Global Musical Tempo Transformations using Case Based ... - OFAI

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Case Layout Case 1 Case 2 Performance P1 Performance P2 Performance P3 Problem Description S1 R1 Solutions P1 P2 Problem Description S1 R2 Solutions P3 Requirements R1 Score S1 Requirements R2 S1 R1 Alternative Case Layout Case 1 Case 2 Problem Description P1 P2 Problem Description S1 R1 Solutions P1 P2 R2 P3 Solutions R2 P3 (a) (b) Figure 3.4: (a) The relation between score, performance requirements, and performances. (b) Two types of case layout, both representing the constellation shown in (a). available performance requirements. In this way, the constellation shown in figure 3.4 (a) again leads to two separate cases, as shown in figure 3.4 (b) bottom. Solving a problem then implies using the performance of a similar previously played melody to perform a new melody. An interesting question is which part of the musician’s knowledge of how to perform a melody can be transferred from one problem to another, and what kind of knowledge is needed explicitly to actually realize such a transfer. The actual problem solving steps where explicit domain knowledge is needed, are the Retrieve and the Reuse steps (we leave the learning oriented steps Revise and Retain aside here). For the retrieval of similar problems, the distance between problem descriptions must be assessed. That is, we must be able to specify how similar two scores are, and how similar two sets of performance requirements are. For this distance assessment to be useful, it must return small distance values for problems where the solution of one problem can be easily used to construct a good solution for the other problem. This may imply that the distance assessments should not be done directly on the problem descriptions itself, but on a derived, more abstract representation of it (e.g. a musical analysis of the score). For effective reuse of a performance that was retrieved 46
ased on similarity between problem descriptions, we need to know how the (expressivity of a) performance relates to the score and performance requirements. As we have seen in chapter 2, the nature of this relation is the topic of ongoing research and is far from being completely known. Nevertheless, some relevant aspects of musical expressivity are commonly agreed upon, e.g.: • expressivity serves to clarify musical structure • expressivity serves to express affective intentions In the next subsections, we will review some types of musical domain knowledge that we believe will be useful in a CBR system for transformation and generation of music performances. 3.5.1 Music Analysis The Implication/Realization Model Narmour [87, 88] has proposed a theory of perception and cognition of melodies, the Implication/Realization model, or I/R model. According to this theory, the perception of a melody continuously causes listeners to generate expectations of how the melody will continue. The sources of those expectations are two-fold: both innate and learned. The innate sources are ‘hard-wired’ into our brain and peripheral nervous system, according to Narmour [87], whereas learned factors are due to exposure to music as a cultural phenomenon, and familiarity with musical styles and pieces in particular. The innate expectation mechanism is closely related to the gestalt theory for visual perception as proposed by Koffka [68] and Köhler [69] and for audition by Bregman [16]. Gestalt theory states that perceptual elements are (in the process of perception) grouped together to form a single perceived whole (a ‘gestalt’). This grouping follows certain principles (gestalt principles). The most important principles are proximity (two elements are perceived as a whole when they are perceptually close), similarity (two elements are perceived as a whole when they have similar perceptual features, e.g. color or form, in visual perception), and good continuation (two elements are perceived as a whole if one is a ‘good’ or ‘natural’ continuation of the other). Narmour claims that similar principles hold for the perception of melodic sequences. In his theory, these principles take the form of implications. Any two consecutively perceived notes constitute a melodic interval, and if this interval is not conceived as complete, or closed, it is an implicative interval, an interval that implies a subsequent interval with certain characteristics. In 47
Page 1 and 2: Global Musical Tempo Transformation
Page 3 and 4: Contents 1 Introduction 9 1.1 Expre
Page 5 and 6: List of Figures 2.1 Time Maps; (a)
Page 7: List of Tables 5.1 Annotation error
Page 10 and 11: nominal performance). Even when (sk
Page 12 and 13: sity of ways in which a piece can b
Page 14 and 15: Another fundamental question is whe
Page 16 and 17: gain importance, which could accoun
Page 18 and 19: present throughout the whole piece.
Page 20 and 21: t’ g t t’ t’ t g f f s’ t
Page 22 and 23: music expressively, they provide a
Page 24 and 25: dependencies between curves at diff
Page 26 and 27: Harmonic intonation adjust pitches
Page 29 and 30: Chapter 3 Case Based Reasoning In t
Page 31 and 32: Solved Problems Unsolved Problem Pr
Page 33 and 34: Eager Learning Domain Model Problem
Page 35 and 36: Problem New Case RETRIEVE Learned C
Page 37 and 38: lem descriptions of the cases in th
Page 39 and 40: solutions (see [22, 3, 123]). We wi
Page 41 and 42: 3.3.5 The Retain Task When a good s
Page 43 and 44: order to treat case information in
Page 45: which use the knowledge of the doma
Page 49 and 50: According to the I/R model, the abo
Page 51 and 52: Retrieve task of the system. The re
Page 53 and 54: {〈x 1 , w 1 〉, · · · 〈x m
Page 55 and 56: Computing Similarity by compression
Page 57 and 58: Chapter 4 Research Goals 4.1 The Br
Page 59 and 60: 4.2 Focus of Attention in This Rese
Page 61: Case Retrieval Defining a way to de
Page 64 and 65: Performance recording .wav Performa
Page 66 and 67: is more appropriate for comparing w
Page 68 and 69: events corresponding to Transformat
Page 70 and 71: insertion, ornamentation, transform
Page 72 and 73: settings for larger sets of perform
Page 74 and 75: Tr1a Tr1b Tr1c Tr2a Tr2b Tr2c Error
Page 76 and 77: Tagging Interval Pairs This step co
Page 78 and 79: of the musical score (notes and cho
Page 80 and 81: I/R based retrieval In the second s
Page 82 and 83: In constructive adaptation, partial
Page 84 and 85: ing rules that specify which annota
Page 86 and 87: een scarcely used, or not at all),
Page 89 and 90: Chapter 6 Conclusions and Planned R
Page 91 and 92: 6.2.2 Performance Annotation We hav
Page 93 and 94: Related publications: • M. Gracht
Page 95 and 96: The other direction of evaluating t
Page 97 and 98:
Bibliography [1] A. Aamodt. Towards
Page 99 and 100:
[20] Sergio Canazza, Giovanni De Po
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[42] A. Gabrielsson. Once again: Th
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Page 105 and 106:
[93] E. Plaza and J. Ll. Arcos. Con
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[117] N.P. Todd. A computational mo
Page 109:
melody lead, 12 Model Based Reasoni
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