Panayotis Mavromatis

ABSTRACT Hidden Markov Models (HMMs) have been successfully employed in the exploration and modeling of musical structure, with applications in Music Information Retrieval. This paper focuses on an aspect of HMM training that remains relatively unexplored in musical applications, namely the determination of HMM topology. We demonstrate that this complex problem can be effectively addressed through search over model topology space, conducted by HMM state merging and/or splitting. Once successfully identified, the HMM topology that is optimal with respect to a given data set can help identify hidden (latent) variables that are important in shaping the data set’s visible structure. These variables are identified by suitable interpretation of the HMM states for the selected topology. As an illustration, we present two case studies that successfully tackle two classic problems in music computation, namely (i) algorithmic statistical segmentation and (ii) meter induction from a sequence of durational patterns.

An experiment that investigates how a tonal context affects pitch recognition is presented. Melodic sequences that were composed to invoke varying degrees of tonality were rated by musicians (N = 34) for perceived strength of tonality. The sequences were then used in a pitch memory test based on a delayed-tone recognition paradigm. Listeners (N = 48) were asked to compare the first note of each melody (the standard) with a final, appended comparison tone that was either the same pitch or transposed by one semitone. The results showed that various factors including the presence of an interference tone one semitone away from the standard tone, the degree of tonality of the melodic sequence, and the tonal fitness of the standard and comparison tones predicted listener responses. In particular, the fitness of the comparison tone was a key factor in how listeners performed in the recognition task: comparison tones with higher fitness values increased performance when the comparison and standard were the same but decreased performance when they were different. These results illustrate how tonality can both facilitate and interfere with pitch encoding and recognition, providing a detailed and definitive perspective on how pitch memory is influenced by tonal contexts.

We describe a data representation for voice leading between two sonorities in a chorale texture, and a similarity measure for these voice leadings. These tools are used in an empirical study of the relationship between voice leading and harmonic function in a corpus of Bach chorales and a corpus of Lutheran chorales from a hundred years earlier. Common voice-leading types

This article presents a general-purpose formalism for modeling musical syntax as a probabilistic musical grammar. The formal probabilistic framework offers a precise yet flexible characterization of musical style as structure and process. Moreover, the grammar can be built algorithmically from a sample of musical examples, using a statistical grammar induction technique known as hidden Markov models (HMMs). The two fundamental assumptions of HMMs—termed finite memory and stationarity—are analyzed to show that the framework is expressive enough to capture a broad range of syntactic constraints in music. It is argued that the HMM technique draws its power from the ability to identify hidden structures that are important for shaping the musical surface. Thus, HMM-based grammar induction offers a practical, accurate, and methodologically sound tool for fine-grained modeling of musical style.As a concrete illustration, this article builds a formal grammar of rhythm for the Palestrina style. The grammar’s structure and components are carefully explained, and the formalism is compared with existing approaches to style characterization. Many traditional counterpoint rules are shown to naturally correspond with the grammar’s formal structure and are thus supported or refined. Other rules are disconfirmed or shown to lie outside the formalism’s scope. The long-standing problem of Renaissance meter is discussed in light of these results. Thus, through the Palestrina case study, the problem of grammar induction is framed in terms of traditional concerns in music scholarship in order to motivate application of the technique, illustrate its usefulness, and place it in a historical and methodological context within music theory research.

... Morwaread Farbood*, Gary Marcus†, Panayotis Mavromatis*, and David Poeppel†§ ... Key perception is often studied through the examination of the statistical distribution of pitch classes (Longuet-Higgins & Steedman, 1971; Krumhansl & Kessler, 1982; Vos & Van Geenen, 1996 ...

