A Transformational Approach to Harmony Improvisation

Programme Committee and …

2012

In this paper we propose a computational model for stochastic melodic synthesis based on an approach developed through reactive multiagent systems. In general automatic musical composition approaches, the states transition probabilities are obtained from statistical analysis of musical segments provided by the user, which tends to generate musical results very similar to the initial musical segments. As alternative to these characteristics, we consider a computational model in three layers: the first layer aims to generate transition probabilities matrices (pitches and durations of musical notes, in this context) to supply the second layer. The second layer produces probabilistic models for generation of the melodic segments (P M M SG), through the interaction with the user, in order to supply the stochastic melodic synthesis process at the third layer. This model aims to reduce the influence of the composer in the final composition, in order to build melodic structures not originally conceived by the composer. Nevertheless, this work does not cope with the aesthetic quality of the melodic results, since the work focus is the spontaneous generation of the initial information that will guide the stochastic melodic synthesis.

Applied Sciences

This paper presents a methodology for generating cross-harmonizations of jazz standards, i.e., for harmonizing the melody of a jazz standard (Song A) with the harmonic context of another (Song B). Specifically, the melody of Song A, along with the chords that start and end its sections (chord constraints), are used as a basis for generating new harmonizations with chords and chord transitions taken from Song B. This task involves potential incompatibilities between the components drawn from the two songs that take part in the cross-harmonization. In order to tackle such incompatibilities, two methods are introduced that are integrated in the Hidden Markov Model and the Viterbi algorithm. First, a rudimentary approach to chord grouping is presented that allows interchangeable utilization of chords belonging to the same group, depending on melody compatibility. Then, a “supporting” harmonic space of chords and probabilities is employed, which is learned from the entire dataset of the ...

Proceedings of the SMC Conferences, 2017

Music constraint systems provide a rule-based approach to composition. Existing systems allow users to constrain the harmony, but the constrainable harmonic information is restricted to pitches and intervals between pitches. More abstract analytical information such as chord or scale types, their root, scale degrees, enharmonic note representations, whether a note is the third or fifth of a chord and so forth are not supported. However, such information is important for modelling various music theories. This research proposes a framework for modelling harmony at a high level of abstraction. It explicitly represents various analytical information to allow for complex theories of harmony. It is designed for efficient propagationbased constraint solvers. The framework supports the common 12-tone equal temperament, and arbitrary other equal temperaments. Users develop harmony models by applying user-defined constraints to its music representation. Three examples demonstrate the expressive power of the framework: (1) an automatic melody harmonisation with a simple harmony model; (2) a more complex model implementing large parts of Schoenberg's tonal theory of harmony; and (3) a composition in extended tonality. Schoenberg's comprehensive theory of harmony has not been computationally modelled before, neither with constraints programming nor in any other way.

Journal of Creative Music Systems, 2016

Melodic harmonisation is a sophisticated creative process that involves deep musical understanding and a specialised knowledge of music relating to melodic structure, harmony, rhythm, texture, and form. In this article a new melodic harmonisation assistant is presented that is adaptive (learns from data), general (can cope with any tonal or non-tonal harmonic idiom) and modular (learns different aspects of harmonic structure such as chord types, chord transitions, cadences, and voice-leading). This melodic harmonisation system can be used not only to mimic given harmonic styles, but to generate novel harmonisations for diverse melodies and create new harmonic spaces, allowing for the imposition of user-defined chord constraints, leading to new unforeseen harmonic realisations. The various components of the proposed model are explained, then, a number of creative harmonisations of different melodies are presented to illustrate the potential of the system. 1 Introduction Creative music systems are often criticised as not "really" being creative per se; underlying this criticism is the belief that the actual human programmer is the true source of creativity. However, machine learning has made such criticisms more difficult to maintain, as a machine may acquire knowledge from data, constructing a new conceptual space without human intervention, creating new unforeseen output (Wiggins et al., 2009). Adaptability, flexibility, independence, and autonomy are features associated with creativity (see key components of creativity in Jordanous (2013)); general representations and machine learning techniques allow creative systems to be open to new environments, to evolve, to transform existing concepts, and to construct new ones, creating new and unexpected results. A model of creativity has been proposed by Boden (2009) whereby a conceptual space may be explored by an agent in order to: generate new creative instances (exploratory creativity); transform the rules of the conceptual space, changing the conceptual space itself (transformational creativiy); or, create new blended spaces by combining different conceptual spaces that share structural similarities (combinational creativity). In the current study the conceptual spaces are learned in a bottom-up fashion from data, and are structured in a modular way so as to allow (at a later stage) to combine different modules from different spaces, thus creating new blended spaces. At this stage, the system is indicated to exhibit exploratory creativity, by composing harmonies that potentially excess the harmonic borders of a corpus. This article focuses on melodic harmonisation as a creative musical act. Some researchers follow the knowledge-engineering approach whereby experts encode the essential rules for harmonisation in a certain tonal style (from the Bach chorale expert system by Ebcioglu (1988) to the explicitly structured knowledge paradigm by Phon-Amnuaisuk & Wiggins (1999) and Phon-Amnuaisuk et al.

