Towards a Harmonic Complexity of Musical Pieces (original) (raw)

Towards a general computational theory of musical structure

, for their guidance and support throughout this research study, and for all their invaluable comments and advice that helped me crystallise the views presented in this thesis. My colleagues from the Faculty of Music and the Department of Artificial Intelligence at the University of Edinburgh for providing an inspiring intellectual environment in which this work matured; especially, the meetings of the AI-Music Group and the Musical Communication Colloquium have been an indispensable source of ideas. The University of Edinburgh for making this research study possible by offering me a threeyear postgraduate research award. My friends who, with their constant support, love and good humour, have made my stay in Edinburgh unforgettable; especially, Evie Athanassiou for sharing so much with me in both stressful and happy times. My parents and brothers for their continuous wholehearted support throughout these years. v 5. Representation of the Musical Surface 5.1 The Common Hierarchical Abstract Representation for Music (CHARM) 5.1 Musical Surface 5.3 Pitch and Pitch Interval Representation 5.3.1 The General Pitch Interval Representation (GPIR) 5.3.2 Applications and Uses of the GPIR 5.3.3 Transcription of melodies based on the GPIR 6. Microstructural Module (Local Boundaries, Accents, Metre) 6.1 Musical Rhythm 6.2 The Gestalt principles of proximity and similarity in theories of rhythm 6.3 The Local Boundary Detection Model (LBDM) 6.3.1 The Identity-Change and Proximity Rules 6.3.2 Applying the ICR and PR rules on three note sequences 6.3.3 Applying the ICR and PR rules on longer melodic sequences 6.3.4 Further comments of the application of the LBDM rules 6.3.5 The refined LBDM 6.4 Phenomenal Accentuation Structure 6.5 Metrical Structure 7. Macrostructural Module I (Musical Parallelism and Segmentation) 7.1 Similarity and pattern-matching 7.2 Overlapping of patterns 7.3 Pattern-matching and pitch-interval representation 7.4 The String Pattern-Induction Algorithm (SPIA) 7.5 The Selection Function 7.6 Segmentation based on musical parallelism 7.7 Interaction with microstructural module 8. Macrostructural Module II (Musical Categories) 8.1 A working formal definition of similarity and categorisation 120 8.2 The Unscramble Algorithm 8.3 An illustrative example 8.3.1 Category formation 8.3.2 Category membership prediction 8.4 A musical example 8.5 Relative merits of the Unscramble algorithm vi 9. Overall Model and Four Analyses 9.1 Overall model based on the GCTMS 9.1.1 Musical input 9.

Musical Harmony Analysis with Description Logics

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Symbolic representations of music are emerging as an important data domain both for the music industry, and for computer science research, aiding in the organization of large collections of music and facilitating the development of creative and interactive AI. An aspect of symbolic representations of music, which differentiates it from audio representations, is their suitability to be linked with notions from music theory which have been developed over the centuries. One core such notion is that of functional harmony, which involves analyzing progressions of chords. This paper proposes a description of the theory of functional harmony within the OWL 2 RL profile and experimentally demonstrates its practical use.

Chapter 5 Computational Analysis of Musical Form

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Can a computer understand musical forms? Musical forms describe how a piece of music is structured. They explain how the sections work together through repetition, contrast, and variation: repetition brings unity, and variation brings interest. Learning how to hear, to analyse, to play, or even to write music in various forms is part of music education. In this chapter, we briefly review some theories of musical form, and discuss the challenges of computational analysis of musical form. We discuss two sets of problems, segmentation and form analysis. We present studies in music information retrieval (MIR) related to both problems. Thinking about codification and automatic analysis of musical forms will help the development of better MIR algorithms.

Quantifying Harmony: The Mathematical Essence of Music

This research delves into the intricate correlation between music and mathematics, examining how mathematical principles play a fundamental role in shaping various aspects of musical theory and composition. Starting from Pythagoras' early insights on harmonic intervals to the complex patterns found in the Fibonacci sequence and fractal geometry, this study uncovers the deep connections between numerical concepts and musical notes. By extensively exploring historical perspectives, theoretical frameworks, and practical applications, we gain valuable insight into how mathematical ideas influence the melodies, harmonies, and rhythms that elevate our auditory experiences.

Complexity Measures of Music

2017

We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes, with the interesting result that the complexity index of the crucial events is mu ~ 2, which is the same inverse power-law index of the dynamics of the brain. The search technique analyzes music volume and confirms the results of the earlier work, thereby contributing to the explanation as to why the brain is sensitive to music, through the phenomenon of complexity matching. Complexity matching has recently been interpreted as the transfer of multifractality from one complex network to another. For this reason we also examine the mulifractality of music, with the observation that the multifractal spectrum of a computer performance is significantly narrower than the multifractal spectrum of a human performance of the same musical score. We conjecture ...

Computational Analysis of Musical Form

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First-order logic classification models of musical genres based on harmony

2009

We present an approach for the automatic extraction of transparent classification models of musical genres based on harmony. To allow for human-readable classification models we adopt a first-order logic representation of harmony and musical genres: pieces of music are represented as lists of chords and musical genres are seen as context-free definite clause grammars using subsequences of these chord lists. To induce the context-free definite clause grammars characterising the genres we use a first-order logic decision tree induction algorithm, Tilde. We test this technique on 856 Band in a Box files representing academic, jazz and popular music. We perform 2-class and 3-class classification tasks on this dataset and obtain good classification results: around 66% accuracy for the 3-class problem and between 72% and 86% accuracy for the 2-class problems. A preliminary analysis of the most common rules extracted from the decision tree models built during these experiments reveals a list of interesting and/or well-known jazz, academic and popular music harmony patterns.

On the Complexity Analysis and Visualization of Musical Information

Entropy

This paper considers several distinct mathematical and computational tools, namely complexity, dimensionality-reduction, clustering, and visualization techniques, for characterizing music. Digital representations of musical works of four artists are analyzed by means of distinct indices and visualized using the multidimensional scaling technique. The results are then correlated with the artists’ musical production. The patterns found in the data demonstrate the effectiveness of the approach for assessing the complexity of musical information.

Computational Accounts of Music Understanding

1991

Abstract We examine various computational accounts of aspects of music understanding. These accounts involve programs which can notate melodies based on pitch and duration information. It is argued that this task involves significant musical intelligence. In particular, it requires an understanding of basic metric and harmonic relations implicit in the melody. We deal only with single-voice, tonal melodies.

Dimensionality Reduction in Harmonic Modeling for Music Information Retrieval

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A 24-dimensional model for the ‘harmonic content’ of pieces of music has proved to be remarkably robust in the retrieval of polyphonic queries from a database of polyphonic music in the presence of quite significant noise and errors in either query or database document. We have further found that higher-order (1st- to 3rd-order) models tend to work better for music retrieval than 0th-order ones owing to the richer context they capture. However, there is a serious performance cost due to the large size of such models and the present paper reports on some attempts to reduce dimensionality while retaining the general robustness of the method. We find that some simple reduced-dimensionality models, if their parameter settings are carefully chosen, do indeed perform almost as well as the full 24-dimensional versions. Furthermore, in terms of recall in the top 1000 documents retrieved, we find that a 6-dimensional 2nd-order model gives even better performance than the full model. This represents a potential 64-times reduction in model size and search-time, making it a suitable candidate for filtering a large database as the first stage of a two-stage retrieval system.

Towards a Harmonic Complexity of Musical Pieces (original) (raw)

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