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Human-Centred Artificial Intelligence in Sound Perception and Music Composition
Abstract
Previous algorithms created for the harmonization of a melody have highlighted difficulties in finding a solution that could be significant and important not only from the point of view of listening but also from that of composition, that is, also respecting the rules of musical grammar that tradition handed down to us. This article describes a model for the harmonization of melody (non-modulating) derived from common concepts in music theory (such as Schenker’s theory) applied in compliance with the rules of musical grammar. The fundamental structure is characterized by a self-learning system based: on the Markovian stochastic process, for the definition of rules both for the concatenation of the chords and for the correct melodic movement of the sounds between two consecutive chords; on the Viterbi algorithm, for identifying the correct chord for each sound of the melody. The core of the algorithm allows the sounds of each chord to follow a correct trend (ascending or descending) such as to give each of them the real decisive impulse (which every listener is able to recognize). Examples of musical fragments harmonized in this way show that the apparatus of the composition rules and that of the listening rules must be thought of as coinciding (or at least partially in possession of common elements).
The interest of musicians and computer scientists in AI-based automatic melody harmonization has increased significantly in the last few years. This research area has attracted the attention of both teachers and students of Theory, Analysis and Composition, looking for support tools for the learning process. The main problem is that the systems designed and developed up to now harmonize a melody written by a user without considering the didactic and therefore cognitive aspects at the basis of a “significant learning”: given a melody, the system returns a harmonization finished without any user input. This paper describes a self-learning algorithm capable of harmonizing a musical melody, with the aim of supporting the student during the study of Theory, Analysis and Composition. The algorithm, on the basis of the ascending and descending movement of the sounds of the melody (soprano), proposes the sounds for the bass line: the Viterbi algorithm was applied to evaluate the probability of the best match between the melody sounds and the provided Markov chains, to reach the “optimal” state sequences. Subsequently, the algorithm allows the user to complete the chords for each sound of the bass line (tenor and alto), or to create the complete chords. Examples of musical fragments harmonized in this way demonstrate that the algorithm is able to respect the concatenation rules of the tonal functions which characterize classical tonal music.
We present FlowComposer, a web application that helps users compose musical lead sheets, i.e. melodies with chord labels. Flow-Composer integrates a constrained-based lead sheet generation tool in which the user retains full control over the generation process. Users specify the style of the lead sheet by selecting a corpus of existing lead sheets. The system then produces a complete lead sheet in that style, either from scratch, or from a partial lead sheet entered by the user. The generation algorithm is based on a graphical model that combines two Markov chains enriched by Regular constraints, representing the melody and its related chord sequence. The model is sampled using our recent result in efficient sampling of the Regular constraint. The paper reports on the design and deployment of FlowComposer as a web-service, part of an ecosystem of online tools for the creation of lead sheets. FlowCom-poser is currently used in professional musical productions, from which we collect and show a number of representative examples.
Few algorithms for automated music composition are able to address the combination of harmonic structure, metrical structure, and repetition in a generalized way. Markov chains and neural nets struggle to address repetition of a musical phrase, and generative grammars generally do not handle temporal aspects of music in a way that retains a coherent metrical structure (nor do they handle repetition). To address these limitations, we present a new class of generative grammars called Probabilistic Temporal Graph Grammars, or PTGG's, that handle all of these features in music while allowing an elegant and concise implementation in Haskell. Being probabilistic allows one to express desired outcomes in a probabilistic manner; being temporal allows one to express metrical structure; and being a graph grammar allows one to express repetition of phrases through the sharing of nodes in the graph. A key aspect of our approach that enables handling of harmonic and metrical structure in addition to repetition is the use of rules that are parameterized by duration, and thus are actually functions. As part of our implementation, we also make use of a music-theoretic concept called chord spaces.
The use of sophisticated computer systems in the design and performance of music has taken place in the context of a society that demands novelty and expects technology to play a leading role in extending the boundaries of what is musically possible. This article describes a different approach to the use of technology in composition and an alternative technology that grew out of research into the complex rhythmic intricacies of Indian drum music. The authors present the new version of their Bol Processor and explain its time accuracy, flexibility and capacity to manipulate highly complex polymetric symbols. The authors’ work has inspired further developments by Indian researchers who are rising to the challenge of developing a technology built around concepts familiar to the Indian musical mind as an alternative to models dependent upon Western concepts.
We present a survey of research into automated and semiautomated computer systems for expressive per- formance of music. We will examine the motivation for such systems and then examine the majority of the systems developed over the last 25 years. To highlight some of the possible future directions for new research, the review uses primary terms of reference based on four elements: testing status, expressive representation, polyphonic ability, and performance creativity.
Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We first summarize the basics of HMMs, and then review several recent related learning algorithms and extensions of HMMs, including in particular hybrids of HMMs with artificial neural networks, Input-Output HMMs (which are conditional HMMs using neural networks to compute probabilities), weighted transducers, variable-length Markov models and Markov switching state-space models. Finally, we discuss some of the challenges of future research in this very active area. 1 Introduction Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many applications in artificial intelligence, pattern recognition, speech recognition, and modeling of bi...