This article presents a method of inductive inference whose aim is to build formal quantitative models of musical structure. The models are constructed by statistical extraction of significant patterns from a musical corpus. The minimum description length (MDL) principle is used to select the best model from among the members of a non-parametric model family characterized by an unbounded parameter

Background and Aims This paper presents an experimental investigation into how the tonal interpretation of a pitch affects its retention in short-term memory. The hypothesis that a clear tonal context facilitates the retention of pitches over longer time-spans as compared to tonally ambiguous or atonal contexts has been examined before in previous work (Cuddy, Cohen, & Mewhort, 1981; Cuddy, Cohen, & Miller, 1979; Dewar, Cuddy, & Mewhort, 1977; Krumhansl, 1979). We present two experiments that aim to partly replicate previous findings while controlling for additional parameters. In contrast to the conclusions drawn from previous experiments, we postulate that it is impossible to conclude that tonal context aids pitch memory because subjects are in actuality responding to the tonal fitness of a probe tone, as described by Krumhansl and Kessler (1982), and are not actually executing a pitch recall task. As in the case of Krumhansl’s (1979) studies, we use Deutsch’s (1972) experimental ...

... The decomposition of the melody into "chunks" is consistent with psychological theories of sequence 94 Music Analysis East and West Page 3. representation (Miller 1956; Cowan 2001), which suggest its purpose may be to reduce processing load in real-time tasks such as ...

Abstract. Hiden Markov Models (HMMs) have been successfully em-ployed in the exploration and modeling of musical structure, with appli-cations in Music Information Retrieval. This paper focuses on an aspect of HMM training that remains relatively unexplored in musical applica-tions, namely the determination of HMM topology. We demonstrate that this complex problem can be effectively addressed through search over model topology space, conducted by HMM state merging and/or split-ting. Once successfully identified, the HMM topology that is optimal with respect to a given data set can help identify hidden (latent) vari-ables that are important in shaping the data set’s visible structure. These variables are identified by suitable interpretation of the HMM states for the selected topology. As an illustration, we present two case studies that successfully tackle two classic problems in music computation, namely (i) algorithmic statistical segmentation and (ii) meter induction from a seque...

Abstract. This paper presents a method for analyzing expressive tim-ing data from music performances. The goal is to uncover rules which explain a performer’s systematic timing manipulations in terms of struc-tural features of the music such as form, harmonic progression, texture, and rhythm. A multi-tiered approach is adopted, in which one first iden-tifies a continuous tempo curve by performing non-linear regression on the durations of performed time spans at all levels in the metric hier-archy. Once the effect of tempo has been factored out, subsequent tiers of analysis examine how the performed subdivision of each metric layer (e.g., quarter note) typically deviates from an even rendering of the next lowest layer (e.g., two equal eighth notes) as a function of time. Struc-tural features in the music are identified that contribute to a performer’s tempo fluctuations and metric deviations. 1

We present a probabilistic model of melodic process in modern Greek church chant. This largely oral tradition often relies on memorization and improvisation skills that are passed on from teacher to student by example, without explicit appeal to rules. The researcher is thus faced with the challenge of inferring the rules of the idiom from a sample corpus of chants. The structure of the rules will point to the mental representation of melody that underlies learning, recall, and improvisation. Our analysis is performed in two stages. In the first stage, a Hidden Markov Model (HMM) is trained on the corpus of chants, using a variant of the algorithm developed by Stolcke and Omohundro. As a termination criterion for this training stage, we use Rissanen’s Minimum Description Length principle. In the second stage, the optimal HMM is analyzed; its states can be interpreted as probabilistic rules that determine the course of melody, given its preceding melodic and textual context. Our find...

... The decomposition of the melody into "chunks" is consistent with psychological theories of sequence 94 Music Analysis East and West Page 3. representation (Miller 1956; Cowan 2001), which suggest its purpose may be to reduce processing load in real-time tasks such as ...

This article presents a method of inductive inference whose aim is to build formal quantitative models of musical structure. The models are constructed by statistical extraction of significant patterns from a musical corpus. The Minimum Description Length (MDL) principle is used to select the best model from among members of a non-parametric model family characterized by an unbounded parameter set. The chosen model achieves optimal compromise between goodness-of-fit and model complexity, thereby avoiding the over-fitting normally associated with such a family of models. The MDL method is illustrated through its application to the Hidden Markov Model framework. We derive an original mathematical expression for the MDL complexity of Hidden Markov Models (HMMs) that employ a finite alphabet of symbols; these models are particularly suited to the symbolic modeling of musical structure. As an illustration, we use the proposed HMM complexity expression to construct a model for a common me...

