Generative Theory Of Tonal Music Research Articles

Enacting musical maquettes: A cognition-inspired compositional approach

This paper is a practice-led case study on Fred Lerdahl's "Cognitive Constraints on Compositional Systems". The model attempts to define an artificial compositional grammar in terms of a "universal listening syntax" based on Lerdahl's co-authored A Generative Theory of Tonal Music. Through demonstrating the practical application of the constraints, the author reflects on the model's usefulness in light of the contemporary compositional context. Notably, the theory presents abstracted pitch and rhythmic material as an aesthetically neutral syntax, therefore it can only provide stylistically ambiguous infrastructures akin to a musical maquette that needs to be further enacted at the composer's discretion.

Implementation of melodic morphing based on generative theory of tonal music

This paper proposes a new morphing method to generate a melody, given two melodies represented by time-span trees obtained from the generative theory of tonal music (GTTM). In this paper, we define a feature structure based on a time-span tree and the distance between two structures. Next, we construct a lattice of subsumption relations among these structures and define three algebraic operations: reduction, meet, and join. First, we conduct these operations in the pure algebraic domain and a new melody is as an interpolation in the lattice; thereafter, we render the obtained tree into a music melody, assigning a priority order among candidate branches. We confirmed that our morphing algorithm generated new variations with satisfactory quality.

Zur Suche nach Logik und Bedeutung von Musik. Geschichte und Gegenwart von Interdisziplinarität im Bereich musiktheoretischer Forschung

This essay reviews the impact of (music) psychology on music theory from the late 19th century until the present. From the beginning, music psychology’s focus on musical listening has been the main reason for this impact. The changes in Hugo Riemann’s theory from physical explanations (especially for major-minor-polarity), derived, amongst others, from Hermann von Helmholtz’ research, to a phenomenological model has been deeply influenced by the “Tonpsychologie” of Carl Stumpf who, in turn, can be termed one of the founders of gestalt theory. For Riemann, the idea that “facts of consciousness” had priority over physical conditions gained paramount importance. In particular, it seemed to explain the impression of consonance as release and dissonance as striving force more feasibly than ratios of oscillation speeds. Ernst Kurth took up this idea. His work relies on the gestalt experience, more specifically on the experience of energetic force, another foundation derived from Arthur Schopenhauer’s philosophy. Kurth’s music theory introduced a novel spatial, dynamic principle of form. Although Robert Hatten’s idea of an “energetic shaping through time” and his theory of gestures reference Kurth’s ideas, the linguistic roots of his “topic”-oriented concept betray substantial differences to Kurth’s process-based idea of musical form. Fred Lerdahl’s and Ray Jackendoff’s Generative Theory of Tonal Music connects to gestalt theoretical principles, linked, however, as only in early gestalt theory, to the idea of perceptual universals, presupposing that gestalt formations (e. g., the grouping of durations) are processed “automatically”. More recent gestalt theory has replaced this universalist idea by a stronger focus on learning. Subsequent theories of musical cognition retain the gestalt term as a prominent model. The focus of research, however, is usually not derived from questions about the cognition of musical structure alone, but guided by the intention to formalize cognition models with the help of computer programming languages, often without properly reflecting the modes of thinking and listening that such models presuppose.

Asymmetric binarity as a cognitive universal: The rhythm of syntactic structures

Abstract In syntactic and rhythmic structure, universal rules group elements hierarchically and asymmetrically. In syntax, the operation ‘merge’ is theorized to combine elements in phrasal structures, with one element governing the other, recursively, to form sentences. In rhythm, a similar asymmetric hierarchy of beats is proposed in the Generative Theory of Tonal Music. Just like syntactic processing, assigning beats into rhythmic strings, ‘beat induction,’ is automatic and subconscious. Merge and beat induction assign structure not only to grammatical phrases, but also to inherently unstructured sequences. Prompted by overlapping neural support for the processing of both language and music, this study tested whether the process of assigning asymmetric binarity has a domain-general neural substrate. Structurally comparable syntactic and rhythmic stimuli were presented in a functional MRI experiment, with region-of-interest analyses focusing on core regions of the language network, inferior frontal and posterior superior temporal cortex. Results support prior research suggesting overlap in brain regions responsible for both rhythmic and syntactic processing, specifically in the inferior frontal operculum. However, the function of these regions for syntactic and rhythmic input is likely different, as syntactic and rhythmic grammaticality were not processed symmetrically within each region. These results suggest that the left inferior frontal operculum and the posterior superior temporal gyrus are domain general in their overall cortical roles, yet domain-specific in the type of processes they support within the domains of syntactic and rhythmic processing.

