Generative Theory Of Tonal Music Research Articles

Interactive Music Summarization Based on Generative Theory of Tonal Music

This paper presents an algorithm that checks for melodic similarity and a music summarization system called “Papipuun.” First, we developed a data structure for representing polyphony based on a time-span reduction in the generative theory of tonal music (GTTM) and the deductive object-oriented database (DOOD). A least upper bound operation is introduced to check the similarity of polyphonies represented in our method. Next, Papipuun performs quick listening in a manner similar to stylus skipping on a scratched record, but the skipping occurs correctly at punctuations of musical phrases, not arbitrarily. Papipuun can produce a music summary of good quality with a symbolic approach, reflecting the atmosphere of an entire piece through interaction with the user. In a pre-processing phase of Papipuun, a user analyzes an input piece by time-span reduction, using a dedicated tool called TS-Editor. For the real-time phase, the user interacts with the main system, Summarizer, to perform music summarization. The summarizer ascertains a piece structure by similarity checking. When the user identifies fragments to be skipped, Summarizer deletes them and concatenates the rest.

Modal Pitch Space — A Theoretical and Analytical Study

This paper presents an approach to the pitch space of the seven diatonic modes. The proposed theory is an expansion of Fred Lerdahl's tonal pitch space model; its purpose is a more accurate description of the situations involved in the analysis of diatonic modal music. The original methodology and set of algebraic calculating formulae is retained, but it is applied on modal instead of tonal space, on the basis that the latter is a subset of the former. In connection to Fred Lerdahl's theory, melodic motion, chord attraction and various cadence types are described within the modal context. Apart from the calculation of the pitch and the chordal and regional space algebraic representations, geometrical representations of all three levels of the modal pitch space are also included. Finally, the stability conditions arising from the new model are used as criteria to build the time span reduction and prolongational reduction parts of the Generative Theory of Tonal Music (GTTM) analysis of modal music. Two short GTTM analyses of 20th century modal music are being presented to illustrate the new model's analytical use.

Describing Melodic Structure Using a MusicTracker — Issues in Notation Andsound

This paper describes preliminary research towards the development of a system that can be used to investigate the mechanisms and representations underlying segmentation and phrase structure in music. It discusses the use of rules and principles in The Generative Theory of Tonal Music (Lerdahl and Jackendoff, 1983) and Implication Realization Model (Narmour, 1990). It also discusses the limitations of score notation as the basis for analysis and modelling of melodic segmentation, with reference to the problems associated withtranscribing non-Western music that uses different scales and exploits different organisations of melodic descriptors. This discussion provides a rationale for a methodology thatcan be applied to recorded music rather than notation. It describes MusicTracker — a toolthat extracts measures of change in pitch, dynamics and timbre fromrecordings of monophonic melodies. The use of this tool is illustrated with short fragments of musicfrom Japan, Burundi and Gabon.

Performance and Hypermetric Transformation

In the course of the introductory commentary on hypermeter in A 
 Generative Theory of Tonal Music (GTTM), Lerdahl and Jackendoff discuss 
 the opening measures of Mozart’s Symphony No. 40 in G Minor, a hypermetrically ambiguous 
 passage in which “the performer’s choice . . . can tip the balance one way or the 
 other for the listener.” Through reflections on concepts from more recent psychological 
 inquiry into performance, and on the interpretations of the passage that are projected 
 in four well-known recordings of the Symphony, I will develop a set of theoretical 
 principles that describe the “balance-tipping” effects of performance-specific elements 
 on hypermetric structures inferred by the listener. This special case will lead 
 to a more general reconsideration of the place of performance in the design of the 
 Lerdahl-Jackendoff theory. The article proceeds in five parts: (1) an introduction 
 to the main theoretical concepts to be discussed, including a brief consideration 
 of current debates with which the study intersects; (2) a critical discussion of 
 the relationship between hypermeter and performance that is proposed in GTTM; 
 (3) an attempt at extending the theory of accent types to include a special class 
 of phenomenal accents that is under the performer’s control; (4) a close reading 
 of four recordings, facilitated by quantitative performance analyses, and an attempt 
 at explaining their hypermetric patterns as transformations of perfectly regular 
 underlying structures; and (5) concluding remarks of a more general nature on the 
 relationship between structure and performance in GTTM.

