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51 See London, ‘Some Theories of Emotion in Music and their Implications for Research in Music Psychology’, 24.Google Scholar

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55 Edmund Husserl, The Phenomenology of Internal Time-Consciousness (The Hague, 1905–10; repr. 1964); summarized in Izchak Miller, Husserl, Perception, and Temporal Awareness (Cambridge, MA, 1984), 120ff.; revisited in David Lewin, ‘Music Theory, Phenomenology, and Modes of Perception’, Music Perception, 3 (1986), 327–92 (pp. 329ff.).Google Scholar

56 Peretz, Gagnon and Bouchard, ‘Music and Emotion’, 124.Google Scholar

57 See Dan Sperber and Deirdre Wilson, Relevance: Cognition and Communication (Oxford, 1995), 118; Emery Schubert, ‘Correlation Analysis of Continuous Emotional Response to Music: Correcting for the Effects of Serial Correlation’, Musicae scientiae, special issue 2001/02, 213–36.Google Scholar

58 On the basis of listeners' retrospective accounts, John Sloboda confirmed musicians' intuitive notion that melodic appoggiaturas are one of the features of Western classical music capable of triggering a marked emotional response. See Sloboda, ‘Music Structure and Emotional Response: Some Empirical Findings’, Psychology of Music, 19 (1991), 111–20.Google Scholar

59 Hence this view is opposed to that famously (though not uncontroversially) espoused by Leonard Meyer, who most recently concludes that states of feeling become emotional experiences ‘when they are at least tinged by uncertainty’ (‘Music and Emotion’, 353), something which music achieves through the physical-somatic conditions created by the statistical parameters being qualified through the action of syntactic and native processes which uniquely characterize the art form (p. 346). These generate arousal, so directing attention to what is still to come, thereby giving rise to implication. Since what is implied can never be more than probable, meaningful attention to music is necessarily characterized by uncertainty as to how past and present patterns will be continued and, ultimately, resolved (p. 354). Yet here – on the contrary – we are saying that informed anticipation is a key element in one's aesthetic response to music. See Ockelford, ‘Implication and Expectation in Music: A Zygonic Model’ (forthcoming, Psychology of Music, 2005).Google Scholar

60 Suzanne Langer, Philosophy in a New Key: A Study in the Symbolism of Reason, Rite and Art (Cambridge, MA, 1942; repr. 1957), 226ff.Google Scholar

61 Ibid.Google Scholar

62 Thomas Stearns Eliot, The Sacred Wood: Essays on Poetry and Criticism (London, 1920; repr. 1997), 54.Google Scholar

63 Ibid., 85.Google Scholar

64 See Eliot, Thomas Stearns, The Use of Poetry and the Use of Criticism (London, 1933), 118–19.Google Scholar

65 Reflecting further on the comparison with language, while it is the meanings of words that tend to elicit an emotional response, it is their syntactical structure and sonic qualities that induce the aesthetic component of our reaction to a text (beauty, felicity of expression and so forth). Repetition (the foundation of structure in music) sometimes plays a part: through rhyme, assonance, alliteration, anaphora and metre, for example. See Carlos Chavéz, Musical Thought (Cambridge, MA, 1961), 39, 40; Leonard Bernstein, The Unanswered Question (Cambridge, MA, 1976), 147–8; Ockelford, ‘A Theory Concerning the Cognition of Order in Music’, 168.Google Scholar

66 See London, ‘Some Theories of Emotion in Music’, 25.Google Scholar

67 See Dempster, Douglas, ‘Is There Even a Grammar of Music?‘, Musicae scientiae, 2 (1998), 55–65 (p. 58).CrossRefGoogle Scholar

68 See Rothgeb, John, ‘Thematic Content: A Schenkerian View’, Aspects of Schenkerian Theory, ed. David Beach (New Haven and London, 1983), 39–60 (p. 39): ‘Music, lacking access to the kinds of direct association with the phenomenal world central to most other art forms, was able to satisfy the universal requirement of association only through the “likeness of itself” – through self-repetition.’ Also Basil de Selincourt, ‘Music and Duration’, Reflections on Art, ed. Suzanne Langer (London, 1958), 152–60 (p. 156): ‘The value of repetition in music belongs of course to the peculiar inwardness of the art. A musical composition must be content to be itself. The reference and relations into which analysis resolves its life-current need point to no object, no event; they take the form of the creative impulse which is their unity and they repeat one another because iteration is the only outward sign of identity which is available to them.‘Google Scholar

69 Edward Cone, ‘On Derivation: Syntax and Rhetoric’, Music Analysis, 6 (1987), 237–55 (p. 237).Google Scholar

70 Ockelford, ‘The Role of Repetition in Perceived Musical Structures’, 141.Google Scholar

71 See Ockelford, The Cognition of Order in Music.Google Scholar

72 See Zbikowski, Lawrence, ‘Metaphor and Music Theory’, Music Theory Online, 4 (1998), vol. 1; and Conceptualizing Music: Cognitive Structure, Theory, and Analysis (New York, 2002). Building on the work of George Lakoff, Zbikowski shows how such notions are underpinned by culture-specific conceptual metaphors, mapped onto the domain of music-space from our perception of the physical world.Google Scholar

