An explicitly structured control model for exploring search space: chorale harmonisation in the style of J.S. Bach

In this research, we present our computational model which performs four part har-monisation in the style of J.S. Bach. Harmonising Bach chorales is a hard AI problem, comparable to natural language understanding. In our approach, we explore the issue of gaining control in an explicit way for the chorale harmonisation tasks. Generally, the control over the search space may be from both domain dependent and domain inde-pendent control knowledge. Our explicit control emphasises domain dependent control knowledge. The control gained from domain d ependent control enables us to map a clearer relationship between the control applied and its effects. Two examples of do-main dependent control are a plan of tasks to be done and heuristics stating properties of the domain. Examples of domain independent control are notions such as temperature values in an annealing method; mutation rates in Genetic Algorithms; and weights in Artificial Neural Networks.The appeal of the knowledge based approach lies in the accessibility to the control if required. Our system exploits this concept extensively. Control is explicitly expressed by weaving different atomic definitions {i.e. the rules, tests and measures) together with appropriate control primitives. Each expression constructed is called a control definition, which is hierarchical by nature.One drawback of the knowledge based approach is that, as the system grows bigger, the exploitation of the new added knowledge grows exponentially. This leads to an intractable search space. To reduce this intractability problem, we partially search the search space at the meta-level. This meta-level architecture reduces the complexity in the search space by exploiting search at the meta-level which has a smaller search space.The experiment shows that an explicitly structured control offers a greater flexibility in controlling the search space as it allows the control definitions to be manipulated and modified with great flexibility. This is a crucial clement in performing partial search over a big search space. As the control is allowed to be examined, the system also potentially supports elaborate explanations of the system activities and reflections at the meta-level

Computer Aided Statistical Analysis of Motive Use and Compositional Idiom

This thesis discusses the creation of a means of pitch-based data representation which allows automated logging and analysis of melodic motivic material. This system also allows analysis of a number of attributes of a composition which are not readily apparent to human analysis. By using a numerical data format which treats motivically related material as equivalent, groups of tonally equivalent intervals (n-tuples) can be logged and have statistical procedures carried out on them. This thesis looks at four applications of this approach: measuring the most commonly occurring motivic material; creating a transition matrix showing probabilities of movement between intervals; measuring the extent of disjunct or conjunct writing; and measuring concentration of motivic writing (the extent to which motives are reused). Following the discussion of the data representation system, a set of expositions taken from the piano sonatas of Haydn, Mozart, and Clementi are converted to this method of data representation, and results are collected for the above four applications. The implications of the results of this analysis are discussed, and further potential applications of the system are explored

Computer Aided Statistical Analysis of Motive Use and Compositional Idiom

This thesis discusses the creation of a means of pitch-based data representation which allows automated logging and analysis of melodic motivic material. This system also allows analysis of a number of attributes of a composition which are not readily apparent to human analysis. By using a numerical data format which treats motivically related material as equivalent, groups of tonally equivalent intervals (n-tuples) can be logged and have statistical procedures carried out on them. This thesis looks at four applications of this approach: measuring the most commonly occurring motivic material; creating a transition matrix showing probabilities of movement between intervals; measuring the extent of disjunct or conjunct writing; and measuring concentration of motivic writing (the extent to which motives are reused). Following the discussion of the data representation system, a set of expositions taken from the piano sonatas of Haydn, Mozart, and Clementi are converted to this method of data representation, and results are collected for the above four applications. The implications of the results of this analysis are discussed, and further potential applications of the system are explored