What is musical intuition? Tonal theory as cognitive science

Lerdahl and Jackendoff's Generative Theory of Tonal Music (GTTM) is an important contribution to cognitive science. Jackendoff claims it is a computationalist theory and that the mental representations it postulates are unconscious. Thus GTTM looks to be a kind of cognitive science remote from the folk-psychological. I argue that this picture of GTTM is mistaken: GTTM is at least as much music analysis as cognitive science. Jackendoff's metatheory fails to explain how a listener can tell that a structural description corresponds to the way she hears, how analytically minded listeners can communicate about their hearing, and how a reader of their book can comprehend it. I suggest an alternative construal, on which GTTM's analytical vocabulary functions as a public language and its mental representations are perceptual beliefs. Interesting philosophical problems ensue about knowledge of musical structure and knowledge about what structures one hears. There is a paradox: one wants an analysis to be true to a hearing, yet to be illuminating. Though analysis and hearing coincide in content at an abstract level, they do not coincide in conceptual content. What sort of knowledge then underlies the inference from perceptual to music-analytical representation? I argue that such knowledge is a priori.

Simulating meter perception in acoustic signals

A model of meter perception is presented in which an acoustic signal provides parametric input to a pattern-forming dynamical system. Under rhythmic stimulation, the system undergoes bifurcations that give rise to patterns of self-sustained oscillations. The temporal structure of these patterns reflects the perceived temporal organization of acoustic signals that has been described by both linguists and music theorists [M. Liberman and A. M. Prince, Ling. Inq. 8, 249–336 (1977); F. Lerdahl and R. Jackendoff, Generative Theory of Tonal Music (MIT, Cambridge, 1983)]. These patterns are stable, yet flexible: They can persist in the absence of input and in the face of conflict, yet they can reorganize given a strong indication of a new temporal structure. Both continuous and discrete time models will be discussed and their application to acoustic signals will be demonstrated.

Perception and Cognition of Music

Part 1: Musicological Approaches. S. Arom, G. Leothaud, F. Voisin, Experimental Ethnomusicology: An Interactive Approach to the Study of Musical Scales. D. Cohen, R. Katz, Attitudes to the Time Axis and Cognitive Constraints: The Case of Arabic Vocal Folk Music. E. Rigbi-Shafrir, Radical Subjectivization of Time in the Music of the Fin-de-siecle: An Example by Max Reger. P. Verdix, Cognitive Sciences and Historical Sciences in Music: Ways Towards Conciliation. Part 2: Development Approaches. R.M. Abrams, K.K. Gerhardt, Some Aspects of the Foetal Sound Environment. S. Trehub, E. Schellenberg, D. Hill, The Origins of Music Perception and Cognition: A Developmental Approach. T. Umemoto, Developmental Approaches to Music Cognition and Behaviour. K.E. Behne, The Development of Musikerleben in Adolescence: How and Why Young People Listen to Music. A.C. Lehmann, The Acquisition of Expertise in Music: Efficiency of Deliberate Practice as a Moderating Variable in Accounting for Sub-expert Performance. Part 3: Biological Approaches. A.D. Parel, I. Peretz, Is Music Autonomous from Language? A Neurophysiological Appraisal. M. Besson, Electrophysiological Studies of Music Processing. Part 4: Acoustical and Computational Approaches. J.M. Hajda, R.A Kendall, E.C. Carterette, M.L. Harshberger, Methodological Issues in Timbre Research. Part 5: Structural Approaches. L.L. Cuddy, Tonal Relations. I. Cross, Pitch Schemata. I. Deliege, M. Melen, Cue Abstraction in the Representation of Musical Form. J.J. Nattiez, What is the Pertinence of Lerdahl-Jackendoff Theory. F. Lerdahl, Composing and Listening: A Reply to Nattiez. M. Imberty, Epistemic Subject, Psychological Subject: Regarding Lerdahl and Jackendoff's Generative Theory of Tonal Music. M. Imberty, Intertwining the Objectivity of Cognitive Analysis and the Subjectivity of the Oeuvre's Interpretations.