73 Ockelford, ‘The Magical Number Two, Plus or Minus One’.Google Scholar

74 See Narmour, Eugene, ‘Music Expectations by Cognitive Rule-Mapping’, Music Perception, 17 (2000), 329–98 (p. 364).Google Scholar

75 Observe that relationships (whether or not they are zygonic) which link different values use half-arrowheads (in contradistinction to full arrowheads, which are indicative of identity). Note also that some arrowheads are open and some are filled – the former showing a link between single values, and the latter indicating a compound connection within or between ‘constants’ (typically, values extended in time) – implying a network of relationships the same. For fuller explanations, see Ockelford, The Cognition of Order in Music.Google Scholar

76 A fuller discussion of key issues in zygonic theory, including what counts as sameness and similarity, and how these interact with the notions of salience, categorization and derivation, is to be found elsewhere. See Ockelford, ‘On Similarity, Derivation, and the Cognition of Musical Structure’.Google Scholar

77 See Garnham, Alan, Jane Oakhill and Philip Johnson-Laird, ‘Referential Continuity and the Coherence of Discourse’, Cognition, 11 (1982), 29–46.Google ScholarPubMed

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79 Cf. Meyer's reason for preferring the notion of implication to that of causation in music theory and analysis: that the former makes more sense in the context of uncertainty, which he holds to be the catalyst of emotional response to music (see, for example, Meyer, Style and Music: Theory, History, and Ideology, Philadelphia, 1989, 84ff.; ‘Music and Emotion, Distinctions and Uncertainties’, 346–7). However, as I argue above, since informed anticipation appears to play a central role in musical affect, uncertainty cannot, and it is because relationships between objects in music are only metaphorical that the concept of implication is preferable to that of causation. See also Sperber and Wilson, Relevance, 72, who contend that ‘for a representation to be amenable to logical processing, all that is necessary is for it to be well-formed’ (rather than semantically complete – that is, representative of a state of affairs in a possible or actual world). In Sperber and Wilson's terms, logic in language (that is semantically complete, and therefore capable of being true or false) can be described as propositional, whereas logic in music would be considered non-propositional (see also Dempster, ‘Is There Even a Grammar of Music?’, 61). In language, Sperber and Wilson contend (p. 84), ‘logical implication’ is a syntactic relation which holds purely by virtue of the formal properties of assumptions, involving no reference to their semantic properties. This supports the notion that logical implication – the keystone of zygonic theory – is applicable to music too. A comparable line of argument is advanced by Bob Snyder, Music and Memory (Cambridge, MA, 2000), 230: ‘By causing musical events to “point to” other musical events, it connects those events in a relation of implication… . Musical linearity is like a metaphor of physical causation, and indeed linearity is an attempt to make musical events seem to cause each other. (Note that much of the linearity in verbal narrative structures is based on causation – events are connected to other events through earlier events causing the later events.)’ See also Fred Maus, ‘Narrative, Drama and Emotion in Instrumental Music’, Journal of Aesthetics and Art Criticism, 55 (1997), 293–303.Google Scholar

80 See Raffman, Diana, Language, Music, and Mind (Cambridge, MA, 1993).Google Scholar

81 Tim Horton, ‘The Compositionality of Tonal Structures: A Generative Approach to the Notion of Musical Meaning’, Musicae scientiae, 5 (2001), 131–56 (p. 143).Google Scholar

82 Leonard Meyer, Emotion and Meaning in Music (Chicago, 1956), 49.Google Scholar

83 Arnold Schoenberg, Fundamentals of Musical Composition (London, 1967), 1.Google Scholar

84 Ibid., 8.Google Scholar

85 Thus creating an effect in some ways comparable to that produced by the technique of photomontage when it is used to form the image of a human face from many smaller pictures of faces. The expressions (happy, sad, etc.) on these individual physiognomies need not correspond to those evinced by the single, larger face. Hence there could be a number of smaller, sad images coming together to make a happy whole. So it is with minor chords in a major context and vice versa: by focusing one's attention on the detail, a particular aesthetic response may come to the fore; by attending more globally, a different reaction may be engendered. In fact, it is likely there will be an interaction between the two: the effect of a major tonality will be coloured by the minor elements within it (and vice versa). In his Auditory Scene Analysis (Cambridge, MA, 1990), Albert Bregman makes a similar observation in relation to the perception of Webern's arrangement of the Ricercar from Bach's The Musical Offering (p. 471). John Sloboda observes in ‘Music Structure and Emotional Response’ (p. 115) that sequences based on the cycle of fifths often underlie passages that listeners describe as being particularly laden with emotion. The current theory suggests that this may occur through the predictable transformation of motives from major to minor (and back) that repeated transposition within the framework of the diatonic major scale necessarily engenders.Google Scholar

86 Ockelford, Repetition in Music: Theoretical and Metatheoretical Perspectives, RMA Monographs, 13 (London, 2005).Google Scholar