Implicit Counterpoint in Gjerdingen's Schemata

Robert Gjerdingen has claimed that schema finding diverges from contrapuntal pitch reduction, Schenkerian or otherwise. Commentators have criticized his approach (see the reviews by Joel Lester in Journal of Music Theory [1990] and Kofi Agawu in Music Theory Spectrum [1991]) and have discussed intersections between schemata and contrapuntal reduction (see the articles by Folker Froebe and Oliver Schwab-Felisch in Music Theory and Analysis [2014] and by Stefan Rohringer in Zeitschrift der Gesellschaft für Musiktheorie [2015]). Here I address this conundrum from a different angle: I propose that schema analysis may be approximated by two heuristics, which are closely related to the issue identified in Fred Lerdahl and Ray Jackendoff's A Generative Theory of Tonal Music (1983) as finding the head of a time span. By giving the highest priority to tritone resolutions within a metric segment and otherwise realigning consonances with strong beats by removing dissonances, it is possible to approximate the reductive workings of schema analysis. This is demonstrated through a preliminary sample of two hundred tacit reductive decisions from Gjerdingen's Music in the Galant Style. I suggest the possibility that Gjerdingen's locally top-down search for complete patterns interacts with a more bottom-up, implicit reductive process, regardless of the identity of the emergent schema. I also discuss some of the potential implications of the heuristics for theory and analysis as well as for interdisciplinary work on schema finding.

Editorial: The beginning of the human language story

In syntactic and rhythmic structure, universal rules group elements hierarchically and asymmetrically. In syntax, the operation ‘merge’ is theorized to combine elements in phrasal structures, with one element governing the other, recursively, to form sentences. In rhythm, a similar asymmetric hierarchy of beats is proposed in the Generative Theory of Tonal Music. Just like syntactic processing, assigning beats into rhythmic strings, ‘beat induction,’ is automatic and subconscious. Merge and beat induction assign structure not only to grammatical phrases, but also to inherently unstructured sequences. Prompted by overlapping neural support for the processing of both language and music, this study tested whether the process of assigning asymmetric binarity has a domain-general neural substrate. Structurally comparable syntactic and rhythmic stimuli were presented in a functional MRI experiment, with region-of-interest analyses focusing on core regions of the language network, inferior frontal and posterior superior temporal cortex. Results support prior research suggesting overlap in brain regions responsible for both rhythmic and syntactic processing, specifically in the inferior frontal operculum. However, the function of these regions for syntactic and rhythmic input is likely different, as syntactic and rhythmic grammaticality were not processed symmetrically within each region. These results suggest that the left inferior frontal operculum and the posterior superior temporal gyrus are domain general in their overall cortical roles, yet domain-specific in the type of processes they support within the domains of syntactic and rhythmic processing.

Music syntactic processing

Music Syntax refers to the principle of combining discrete key elements into hierarchical system. Organization of pitches based on tonality harmony is the most important music syntax which affects the expectation, the construction and the feedback on the music events of the audience from which aesthetic musical experience is finally produced. Lerdahl and Jackendoff proposed a musical tree-structure that parallel to linguistic syntax in their generative theory of tonal music (GTTM). And Rohrmeier further specified hierarchical generativerules of pitch syntax in the generative syntax model (GSM). Both the GTTM and the GSM put forward the analogy between music syntax and linguistic syntax. But what is obviously different from language processing is that the processing of music syntax of the audience reveals a cross-empiricalness effects. Whether in early studies of behavioristics or in recent studies of EPR, most evidences support that there is a syntax diagram guiding people’s musical expectations without much association with their musical experiences among western audience, at least in the sense of simple linear syntax. Therefore, the acquisition of music syntax under the non-explicit conditions arouses researchers’ thinking on music syntax processing mechanism. Current studies have not reached a consensus on processing of syntactic structure, and two antagonistic theories “Cognitivism” and “Physicalism” have generated. “Cognitivism” put forward that since pitch syntax reflects abstract cognitive structural relations between sounds and meanings, syntactic integration requires the help of scheme drive of long-term memory, of which MUSACT and the shared syntactic integration resource hypothesis (SSIRH) are the representative theories. While “Physicalism” considered that it only needs the help of short-term memory in perception drive because pitch syntax has a property of psychoacoustics derived from voice frequency. And the periodicity pitch model (PP) and its derivate, the auditory short-term memory (ASTM), are the representative theories. Both theories demonstrated their viewpoints respectively from the angle of theoretical model, behavioral studies and cognitive neuroscience.

