as tonic, mediant and dominant. Given that the experiments were aural ones, it is not possible to distinguish a flat mediant (e.g. Emusic flat sign) from a sharp supertonic (e.g. Dmusic sharp sign). In Krumhansl's plots an increase in the y value of a data point indicates an increase in the subjective rating, the scale of possible values running from 1 ('very bad') to 7 ('very good'). See Krumhansl, Cognitive Foundations, p. 21.
15. Butler, 'On Pitch-Set Properties'.
16. See M. Gillies, Notation and Tonal Structure in Bartók's Later Works (New York: Garland, 1989).
17. The term 'cell Z' was actually first used by Leo Treitler in 'Harmonic Procedure in the Fourth Quartet of Béla Bartók', Journal of Music Theory, 3 (1959), pp. 292-8.
18. J. J. Bharucha, 'Event Hierarchies, Tonal Hierarchies, and Assimilation: A Reply to Deutsch and Dowling', Journal of Experimental Psychology: General, 113 (1984), pp. 421-5.
19. Lévi-Strauss, C., The Raw and the Cooked (London: Penguin, 1986), pp. 16-22.
20. This figure, which Lendvai describes as hypermajor or hyperminor, depending on the modality of the underlying triad, was described as 'your leitmotif' in a letter written to Geyer in September 1907. János Demény (ed.), Béla Bartók Letters (London: Faber, 1971), p. 87.
21. According to Benjamin Suchoff, 'All melody-sections, interludes and the postlude are polymodal collections, based on G, E and D as fundamental notes, which combine Phrygian and Lydian pentachords for the most part.' Suchoff, 'Fusion of National Styles: Piano Literature, 1908-11', in M. Gillies (ed.), The Bartók Companion (London: Faber, 1993), pp. 124-45 (p. 127).