2010

Abstract. In this paper, we describe a method of generating harmonic progressions using case-based analysis of existing material that employs a variable-order Markov model. Using a unique method for quantifying harmonic complexity and tension between chord transitions, as well as specifying a desired bass-line, the user specifies a 3 dimensional vector, which the realtime generative algorithm attempts to match during chord sequence generation.

Generating equivalent chord progressions to enrich guided improvisation : application to rhythm changes

This paper presents a method taking into account the form of a tune upon several levels of organisation to guide music generation processes to match this structure. We first show how a phrase structure grammar can represent a hierarchical analysis of chord progressions and be used to create multi-level progressions. We then explain how to exploit this multi-level structure of a tune for music generation and how it enriches the possibilities of guided machine improvisation. We illustrate our method on a prominent jazz chord progression called 'rhythm changes'. After creating a phrase structure grammar for 'rhythm changes' with a professional musician, the terminals of this grammar are automatically learnt on a corpus. Then, we generate melodic improvisations guided by multi-level progressions created by the grammar. The results show the potential of our method to ensure the consistency of the improvisation regarding the global form of the tune, and how the knowledge of a corpus of chord progressions sharing the same hierarchical organisation can extend the possibilities of music generation.

Lecture Notes in Computer Science, 2016

We present Conchord, a system for real-time automatic generation of musical harmony through navigation in a novel 12-dimensional Tonal Interval Space. In this tonal space, angular and Euclidean distances among vectors representing multi-level pitch configurations equate with music theory principles, and vector norms acts as an indicator of consonance. Building upon these attributes, users can intuitively and dynamically define a collection of chords based on their relation to a tonal center (or key) and their consonance level. Furthermore, two algorithmic strategies grounded in principles from function and root-motion harmonic theories allow the generation of chord progressions characteristic of Western tonal music.

Guide to Computing for Expressive Music Performance, 2012

This chapter describes a music analysis system based on a generative theory of tonal music (GTTM). Musical theory provides methodologies for analyzing and transcribing musical knowledge, experiences, and skills from a musician's way of thinking. Our concern is whether the concepts necessary for music analysis are sufficiently externalized in musical theory. Given its ability to formalize musical knowledge, we consider the GTTM to be the most promising theory among the many that have been proposed because it captures the aspects of musical phenomena based on the Gestalt in the music and follows relatively rigid rules. It also describes music expectation and melody morphing methods that use the analysis results from our music analysis system. The music expectation method predicts the next notes needed to assist musical novices in playing improvisations. The melody morphing method generates an intermediate melody between two melodies in a systematic order in accordance with a certain numerical measure.

Soft Computing, 2004

we describe variable markov models we have used for statistical learning of musical sequences, then we present the factor oracle, a data structure proposed by Crochemore & al for string matching. We show the relation between this structure and the previous models and indicate how it can be adapted for learning musical sequences and generating improvisations in a real-time context. Modeling musical sequences Statistical modeling of musical sequences has been experimented since the very beginnings of musical informatics (see [Con03] for a review and criticism of most existing models, and [Zic87] for one of the first available real-time interactive system). The idea behind context models, which we are mostly interested in here, is that events in a musical piece can be predicted from the sequence of preceding events. The operational property of such models is to provide the conditional probability distribution over an alphabet given a sequence. For example, if w is musical sequence, σ a symbol belonging to the musical alphabet Σ, P(σ|w) is the probability that σ will follow w, i.e. the probability of wσ given w. This distribution P will be used for generating new sequences or for computing the probability of a given one. First experiments in context based modeling made intensive use of Markov chains. [Ron&al96] explain that this idea dates back to Shannon : complex sequences do not have obvious underlying source, however, they exhibit a property called short memory property by the authors; there exists a certain memory lengh L such that the conditional probability distribution on the next symbol σ does not change significantly if we condition it on suffixes of w longer than L. In the case of Markov chains, L is the order. However, the size of Markov chains is O(|Σ| L), so only low order models have been actually experimented. To cope with the model order problem, in earlier works [Dub98,Dub02,Dub03,Ass99] we have proposed a method for building musical style analyzers and generators based on several algorithms for prediction of discrete sequences using Variable Markov Models (VMM). The class of these algorithms is large and we focused mainly on two variants of predictorsuniversal prediction based on Incremental Parsing (IP) and prediction based on Probabilistic Suffix Trees (PST). The IP method is derived from Information Theory. J. Ziv and A. Lempel [Ziv78] first suggested the core of this method called Incremental Parsing in the context of lossless compression research. IP builds a dictionary of distinct motifs by making a single left to right traversal of a sequence, sequentially adding to a dictionary every new phrase that differs by a single last character from the longest match that already exists in the dictionary. Using a tree representation for the dictionary, every node is associated with a string, whose characters appear as labels on the arcs that lead from the root to that node. Each time the parsing algorithm reaches a longest-match node it means that the node's string has already occurred in