Listening as a Creative Act

Some important theories of music cognition, such as Lerdahl and Jackendoff’s (1983)A Generative Theory of Tonal Music, posit an archetypal listener with an ideal interpretation of musical structure, and many studies of the perception of structure focus on what different listeners have in common. However, previous experiments have revealed that listeners perceive musical structure differently, depending upon their music background and their familiarity with the piece. It is not known what other factors contribute to differences among listeners’ formal analyses, but understanding these factors may be essential to advancing our understanding of music perception.We present a case study of two listeners, with the goal of identifying the differences between their analyses, and explaining why these differences arose. These two listeners analyzed the structure of three performances, a set of improvised duets. The duets were performed by one of the listeners and Mimi (Multimodal Interaction for Musical Improvisation), a software system for human-machine improvisation. The ambiguous structure of the human-machine improvisations as well as the distinct perspectives of the listeners ensured a rich set of differences for the basis of our study.We compare the structural analyses and argue that most of the disagreements between them are attributable to the fact that the listeners paid attention to different musical features. Following the chain of causation backwards, we identify three more ultimate sources of disagreement: differences in the commitments made at the outset of a piece regarding what constitutes a fundamental structural unit, differences in the information each listener had about the performances, and differences in the analytical expectations of the listeners.

Computational Reconstruction of Cognitive Music Theory

In order to obtain a computer-tractable model of music, we first discuss what conditions the music theory should satisfy from the various viewpoints of artificial intelligence and/or other computational notions. Then, we look back on the history of cognitive theory of music, i.e., various attempts to represent our mental understandings and to show music structures. Among which, we especially pay attention to the Generative Theory of Tonal Music (GTTM) by Lehrdahl and Jackendoff, as the most promising candidate of cognitive/computational theory of music. We briefly overview the theory as well as its inherent problems, including the ambiguity of its preference rules. By our recent efforts, we have solved this ambiguity problem by assigning parametrized weights, and thus we could implement an automatic tree analyzer. After we introduce the system architecture, we show our application systems.

Perceptual evaluation of musicological cues for automatic song segmentation.