Prolongational structure and schematic form in Tristan's “Alte Weise”

The “alte Weise” melody for solo cor anglais from the beginning of Act III of Tristan und Isolde is submitted to a double analysis. First, it is treated by the techniques of Jackendoff's and my A Generative Theory of Tonal Music, yielding a prolongational structure that resembles a Schenkerian analysis even though it is based on contrasting principles. In the course of this analysis connections are made to other passages in Tristan. Second, the melody is treated according to schematic phrasal norms, yielding surface and underlying phrasal forms. Nattiez's paradigmatic approach is then adapted to demonstrate the underlying phrasal-prolongational coherence of the melody as a whole.

Calculating Tonal Tension

The prolongational component in A Generative Theory of Tonal Music assigns tensing and relaxing patterns to tonal sequences but does not adequately describe degrees of harmonic and melodic tension. This paper offers solutions to the problem, first by adapting the distance algorithm from the theory of tonal pitch space for the purpose of quantifying sequential and hierarchical harmonic tension. The method is illustrated for the beginning of the Mozart Sonata, K. 282, with emphasis on the hierarchical approach. The paper then turns to melodic tension in the context of the anchoring of dissonance. Interrelated attraction algorithms are proposed that incorporate the factors of stability, proximity, and directed motion. A distinction is developed between the tension of distance and the tension of attraction. The attraction and distance algorithms are combined in a view of harmony as voice leading, leading to a second analysis of the opening phrase of the Mozart in terms of voiceleading motion. Connections with recent theoretical and psychological work are discussed.

Parsing, structure, memory and affect

Abstract The Generative Theory of Tonal Music (GTTM) was developed by Fred Lerdahl and Ray Jackendoff (1983) as an approach to the analysis of tonal music based on foundations of human perception. However, in his later work Jackendoff (1987) became more interested in cognitive models and discussed how GTTM could be adapted as a theory of music cognition. Jackendoff s approach assumes that cognition is a capacity which may be reduced to the processing of “mental information”. However, information may abstract away those qualities which are most fundamental to our intuitions about music. The shortcomings of Jackendoff s approach become most apparent when we consider the role of affect in music behavior.

GTSIM A computer simulation of music perception

GTSIM is a computer simulation model of human perception of rhythm, based on Lerdahl and Jackendoff'sA Generative Theory of Tonal Music. GTSIM, a rule-based model with a neural network component, simulates the metric and grouping stages of Lerdahl and Jackendoff's theory. Using a rule-based production system, GTSIM simulates parallel processing, operating left-to-right without backtracking. GTSIM identifies the key of the piece of music and produces hierarchical representations of the metric and grouping structure which conform to Lerdahl and Jackendoff.

Comment L’Interprete et L’Auditeur Organisent-Ils La Progression Temporelle D’Une ŒUvre Musicale? (Analyse, Memorisation et Interpretation)