The rapid development of digital technologies has made it possible to enhance teaching and learning spaces even in a complex discipline such as music composition, where however the right attention is still lacking regarding the learning style of students. Existing software, in most cases, propose methods for harmonizing a melody, but they rarely deal with the problems of the harmonization of music bassline. This article presents an intelligent adaptive algorithm to support the learning process of (dyslexic and non-dyslexic) students in the context of the harmonization of music basslines. The algorithm allows students to harmonize a music bassline, giving them advices (Virtual Tutor) in case of mistakes in the concatenation of the chords. Experiments have shown that this form of adaptive learning of the algorithm can improve students’ ability to find solutions for the harmonization of music bassline. Future improvements of the method are discussed briefly at the end of the paper.
Expressiveness is an important aspect of a music composition. It becomes fundamental in an automatic music composition process, a domain where the Artificial Intelligent Systems have shown great potential and interest. The research presented in this paper describes an empirical approach to give expressiveness to a tonal melody generated by computers, considering both the symbolic music text and the relationships among the sounds of the musical text. The method adapts the musical expressive character to the musical text on the base of the “harmonic function” carried by every single musical chord. The article is intended to demonstrate the effectiveness of the method by applying it to some (tonal) musical pieces written in the 18th and 19th century. Future improvements of the method are discussed briefly at the end of the paper.
There are several automatic music composition algorithms that generate a classical music melody or Jazz and Blues chords and progressions. These algorithms often work by applying a series of music rules which are explicitly provided in order to determine the sequence of the exit codes. In other cases, the algorithms use generation techniques based on Markov Models. The objective of this article is to present an algorithm for the automatic composition of classical tonal music, based on a self-learning model that combines De La Motte’s theory of Functional Harmony in a Markov process. This approach has the advantage of being more general compared to the explicit specification of rules. The article is going to demonstrate the effectiveness of the method by means of some examples of its production and is going to indicate ways to improve the method.
The style of a set of Swedish nursery tunes is described in terms of a generative rule system. A generative rule system producing melodically similar versions of an old Swedish folk song is also presented. Examples of melodies generated by these two rule systems are given. Both these rule systems are similar in several respects. Thus, the marking of the hierarchical constituent structure seems to be one of the important principles in composing simple melodies. The rule systems also show a number of similarities with the Chomsky & Halle (1968) generative phonology of English. For instance, the procedures used for deriving a stress contour from a tree diagram are almost identical. Moreover, in sentences as in melodies this stress, or prominence contour is of decisive importance to the generation of the surface structure, such as meter, harmony, and sequences of pitches. It is believed that such parallels between language and music reflect characteristics of man's perceptual and cognitive capacities.
The recursive character of musical chord sequences makes generative grammar a suitable formalism for describing the rules that constrain such sequences. A small number of rules are presented which generate the members of a large class of complex chord sequences that are generally recognised to be closely related, namely the set of jazz 12-bar blues. The rules are illustrated using a testing corpus of jazz chord sequences, and certain extensions are considered.
This tutorial paper begins with an elementary presentation of the fundamental properties and structure of convolutional codes and proceeds with the development of the maximum likelihood decoder. The powerful tool of generating function analysis is demonstrated to yield for arbitrary codes both the distance properties and upper bounds on the bit error probability for communication over any memoryless channel. Previous results on code ensemble average error probabilities are also derived and extended by these techniques. Finally, practical considerations concerning finite decoding memory, metric representation, and synchronization are discussed.
The principle of local consonance is based on an explicit parametrization of Plomp and Levelt's [J. Acoust. Soc. Am. 38, 548-560 (1965)] consonance curves. It explains the relationship between the spectrum of a sound (its timbre) and a tuning (or scale) in which the timbre will appear most consonant. This relationship is defined in terms of the local minima of a family of dissonance curves. For certain timbres with simple spectral configurations, dissonance curves can be completely characterized, and bounds are provided on the number and location of points of local consonance. Computational techniques are presented which answer two complementary questions: Given a timbre, what scale should it be played in? Given a desired scale, how can appropriate timbres be chosen? Several concrete examples are given, including finding scales for nonharmonic timbres (the natural resonances of a uniform beam, ''stretched'' and ''compressed'' timbres, FM timbres with noninteger carrier-to-modulation ratios), and finding timbres for arbitrary scales.
A new interpretation of the Viterbi decoding algorithm based on the state-space approach to dyamical systems is presented. In this interpretation the optimum decoder solves a generalized regulator control problem by dynamic programming techniques.
The probability of error in decoding an optimal convolutional code transmitted over a memoryless channel is bounded from above and below as a function of the constraint length of the code. For all but pathological channels the bounds are asymptotically (exponentially) tight for rates above R_{0} , the computational cutoff rate of sequential decoding. As a function of constraint length the performance of optimal convolutional codes is shown to be superior to that of block codes of the same length, the relative improvement increasing with rate. The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.
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