The present study evaluated how well boundaries predicted by nine rules, each of them relying on one particular musical cue, can predict perceptual boundaries. The rules were taken from two models: the local boundary detection model (LBDM) by Cambouropoulos (2001) and the generative theory of tonal music (GTTM) by Lerdahl and Jackendoff (1983) in the form quantified by Frankland and Cohen (2004). Furthermore we added the cue timbre change. The predicted boundary profiles from each rule were correlated with perceptual boundary profiles of six songs obtained in a previous study (Bruderer, McKinney, & Kohlrausch, 2009). The individual rule having the highest correlation with the perceptual boundaries was the LBDM-onset. The optimal combination of three rules results in the combination of LBDM-onset, GTTM-rest, and timbre change, yielding a physical correlation of 0.80 to 0.89 between perceptual and model boundary profiles. Analysis of the perceptual cues given for boundaries not predicted by the model suggests that incorporating tempo change and harmonic progression could improve the model predictions. The optimal rule combination for segmentation profiles of polyphonic versions of the same songs as obtained in Bruderer, McKinney, and Kohlrausch (2010) was the combination of the LBDM-onset, timbre change, and the start of a rest.Keywords: segmentation, cues, popular musicSupplemental materials: http://dx.doi.org/10.1037/a0026872.supp(ProQuest: ... denotes formulae omitted.)Listening to music comprises not only the aesthetic experience but also the interpretation of the musical form. Based on the structure of this form, the listener is able to segment a musical piece into smaller parts. The segmentation process has been studied perceptually (e.g., Deliege, 1987; Clarke & Krumhansl, 1990; Krumhansl, 1996; Lar- tillot & Ayari, 2008; Nooijer, Wiering, Volk, & Tabachneck-Schijf, 2008; Pearce, Mullensiefen, & Wiggins, 2008; Lartillot & Ayari, 2009) as well as musicologically (Lerdahl & Jackendoff, 1983) and different types of cues have been identified that convey the structure of music, including change in note duration, breaks, and change in pitch. Some of these cues have been incorporated into musicological models for music segmentation (e.g., Tenney & Polansky, 1980; Cambouropoulos, 2001; Temperley, 2001; Bod, 2002; Ferrand, 2004; Frankland & Cohen, 2004). However, it is not yet clear how well these models are also able to predict boundaries in pieces with a duration of several minutes or those taken from musical genres other than classical music.Several studies tested automatic segmentation algorithms for their correlation with perceptually annotated data. For example, Cambou- ropoulos (2001) tested his model on a set of 52 melodies, for which musicians had manually marked preferred punctuation positions on a musical score. Thom, Spevak, and Hothker (2002) tested the perfor- mance of two algorithms on the Essen folk song collection (Schaf- frath, 1995), which contains segmentation boundaries added by mu- sicologists. They also asked 19 musicians to indicate salient melodic chunks of10 musical excerpts by placing a mark in the musical score above the first note of the chunk. The indicated boundaries, thus, rather represent where experts think a boundary should occur, instead of where they are actually perceived.The goal of the present study was to compare the boundaries predicted by cues taken from musicological models with perceptual boundary profiles obtained in our previous perceptual studies (Brud- erer, McKinney, & Kohlrausch, 2009, 2010). In these studies, we executed several perceptual experiments to better understand how participants segment popular music pieces. In a first experiment, about 20 participants were asked to indicate segment boundaries while listening to the playback of the song. From the boundary indications of all participants about 10 boundaries were selected for each song (see Bruderer et al. …

Review of Danuta Mirka,Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–1791(Oxford University Press, 2009)

[1] Danuta Mirka's Metric Manipulations is a welcome addition to the impressive body of work on rhythm and meter that our field has produced during the past few decades-welcome especially because it brings eighteenth-century theories of rhythm and meter more fully into the current discussion than do most earlier volumes. Like William Rothstein in Phrase Rhythm in Tonal Music, a book to which she refers as of the most important catalysts of [her] study (xi), Mirka fashions an intricate counterpoint of eighteenth-century thought and more recent ideas.[2] She begins to weave this counterpoint in the first chapter (Musical Meter between Composition and Perception), in which she explains the hierarchical metric theories of Kirnberger, Schulz and Koch, then links these to the more recent hierarchical theories of Cooper and Meyer, Yeston, and Lerdahl and Jackendoff.(1) From these hierarchical models, she then turns toward dynamic, perception-based models of meter (a dynamic model being necessary for her later analyses of metric manipulations). Christopher Hasty's theories assume prominence here, but they are blended with those of Jackendoff-not the Jackendoff of A Generative Theory of Tonal Music (1983), but of Consciousness and the Computational Mind (1987); Mirka's analytical approach combines Hasty's idea of projection with Jackendoff's linguistics-inspired notion of a parallel processor.(2) Mirka's processor models listeners' metric perceptions by busily gathering information from a given musical surface and, on the basis of this information, selecting possible metric organizations. Being a multiple-analysis processor, it is prepared to fluctuate between conflicting metric interpretations when confronted with complex contexts. The Hasty-Jackendoff fusion is evident in Mirka's musical examples; under many of the score excerpts, one finds hierarchical dot diagrams, but the dots are joined by projective arrows, a la Hasty.[3] Having introduced her processor, Mirka puts it to work in the analysis of eighteenth-century music. She wisely chooses to focus on a circumscribed body of eighteenth-century repertoire-on two composers (Haydn and Mozart), on one medium (music for strings), and on a five-year span (1787-91). A wealth of wonderful music and, specifically, of metric complexities is included within her chosen limits; there is plenty of grist for the processor's mill. In Chapters 2-6, Mirka describes the workings and the results of the processor in a variety of metric situations. She begins each of these chapters with relevant excerpts from the writings of late eighteenth-century theorists, then presents numerous pertinent analyses of excerpts by Haydn and Mozart. Since the theoretical passages inform the subsequent analyses, one has the feeling that Mirka's processor models the perceptions not of just any listener, but specifically those of an eighteenth-century Kenner.[4] In the second chapter, she describes the types of metric information that the processor adduces during the meter-finding process at the openings of movements. This information includes numerous phenomenal accent types discussed by recent metric theorists, but also a variety of melodic and harmonic factors, parallelism, and streaming (i.e., the manner in which attacks partition into streams). The latter factor is especially relevant to the chosen repertoire; Mirka demonstrates how Haydn and Mozart often throw a monkey wrench into the meter-finding process by indulging in unusual interactions between the bass and upper-voice streams (59-69). The third chapter describes and illustrates the processor's workings once the initial meter-selection has occurred-its tenacious projective activity and the challenges that it encounters (such as missing beats, general pauses, fermatas and syncopations).[5] Chapters Four, Five, and Six deal with various methods of changing meter. As Mirka illustrates with excerpts from Koch and Riepel, eighteenth-century musicians were willing to acknowledge changes in composed meter, although the notated meter usually remained constant in the music of their time. …

