Implementing “A Generative Theory of Tonal Music”†

Hamanaka, Masatoshi; Hirata, Keiji; Tojo, Satoshi

doi:10.1080/09298210701563238

Cited by 73 publications

(33 citation statements)

References 6 publications

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“…Although GTTM can be considered one of the greatest contributions to music theory and music cognition of the last few decades, implementing the theory is difficult because the often vague and ambiguous preference rules lead to a wide range of possible analyses (Clarke 1986;Temperley 2001, ch. 1;Hamanaka, Hirata, and Tojo 2006). The recursive formalization proposed by Lerdahl and Jackendoff suggests a strong connection between language and music.…”

Section: Related Workmentioning

confidence: 99%

Automatic Functional Harmonic Analysis

Haas

Magalhães

Wiering

et al. 2013

Computer Music Journal

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Music scholars have been studying tonal harmony intensively for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of Western tonal harmony that builds on well-known theories of tonal harmony. In contrast to other approaches that remain purely theoretical, we present an implemented system that is evaluated empirically. Given a sequence of symbolic chord labels, HarmTrace automatically derives the harmonic relations between chords. For this, we use advanced functional programming techniques that are uniquely available in the Haskell programming language. We show that our system is fast, easy to modify and maintain, robust against noisy data, and that its harmonic analyses comply with Western tonal harmony theory.For ages, musicians, composers, and musicologists have proposed theories regarding the structure of music to better understand how it is perceived, performed, and appreciated. In particular, tonal harmony exhibits a considerable amount of structure and regularity. The first theories describing tonal harmony date back at least to the 18th century (Rameau 1722). Since then, a rich body of literature that aims at explaining the harmonic regularities in both informal and formal models has emerged (e.g., Lerdahl and Jackendoff 1996). Such models have attracted numerous computer music researchers to investigate the automation of the analysis and generation of harmony. Most of these theories, however, have proven to be very hard to implement (e.g., Clarke 1986). We are not aware of a model that has a working implementation that effectively analyzes tonal harmony and deals robustly with noisy data, while remaining simple and easy to maintain, and scaling well to handle musical corpora of considerable size. In this article we present HarmTrace (Harmony Analysis and Retrieval of Music

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Section: Related Workmentioning

confidence: 99%

Automatic Functional Harmonic Analysis

Haas

Magalhães

Wiering

et al. 2013

Computer Music Journal

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“…In an influential set of talks, Leonard Bernstein (1976) linked musical structure to generative linguistic theory, leading to the development of several explicit theories of musical structure that draw on linguistic formalisms. The most well known theory of this type is Lerdahl and Jackendoff's (1983) generative theory of tonal music (see also Hamanaka, Hirata, & Tojo, 2006;Lerdahl, 2001), but other linguistically-motivated analyses of musical structure have been proposed by Longuet-Higgins (1976), Katz andPesetsky (2011), andRohrmeier (2011). Generally speaking, these proposals link hierarchical organization of (Western tonal) music (motivated to some extent by Schenkerian analysis; Schenker, 1935Schenker, /1979) to a linguistically inspired structure of rules and constraints, leading to a generative theory of harmonic structure.…”

mentioning

confidence: 99%

Processing structure in language and music: a case for shared reliance on cognitive control

Slevc

Okada

2014

Psychon Bull Rev

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The relationship between structural processing in music and language has received increasing interest in the last several years, spurred by the influential Shared Syntactic Integration Resource Hypothesis (SSIRH;Patel, 2003). According to this resource-sharing framework, music and language rely on separable syntactic representations but recruit shared cognitive resources to integrate these representations into evolving structures. The SSIRH is supported by findings of interactions between structural manipulations in music and language. However, other recent evidence suggests that such interactions can also arise with non-structural manipulations, and some recent neuroimaging studies report largely non-overlapping neural regions involved in processing musical and linguistic structure. These conflicting results raise the question of exactly what shared (and distinct) resources underlie musical and linguistic structural processing. This paper suggests that one shared resource is prefrontal cortical mechanisms of cognitive control, which are recruited to detect and resolve conflict that occurs when expectations are violated and interpretations must be revised. By this account, musical processing involves not just the incremental processing and integration of musical elements as they occur, but also the incremental generation of musical predictions and expectations, which must sometimes be overridden and revised in light of evolving musical input.

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“…How to formulate such cases is an important future issue. 3 In practice, it is not necessary to stick to existing pieces.…”

Section: Constraints Of Hierarchical Phrase Structuresmentioning

confidence: 99%

“…In GTTM, a musical piece is abstracted step by step by discarding less important elements and the whole piece is understood as a hierarchical tree structure. For example, Hamanaka et al have implemented GTTM on a computer and analyzed musical pieces [3]. However, this model does not have a strategy for composing new pieces.…”

Section: Introductionmentioning

confidence: 99%

Describing Global Musical Structures by Integer Programming on Musical Patterns

Tanaka

Fujii

2015

Mathematics and Computation in Music

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Abstract. Music can be regarded as sequences of localized patterns, such as chords, rhythmic patterns, and melodic patterns. In the study of music generation, how to generate musically adequate sequences is an important issue. In particular, generating sequences by controlling the relationships between local patterns and global structures is a difficult and open problem. Whereas the grammatical approaches that represent global structures are suitable to analyze how the pieces are constructed, they are not necessarily designed to generate new pieces with controlling their characteristics of global structures such as the redundancy of the sequence and the statistical distribution of specific patterns. To achieve this, we must overcome the difficulty of solving computationally complex problems. In this paper, we take an integer-programming-based approach and show that some important characteristics of global structures can be described only by linear equalities and inequalities, which are suitable for the integer programming.

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Implementing “A Generative Theory of Tonal Music”†

Cited by 73 publications

References 6 publications

Automatic Functional Harmonic Analysis

Automatic Functional Harmonic Analysis

Processing structure in language and music: a case for shared reliance on cognitive control

Describing Global Musical Structures by Integer Programming on Musical Patterns

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