[How do the Performer and the Listener Organise the Temporal Progression of a Musical Work? (Analysis, Memorisation and Interpretation)] This article discusses the issue of the deep temporal organisation of a sequence or of a musical work, what might be described as its “motion” in the dynamics of listening and performing. This question is addressed in terms of the concepts of tension and relaxation, as well as in terms of the idea of prolongation as defined in the Generative Theory of Tonal Music. These concepts, however, appear to refer to psychological realities which transcend the bounds of tonal music. For that reason a hypothesis concerning a dynamic macro-structure is put forward; this concept provides a good explanation of the nature of the storage in memory of musical information, of the reconstitution of this information in the course of performance and of aspects of atonal structure otherwise inexplicable within the strict canons of tonal theory. It can therefore be claimed that all musical works originate — in their general cognitive representation as well as in long-term memory — in schemas of temporal order of which the prototype is governed by the alternation of moments of tension and relaxation, truly prolongational structures which are not solely syntactic but also perceptual or sensori-motor in nature. These structures can be shown to account for the dynamic continuity of processes of listening and performance as well as for the continuity of the deep structure of a musical work whether or not it is tonal.

Atonal prolongational structure

The early atonal music of Schoenberg and his school is emblematic of the difficulties in comprehending twentieth-century music. Music theorists have tried to analyze this music either through a modified Schenkerian approach or through pitch-set theory. After discussing limitations in these approaches, this paper develops at length a different theory for atonal music, one that adapts Jackendoff's and my A Generative Theory of Tonal Music in appropriate ways. Analyses of three Schoenberg pieces (from op. 11 and op. 19) illustrate the theory. The paper closes with an informal discussion of atonal pitch space.

The perception of metrical structure: Experimental evidence and a new model

This paper presents experimental results which are in conflict with existing theories of metrical interpretation [H. C. Longuet‐Higgins and C. S. Lee, Perception 11, 115–128 (1989); H. C. Longuet‐Higgins and C. S. Lee, Music Perception 1, 424–441 (1984); F. Lerdahl and R. Jackendoff, A Generative Theory of Tonal Music (MIT, Cambridge, MA, 1983); D. J. Povel and P. Essens, Music Perception 2, 411–440 (1985)] and a new model, based on the algorithm in Longuet‐Higgins and Lee (1982), which accounts for the main features of these results. Musically sophisticated subjects listened to sequences of identical tones in various rhythmic arrangements and transcribed them using standard musical notation. The results disconfirmed key predictions of all four theories, in that subjects displayed a general reluctance to choose interpretations containing an upbeat. However, the results did show that subjects were more prepared to avoid syncopated interpretations than those in which long notes occurred on weak beats. These tendencies are accounted for in the model by the assumption that the listener initially takes the first note of a sequence as the downbeat and is reluctant to abandon this (or later) hypotheses. But the occurrence of syncopations constitutes strong counterevidence and the occurrence of long notes on weak beats weak counterevidence, which can overcome the listener's conservatism. [Work supported by Nuffield Foundation, Royal Society and SERC.]

A Generative Theory of Tonal Music

A Generative Theory of Tonal Music

Theory, Analysis and the Psychology of Music: A Critical Evaluation of Lerdahl, F. and Jackendoff, R., A Generative Theory of Tonal Music

Lerdahl and Jackendoff's recent book A Generative Theory of Tonal Music brings together a range of ideas that are of common interest to music theorists, music analysts and psychologists of music. For this reason, as well as for its specific theoretical contributions, the book is an important landmark. However, it is argued that not only are there shortcomings in the theory when viewed from each of these three perspectives, but that it also fails to pay sufficient attention to the different aims and conceptual frameworks of the three disciplines. This leads to certain difficulties in applying the theory and assessing the status of its constructs. If the three disciplines are to contribute significantly to one another, their method- ological and conceptual differences must be recognised and accommodated.

A Generative Theory of Tonal Music

A Generative Theory of Tonal Music

A Generative Theory of Tonal Music

A Generative Theory of Tonal Music

A Reply to Peel and Slawson's Review of "A Generative Theory of Tonal Music"

A Reply to Peel and Slawson's Review of "A Generative Theory of Tonal Music"

Review: A Generative Theory of Tonal Music, by Fred Lerdahl and Ray Jackendoff

Review: <i>A Generative Theory of Tonal Music</i>, by Fred Lerdahl and Ray Jackendoff