Ranking Metrical Constraints in Music Perception - An Empirical Study

This paper presents the results of an empirical research into the ordering of metrical preference rules/constraints from the group MPR5, as proposed in A Generative Theory of Tonal Music (Lerdahl & Jackendoff, 1983). A hundred and twenty randomly selected undergraduate students (30 musicians and 90 nonmusicians) were played twelve metrical sequences accorded with the MPR5 examples from GTTM , of which half complied with and half contradicted their expectancies. The participants were prompted to press a button when certain they heard a stressed beat. The answer distributions suggest that six constraints can be ranked into three larger groups, as follows: physical stress (dynamic, harmony), melodic stress (pitch, slur, length), ornamental stress (articulation). Musicians achieved better results than nonmusicians, and the response latencies considerably rose in the stimuli contradicting expectancies, but the internal constraint rankings seemed relatively stable irrespective of the two factors (musician/nonmusician; expected/unexpected suggestion).

On the non-existence of music: Why music theory is a figment of the imagination

We argue for an approach to the theory of music which starts from the position that music is primarily a construct of human minds (and secondarily a social construct) and contrast it with the approach implicit in the work of some music theorists, which treats music as though it were an externally defined quasi-Platonic absolute. We argue that a natural conclusion of this approach is that music theory, while already being a kind of folk psychology, can benefit from being more explicitly informed by music cognition studies. We give examples from work in the computational modelling of music cognition, following our approach, which attempts to place each musical phenomenon in an ecological context motivated by evolutionary considerations, and which aims to explain musical phenomena independently of the explicit intervention of the theorist. We argue that only thus can a theory be said veridically to explicate the phenomenology of music. We place our argument in context of the Generative Theory of Tonal Music (Lerdahl & Jackendoff, 1983), Generative Linguistics, and other papers in the current volume, and compare them all with results of modelling studies based on our espoused approach.

The application of GTTM on 20th century modal music: Research based on the analysis of Yannis Constantinidis's “44 Greek miniatures for piano”

This paper examines the adaptation and expansion of Lerdahl’ s & Jackendoff s Generative Theory of Tonal Music so that it may be applied on the analysis of 20th century modal music. Based on the premise that a considerable part of the theory's rules are universal — meaning that the principles of music perception and cognition are the same for all experienced listeners regardless of the musical idiom in which they are experienced — the application of GTTM to musical idioms other than the Western classical one requires formulation of idiom-specific well-formedness and preference rules, and description of the special tonal hierarchy. These tasks may be accomplished through the analytical study of a considerable quantity of music representing a certain idiom, and the description of its features in relation to the four parts of the GTTM methodology. The chosen analytical object — 44 Greek miniatures for piano — is representative of the musical idiom deriving from the amalgamation of Greek modal music and 20th century harmonization techniques, distinctive of the musical style of Greek composer Yannis Constantinidis. An inductive methodological process was used for the individual and comparative analysis of all 44 pieces. This paper includes three complete GTTM sample analyses from the 44 piano pieces, a summary of the stylistic characteristics of the analyzed music, and the formulation of the special well-formedness and preference rules, introduced as either new rules to the theory or adaptations of the existing ones.