The Construction and Evaluation of Statistical Models of Melody and Harmony

This research is concerned with the development of representational and modelling techniques employed in the creation of statistical models of melody and four-part harmony. Previous work has demonstrated the utility of multiple viewpoint systems, along with techniques such as Prediction by Partial Match, in the construction of cognitive models of melodic perception. Primitive viewpoints represent surface and underlying musical attributes, while linked viewpoints model combinations of such attributes. A viewpoint selection algorithm optimises multiple viewpoint systems by minimising the information theoretic measure cross-entropy. Many more linked viewpoints are used in this research than have previously been available, and the results show that many new viewpoints are incorporated into optimised systems. A significant aspect of this work is the proposal and implementation of a set of novel extensions of the multiple viewpoint framework for four-part harmony. Statistical models are constructed with the aim that given a soprano part, alto, tenor and bass parts are added in a stylistically suitable way. Version 1 is as closely related to the modelling of melody as possible (chord replacing note), and is a baseline for gauging expected improvements as the framework is extended and generalised. Three versions of the framework have been implemented, and their performances compared and contrasted. The results indicate that the baseline version has been improved upon. Time complexity issues are discussed in detail, and selected viewpoints are examined from a music theoretic point of view for insights into why they perform well. Finally, melodies and harmonisations of given melodies are generated using the best performing models. The quality of the music suggests that, in spite of the improvements achieved so far, the models are still unable to fully capture the musical style of a corpus. Another six versions of the framework are described, which are expected to contribute further improvements

Artificial intelligence, education and music : the use of artificial intelligence to encourage and facilitate music composition by novices

The goal of the research described in this thesis is to find ways of using artificial intelligence to encourage and facilitate music composition by musical novices, particularly those without traditional musical skills. Two complementary approaches are presented. We show how two recent cognitive theories of harmony can be used to design a new kind of direct manipulation tool for music, known as "Harmony Space", with the expressivity to allow novices to sketch, analyse, modify and compose harmonic sequences simply and clearly by moving two-dimensional patterns on a computer screen linker to a synthesizer. Harmony Space provides novices with a way of describing and controlling harmonic structures and relationships using a single, principled, uniform spatial metaphor at various musical levels; note level, interval level, chord level, harmonic succession level and key level. A prototype interface has been implemented to demonstrate the coherence and feasibility of the design. An investigation with a small number of subjects demonstrates that Harmony Space considerably reduces the prerequisites required for novices to learn about, sketch, analyse and experiment with harmony - activities that would normally be very difficult for them without considerable theoretical knowledge or instrumental skill. The second part of the thesis presents work towards a knowledge-based tutoring system to help novices using the interface to compose chord sequences. It is argued that traditional, remedial intelligent tutoring systems approaches are inadequate for tutoring in domains that require open-ended thinking. The foundation of a new approach is developed based on the exploration and transformation of case studies described in terms of chunks, styles and plans. This approach draws on a characterisation of creativity due to Johnson-Laird (1988). Programs have been implemented to illustrate the feasibility of key parts of the new approach

Modelling the perception and composition of Western musical harmony.

PhD ThesisHarmony is a fundamental structuring principle in Western music, determining how simultaneously occurring musical notes combine to form chords, and how successions of chords combine to form chord progressions. Harmony is interesting to psychologists because it unites many core features of auditory perception and cognition, such as pitch perception, auditory scene analysis, and statistical learning. A current challenge is to formalise our psychological understanding of harmony through computational modelling. Here we detail computational studies of three core dimensions of harmony: consonance, harmonic expectation, and voice leading. These studies develop and evaluate computational models of the psychoacoustic and cognitive processes involved in harmony perception, and quantitatively model how these processes contribute to music composition. Through these studies we examine long-standing issues in music psychology, such as the relative contributions of roughness and harmonicity to consonance perception, the roles of low-level psychoacoustic and high-level cognitive processes in harmony perception, and the probabilistic nature of harmonic expectation. We also develop cognitively informed computational models that are capable of both analysing existing music and generating new music, with potential applications in computational creativity, music informatics, and music psychology. This thesis is accompanied by a collection of open-source software packages that implement the models developed and evaluated here, which we hope will support future research into the psychological foundations of musical harmony.

AI Methods in Algorithmic Composition: A Comprehensive Survey

Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic composition, including grammatical representations, probabilistic methods, neural networks, symbolic rule-based systems, constraint programming and evolutionary algorithms. This survey aims to be a comprehensive account of research on algorithmic composition, presenting a thorough view of the field for researchers in Artificial Intelligence.This study was partially supported by a grant for the MELOMICS project (IPT-300000-2010-010) from the Spanish Ministerio de Ciencia e Innovación, and a grant for the CAUCE project (TSI-090302-2011-8) from the Spanish Ministerio de Industria, Turismo y Comercio. The first author was supported by a grant for the GENEX project (P09-TIC- 5123) from the Consejería de Innovación y Ciencia de Andalucía

Perception based approach on pattern discovery and organisation of point-set data