We outline a formalization and computer implementation of Schenker’s theory of tonality. The theory of Context-Free Grammars and their parsing, which has been developed extensively by computer scientists and computational linguists, offers a natural framework to address our problem. We show how Schenker’s prototypes and transformations can be cast in the form of a ContextFree Grammar. This allows us to implement for the first time a parsing algorithm that automates the analytical process. We develop a computer program using Prolog’s Definite Clause Grammar formalism. The program parses a piece presented in a suitable encoded form, producing a tree that represents a Schenkerian analysis of that piece. If more than one syntactically correct parsing is possible, the program produces corresponding analyses in separate trees. We discuss our work’s implications for music theory and music psychology. BACKGROUND AND AIMS For over twenty five years, music theorists have been trying to implem...

We present a probabilistic model of melodic process in modern Greek church chant. This largely oral tradition often relies on memorization and improvisation skills that are passed on from teacher to student by example, without explicit appeal to rules. The researcher is thus faced with the challenge of inferring the rules of the idiom from a sample corpus of chants. The structure of the rules will point to the mental representation of melody that underlies learning, recall, and improvisation. Our analysis is performed in two stages. In the first stage, a Hidden Markov Model (HMM) is trained on the corpus of chants, using a variant of the algorithm developed by Stolcke and Omohundro. As a termination criterion for this training stage, we use Rissanen’s Minimum Description Length principle. In the second stage, the optimal HMM is analyzed; its states can be interpreted as probabilistic rules that determine the course of melody, given its preceding melodic and textual context. Our find...

An experiment that investigates how a tonal context affects pitch recognition is presented. Melodic sequences that were composed to invoke varying degrees of tonality were rated by musicians (N = 34) for perceived strength of tonality. The sequences were then used in a pitch memory test based on a delayed-tone recognition paradigm. Listeners (N = 48) were asked to compare the first note of each melody (the standard) with a final, appended comparison tone that was either the same pitch or transposed by one semitone. The results showed that various factors including the presence of an interference tone one semitone away from the standard tone, the degree of tonality of the melodic sequence, and the tonal fitness of the standard and comparison tones predicted listener responses. In particular, the fitness of the comparison tone was a key factor in how listeners performed in the recognition task: comparison tones with higher fitness values increased performance when the comparison and s...

Background in music theory. Although classical musicians are expected to master the principles of tonal counterpoint, they find them notoriously difficult to learn. In part, these difficulties arise because traditional counterpoint tutors have two shortcomings. First, most tutors give students elaborate lists of rules, but they do not give advice on how students should organize those rules in specific contexts. Second, traditional tutors tend to formulate the rules in terms of prohibitions: students often learn what not to do than what to do. As a result, they fail to develop effective procedures for creating good counterpoint.

... The decomposition of the melody into "chunks" is consistent with psychological theories of sequence 94 Music Analysis East and West Page 3. representation (Miller 1956; Cowan 2001), which suggest its purpose may be to reduce processing load in real-time tasks such as ...

ABSTRACT Hidden Markov Models (HMMs) have been successfully employed in the exploration and modeling of musical structure, with applications in Music Information Retrieval. This paper focuses on an aspect of HMM training that remains relatively unexplored in musical applications, namely the determination of HMM topology. We demonstrate that this complex problem can be effectively addressed through search over model topology space, conducted by HMM state merging and/or splitting. Once successfully identified, the HMM topology that is optimal with respect to a given data set can help identify hidden (latent) variables that are important in shaping the data set’s visible structure. These variables are identified by suitable interpretation of the HMM states for the selected topology. As an illustration, we present two case studies that successfully tackle two classic problems in music computation, namely (i) algorithmic statistical segmentation and (ii) meter induction from a sequence of durational patterns.

... are many ways to explore the possibility of precise quantitative relations between musical structure and expressive ... Contemporary Music Review 3, 69–88 (1989) 6. Honing, H.: Computational Modeling of Music Cognition: A ... Journal of New Music Research 31, 37–50 (2002) 10. ...