87 See Schubert, ‘Correlation Analysis of Continuous Emotional Response to Music’, 216.Google Scholar

88 Sperber and Wilson, Relevance, 38ff.Google Scholar

89 Richard Davidson, ‘On Emotion, Mood, and Related Affective Constructs’, The Nature of Emotion: Fundamental Questions, ed. Paul Ekman and Richard Davidson (Oxford, 1994), 51–5 (p. 52).Google Scholar

90 Klaus Scherer and Marcel Zentner, ‘Emotional Effects of Music: Production Rules’, Music and Emotion, ed. Juslin and Sloboda, 361–92 (p. 370).Google Scholar

91 Ibid., 364–5.Google Scholar

92 Cook and Dibben, ‘Musicological Approaches to Emotion’, 67.Google Scholar

93 Note that these form a subset of the domain of ‘musical experience/knowledge’ identified in Figure 2.Google Scholar

94 See Schenker, Heinrich, Beethoven: Die letzten Sonaten: Sonate in As Dur Op. 110 (Vienna, 1972), 17.Google Scholar

95 Summarized in Gabrielsson and Lindström, ‘The Influence of Musical Structure on Musical Expression’.Google Scholar

96 For example, Eric Blom, Beethoven's Piano Sonatas Discussed (London, 1938), 230.Google Scholar

97 Other Beethoven sonatas that open with chords with the mediant at the top have spacing that conforms more immediately to that of the harmonic series. For example: op. 2 no. 3; op. 7; op. 10 no. 2; op. 90; op. 101.Google Scholar

98 However, this is a typical feature of Beethoven's late style – see Cooper, Martin, Beethoven: The Last Decade 1817–1827 (Oxford, 1985), 425 – and the opening sonority foreshadows greater extremes of register later in the movement; see, for example, bars 25–8.Google Scholar

99 See Hatten, Musical Meaning in Beethoven.Google Scholar

100 Including the great majority of Beethoven's other piano sonatas.Google Scholar

101 See Timothy Maher and Daniel Berlyne, ‘Verbal and Exploratory Responses to Melodic Musical Intervals’, Psychology of Music, 10 (1982), 11–27.Google Scholar

102 See Ockelford, ‘On Similarity, Derivation, and the Cognition of Musical Structure’.Google Scholar

103 See Cooper, Beethoven, 190.Google Scholar

104 Kinderman, ‘Integration and Narrative Design in Beethoven's Piano Sonata in A♭ Major, Opus 110‘, 117.Google Scholar

105 With the possible exception of the harmony constituting the fourth quaver of bar 3, which can be interpreted as B♭ minor⁷ or D♭ major⁶.Google Scholar

106 Cooper, Beethoven, 188.Google Scholar

107 Kinderman, ‘Integration and Narrative Design in Beethoven's Piano Sonata in A♭ Major, Opus 110‘, 117.Google Scholar

108 Ibid.Google Scholar

109 Ibid., 121.Google Scholar

110 See Cooper, Beethoven, 190–1.Google Scholar

111 Kinderman, ‘Integration and Narrative Design in Beethoven's Piano Sonata in A♭ Major, Opus 110‘, 120.Google Scholar

112 Through a zygonic relationship that combines imitation in the domains of relative pitch and perceived time – a so-called ‘syzygy’ (see Ockelford, The Cognition of Order in Music).Google Scholar

113 Ockelford, Repetition in Music; Rudolph Réti, The Thematic Process in Music (Westport, 1951).Google Scholar

114 Ockelford, Repetition in Music, 121.Google Scholar

115 English translations taken from Kinderman, ‘Integration and Narrative Design in Beethoven's Piano Sonata in A♭ Major, Opus 110‘, 121.Google Scholar

116 Christopher Ballantine, Music and its Social Meanings (Johannesburg, 1984), 74.Google Scholar

117 Cooper, Beethoven, 190.Google Scholar

118 Compare Bach's use of two folksongs in Variation 30 of the Goldberg Variations.Google Scholar

119 See, for example, Kinderman, ‘Integration and Narrative Design in Beethoven's Piano Sonata in A♭ Major, Opus 110'; Maus, ‘Narrative, Drama and Emotion in Instrumental Music'.Google Scholar

120 Ockelford, Repetition in Music, 111ff.Google Scholar

121 That is, transformational configurations can (and often do) sustain zygonic links in addition to their principal structural connection (see Figure 5).Google Scholar

122 ‘Profile’ is a term I coin in The Cognition of Order in Music to mean a series of relative values of pitch (thus being equivalent to ‘rhythm’ in the domain of perceived time) – see Figure 4.Google Scholar

123 Although, as is the case throughout op. 110, this classification identifies only the principal connections among a multiplicity of links; see above, note 108.Google Scholar

124 See Kinderman, ‘Integration and Narrative Design in Beethoven's Piano Sonata in A♭ Major, Opus 110‘, 117.Google Scholar

125 See Kinderman, ‘Integration and Narrative Design in Beethoven's Piano Sonata in A♭ Major, Opus 110‘, 140.Google Scholar

126 Cook and Dibben, ‘Musicological Approaches to Emotion’, 67.Google Scholar