The general topic of the thesis is computer aided music analysis on point-set data utilising theories outlined in Timo Laiho’s Analytic-Generative Methodology (AGM) [19]. The topic is in the field of music information retrieval, and is related to previous work on both pattern discovery and computational models of music. The thesis aims to provide analysis results that can be compared to existing studies. AGM introduces two concepts based on perception, sensation and cognitive processing: interval–time complex (IntiC) and musical vectors (muV). These provide a mathematical framework for the analysis of music. IntiC is a value associated with the velocity, or rate of change, between musical notes. Musical vectors are the vector representations of these rates of change. Laiho explains these attributes as meaningful for both music analysis and as tools for music generation. Both of these attributes can be computed from a point-set representation of music data. The concepts in AGM can be viewed as being related to geometric methods for pattern discovery algorithmsof Meredith, Lemström et al.[24] whointroduce afamily of ‘Structure Induction Algorithms’. These algorithms are used to find repeating patterns in multidimensional point-set data. Algorithmic implementations of intiC and muV were made for this thesis and examined in the use of rating and selecting patterns output by the pattern discovery algorithms. In addition software tools for using these concepts of AGM were created. The concepts of AGM and pattern discovery were further related to existing work in computer aided musicology

Dynamical and topological tools for (modern) music analysis

Is it possible to represent the horizontal motions of the melodic strands of a contrapuntal composition, or the main ideas of a jazz standard as mathematical entities? In this work, we suggest a collection of novel models for the representation of music that are endowed with two main features. First, they originate from a topological and geometrical inspiration; second, their low dimensionality allows to build simple and informative visualisations. Here, we tackle the problem of music representation following three non-orthogonal directions. We suggest a formalisation of the concept of voice leading (the assignment of an instrument to each voice in a sequence of chords) suggesting a horizontal viewpoint on music, constituted by the simultaneous motions of superposed melodies. This formalisation naturally leads to the interpretation of counterpoint as a multivariate time series of partial permutation matrices, whose observations are characterised by a degree of complexity. After providing both a static and a dynamic representation of counterpoint, voice leadings are reinterpreted as a special class of partial singular braids (paths in the Euclidean space), and their main features are visualised as geometric configurations of collections of 3-dimensional strands. Thereafter, we neglect this time-related information, in order to reduce the problem to the study of vertical musical entities. The model we propose is derived from a topological interpretation of the Tonnetz (a graph commonly used in computational musicology) and the deformation of its vertices induced by a harmonic and a consonance-oriented function, respectively. The 3-dimensional shapes derived from these deformations are classified using the formalism of persistent homology. This powerful topological technique allows to compute a fingerprint of a shape, that reflects its persistent geometrical and topological properties. Furthermore, it is possible to compute a distance between these fingerprints and hence study their hierarchical organisation. This particular feature allows us to tackle the problem of automatic classification of music in an innovative way. Thus, this novel representation of music is evaluated on a collection of heterogenous musical datasets. Finally, a combination of the two aforementioned approaches is proposed. A model at the crossroad between the signal and symbolic analysis of music uses multiple sequences alignment to provide an encompassing, novel viewpoint on the musical inspiration transfer among compositions belonging to different artists, genres and time. To conclude, we shall represent music as a time series of topological fingerprints, whose metric nature allows to compare pairs of time-varying shapes in both topological and in musical terms. In particular the dissimilarity scores computed by aligning such sequences shall be applied both to the analysis and classification of music

The Harmonic Implications of the Non-Harmonic Tones in the Four-Part Chorales of Johann Sebastian Bach

This study sought to identify the harmonic implications of the non-harmonic tones in the four-part chorales of Johann Sebastian Bach and to identify if the implications were modern, extended harmonies. The study examined if non-harmonic tones implied traditional or extended harmonies more often, which non-harmonic tones more frequently implied extended harmonies, and which chords typically preceded implied extended harmonies. The study was a corpus analysis of the four-part chorales. The data collected was organized in and analyzed with frequency charts and a chi-square goodness of fit test and chi-square tests of independence from the chordal analysis conducted by the researcher. Harmonic implications of extended harmonies not only exist in the chorales but are also nearly as plentiful as implications of seventh chords. A single non-harmonic tone is most likely to produce an implication of an extended harmony and triads are most likely to precede an extended harmony