We present a probabilistic model of melodic process in modern Greek church chant. This largely oral tradition often relies on memorization and improvisation skills that are passed on from teacher to student by example, without explicit appeal to rules. The researcher is thus faced with the challenge of inferring the rules of the idiom from a sample corpus of chants. The structure of the rules will point to the mental representation of melody that underlies learning, recall, and improvisation. Our analysis is performed in two stages. In the first stage, a Hidden Markov Model (HMM) is trained on the corpus of chants, using a variant of the algorithm developed by Stolcke and Omohundro. As a termination criterion for this training stage, we use Rissanen's Minimum Description Length principle. In the second stage, the optimal HMM is analyzed; its states can be interpreted as probabilistic rules that determine the course of melody, given its preceding melodic and textual context. Our...

ABSTRACT This article presents a general-purpose formalism for modeling musical syntax as a probabilistic musical grammar. The formal probabilistic framework offers a precise yet flexible characterization of musical style as structure and process. Moreover, the grammar can be built algorithmically from a sample of musical examples, using a statistical grammar induction technique known as hidden Markov models (HMMs). The two fundamental assumptions of HMMs—termed finite memory and stationarity—are analyzed to show that the framework is expressive enough to capture a broad range of syntactic constraints in music. It is argued that the HMM technique draws its power from the ability to identify hidden structures that are important for shaping the musical surface. Thus, HMM-based grammar induction offers a practical, accurate, and methodologically sound tool for fine-grained modeling of musical style. As a concrete illustration, this article builds a formal grammar of rhythm for the Palestrina style. The grammar's structure and components are carefully explained, and the formalism is compared with existing approaches to style characterization. Many traditional counterpoint rules are shown to naturally correspond with the grammar's formal structure and are thus supported or refined. Other rules are disconfirmed or shown to lie outside the formalism's scope. The long-standing problem of Renaissance meter is discussed in light of these results. Thus, through the Palestrina case study, the problem of grammar induction is framed in terms of traditional concerns in music scholarship in order to motivate application of the technique, illustrate its usefulness, and place it in a historical and methodological context within music theory research.

This article presents a method of inductive inference whose aim is to build formal quantitative models of musical structure. The models are constructed by statistical extraction of significant patterns from a musical corpus. The minimum description length (MDL) principle is used to select the best model from among the members of a non-parametric model family characterized by an unbounded parameter

We outline a formalization and computer implementation of Schenker's theory of tonality. The theory of Context-Free Grammars and their parsing, which has been developed extensively by computer scientists and computational linguists, offers a natural framework to address our problem. We show how Schenker's prototypes and transformations can be cast in the form of a Context- Free Grammar. This allows us to implement for the first time a parsing algorithm that automates the analytical process. We develop a computer program using Prolog's Definite Clause Grammar formalism. The program parses a piece presented in a suitable encoded form, producing a tree that represents a Schenkerian analysis of that piece. If more than one syntactically correct parsing is possible, the program produces corresponding analyses in separate trees. We discuss our work's implications for music theory and music psychology. BACKGROUND AND AIMS For over twenty five years, music theorists have bee...

We describe a data representation for voice leading between two sonorities in a chorale texture, and a similarity measure for these voice leadings. These tools are used in an empirical study of the relationship between voice leading and harmonic function in a corpus of Bach chorales and a corpus of Lutheran chorales from a hundred years earlier. Common voice-leading types

Background in music theory. Although classical musicians are expected to master the principles of tonal counterpoint, they find them notoriously difficult to learn. In part, these difficulties arise because traditional counterpoint tutors have two shortcomings. First, most tutors give students elaborate lists of rules, but they do not give advice on how students should organize those rules in specific contexts. Second, traditional tutors tend to formulate the rules in terms of prohibitions: students often learn what not to do than what to do. As a result, they fail to develop effective procedures for creating good counterpoint. Aims. This paper addresses these issues in the framework of Intelligent Tutoring Systems. An Intelligent Tutoring System (ITS) is an interactive computer environment that teaches students how to solve problems in a specific domain. Building an effective counterpoint ITS requires techniques from music theory, Artificial Intelligence, and cognitive psychology. ...

Oxford University Press Oxford New York Athens Auckland Bangkok Bogota Buenos Aires Calcutta Cape Town Chennai Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madrid Melhourne Mexico City Mumbai Nairobi Paris Sao Paulo Singapore Taipei Tokyo ...