Adaptation of Grouping Structure Analysis in GTTM to Hierarchical Segmentation of Dance Motion

In this paper, the authors propose the adaptation of the rules used in the grouping structure analysis in Lerdahl and Jackendoff's “A Generative Theory of Tonal Music (GTTM)” to dance motion analysis. The success of the adaptation realizes the segmentation of dance motion in a hierarchical fashion. The analysis method obtained by the trial of the above adaptation consists of the following procedures. A motion-capture data stream of a dance is first divided into a sequence of events by piecewise linear regression. The hierarchical structure of groups each of which consists of a sequence of the events is then extracted by applying the grouping rules adapted to dance motion analysis. The above method is applied to motion-data streams acquired by motion capture systems. The obtained results indicate the following advantages: (1) The structure of hierarchical segmentation is precisely extracted in response to the characteristic of an analyzed dance. (2) The extraction of the hierarchical segmentation provides the possibility of the development of a technique distinguishing the oversegmentation from regular boundaries. (3) The possibility of utilizing the information of hierarchical segmentation for the comparison of dance performances is suggested.

Genesis and Architecture of the GTTM Project

I EXAMINE THE INTELLECTUAL AND MUSIC-THEORETIC origins of A Generative Theory of Tonal Music (Lerdahl & Jackendoff, 1983) and review the crucial steps in theory construction that led to its overall architecture. This leads to a discussion of how shortcomings in GTTM motivated developments in Tonal Pitch Space (Lerdahl, 2001). I conclude with a diagram that encompasses the major components of the expanded GTTM/TPS theory.

Music psychology: The building of a community.

ABSTRACT-Although music psychology as a research topic can be traced back to at least the 1880s, it was not until the 1980s that it became an academic discipline with its own identity. The autobiographies in this issue describe the transformation of music psychology from a topic pursued by isolated individuals in many different disciplines, into a more unified field. The turning point for the field came in the 1980s and 1990s when there was a rapid growth of specialized venues for interdisciplinary research in music: journals, national and international conferences, national and international societies, institutes and centers for research, and educational programs. Research was disseminated as never before, connecting researchers all over the world and forming a community of music psychology practitioners who share a common set of methods and theories. This has resulted in the bringing together of formerly separate lines of research, for example, research on music and the brain has now become an important part of music psychology; the formation of educational programs where students can earn degrees in music psychology; the building of a historiography for the field; and an expansion of research topics to cover all major aspects of music. What defines an area of research as an academic discipline separate from related or parent disciplines? For music psychology an important part of the definition seems to be the existence of a community of researchers from disparate fields. The autobiographies in this issue describe the transformation of music psychology from a research topic pursued by isolated individuals in many different disciplines, into an academic discipline with its own identity. When and why did this transformation take place, and how has it changed research in music psychology? The contributors to this issue have addressed these questions through their own personal stories. As a research topic, music psychology can be traced to at least the 1880s in Germany and Austria. The work of Hermann von Helmholtz (a physicist, physician and physiologist) can be considered the start of empirical research in psychoacoustics and music perception, but there was also an avid interest in higher-order cognitive processing of music. Psychologists (such as Carl Stumpf) and systematic musicologists (for example, Richard Wallaschek) pursued philosophical, theoretical and sometimes empirical work in music cognition (Graziano & Johnson, 2006) . At the same time in late nineteenthcentury Germany, neurologists pursued a similar but completely separate research path investigating acquired impairments in music skill in order to map brain localization of music function (Johnson & Graziano, 2003; Johnson, Graziano, 8c Hayward, in press) . Although dialogue and exchanges of ideas took place between psychologists and musicologists, there were very few substantive interactions between physiologists, psychologists/musicologists and neurologists. These disconnected lines of research - music perception, music cognition, music and brain - continued throughout the twentieth century. As Lola Cuddy and Mari Jones mention, for most of the twentieth century, individual researchers in music were isolated within their specific disciplines. And then, for most of our contributors, it all started to change in the 1980s. During the 1980s and 1990s there was an explosion of activity, out of which emerged an academic discipline - music psychology. In his paper for this volume, Andrew Gregory describes John Sloboda's 1985 book, The Musical Mind, as a landmark publication. Sloboda's book combined a rigorous cognitive approach with an understanding of deeper musical factors; this combination stimulated music psychology research throughout Britain. Sloboda himself identifies the turning point for the field as the 1983 publication of Lerdahl and Jackendoffs Generative Theory of Tonal Music. This detailed, universal theory of musical structure sparked thinking, research, criticism and counter-theories, which have shaped music psychology as a field (Sloboda, 2005). …

Implementing “A Generative Theory of Tonal Music”†

This paper proposes a music analysing system called the automatic time-span tree analyser (ATTA). ATTA derives a time-span tree that assigns a hierarchy of “structural importance” to the notes of a piece of music based on the generative theory of tonal music (GTTM). Although the time-span tree has been applied in music summarization and collaborative music creation systems, these systems use time-span trees manually analysed by experts in musicology. Current systems based on GTTM cannot acquire a time-span tree without manual application of most of the rules, since GTTM does not resolve much of the ambiguity involved in the application of the rules. To solve this problem, we propose a novel computational model of GTTM that re-formalizes the rules through a computer implementation. The main advantage of our approach is that we can introduce adjustable parameters, which enables us to assign priorities to the rules. Our analyser automatically acquires time-span trees by configuring the parameters that cover 17 out of 26 GTTM rules for constructing a time-span tree. Experimental results show that after these parameters were tuned, our method could outperform a baseline performance. We hope to distribute the time-span tree analyser as a tool for various musical tasks, such as searching and arranging music.

Parsing of Melody: Quantification and Testing of the Local Grouping Rules of Lerdahl and Jackendoff's A Generative Theory of Tonal Music

In two experiments, the empirical parsing of melodies was compared with predictions derived from four grouping preference rules of A Generative Theory of Tonal Music (F. Lerdahl & R. Jackendoff, 1983). In Experiment 1 (n = 123), listeners representing a wide range of musical training heard two familiar nursery-rhyme melodies and one unfamiliar tonal melody, each presented three times. During each repetition, listeners indicated the location of boundaries between units by pressing a key. Experiment 2 (n = 33) repeated Experiment 1 with different stimuli: one familiar and one unfamiliar nursery-rhyme melody, and one unfamiliar, tonal melody from the classical repertoire. In all melodies of both experiments, there was good within-subject consistency of boundary placement across the three repetitions (mean r = .54). Consistencies between Repetitions 2 and 3 were even higher (mean r = .63). Hence, Repetitions 2 and 3 were collapsed. After collapsing, there was high between-subjects similarity in boundary placement for each melody (mean r = .62), implying that all participants parsed the melodies in essentially the same (though not identical) manner. A role for musical training in parsing appeared only for the unfamiliar, classical melody of Experiment 2. The empirical parsing profiles were compared with the quantified predictions of Grouping Preference Rules 2a (the Rest aspect of Slur/Rest), 2b (Attack-point), 3a (Register change), and 3d (Length change). Based on correlational analyses, only Attack-point (mean r = .80) and Rest (mean r = .54) were necessary to explain the parsings of participants. Little role was seen for Register change (mean r = .14) or Length change (mean r = ––.09). Solutions based on multiple regression further reduced the role for Register and Length change. Generally, results provided some support for aspects of A Generative Theory of Tonal Music, while implying that some alterations might be useful.

Computational Music Representation Based on the Generative Theory of Tonal Music and the Deductive Object-Oriented Database

Computational Music Representation Based on the Generative Theory of Tonal Music and the Deductive Object-Oriented Database