74 research outputs found
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Automatically calculating tonal tension
Since the early years of the past century, many scholars have focused their efforts towards designing models to better understand the way listeners perceive musical tension. From the existing models, Lerdahl’s has shown strong correlations against tension judgements provided by human listeners and has been used to make accurate predictions of musical tension. However, a full automation of Lerdahl’s model of tension has not yet been made available. This paper presents a computational approach to automatically calculate musical tension according to Lerdahl’s model, with a publicly available implementation
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Tension-driven Automatic Music Generation
The Ancient Greeks are one of the first civilisations we know of to have created algorithms to compose music. Since then, algorithmic techniques have vastly improved with increasingly sophisticated computers. In the last two decades, much research in this area has focused on two goals: designing algorithms which generate music as close as possible to that of human composers and implementing those algorithms to automatically generate music in interactive scenarios, such as video games.
To meet these goals, automatically generated music should:
- focus on higher-level concepts, such as musical tension,
- have long-term structure, and
- be able to adapt to changes in real time.
Combining these three requirements is, however, a challenging task. This dissertation investigates three steps to overcome this challenge. First, we argue that Lerdahl’s model of musical tension is suited to the automatic generation of tonal music that has long-term structure and that matches a given tension profile. By means of an illustrative example, we review Lerdhal’s model and implement a novel computational system to automate it. Second, we show that an effective generation strategy is to combine statistical methods with both rule-based methods and generative grammars to create a music generation system. Third, we implement the system and evaluate it through a collection of computational tests and empirical studies.
Our evaluation shows that:
(1) the system works effectively in real time, as long as the input tension profiles do not contain too many steep transitions,
(2) the hierarchical structure perceived by listeners matches the patterns intended by the system in the generated music, and
(3) tension-changing input profiles are accurately matched by the generated music
Synchronizing Sequencing Software to a Live Drummer
Copyright 2013 Massachusetts Institute of Technology. MIT allows authors to archive published versions of their articles after an embargo period. The article is available at
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Generating Time: Rhythmic Perception, Prediction and Production with Recurrent Neural Networks
In the quest for a convincing musical agent that performs in real time alongside human performers, the issues surrounding expressively timed rhythm must be addressed. Current beat tracking methods are not sufficient to follow rhythms automatically when dealing with varying tempo and expressive timing. In the generation of rhythm, some existing interactive systems ignore the pulse entirely, or fix a tempo after some time spent listening to input. Since music unfolds in time, we take the view that musical timing needs to be at the core of a music generation system.
Our research explores a connectionist machine learning approach to expressive rhythm generation, based on cognitive and neurological models. Two neural network models are combined within one integrated system. A Gradient Frequency Neural Network (GFNN) models the perception of periodicities by resonating nonlinearly with the musical input, creating a hierarchy of strong and weak oscillations that relate to the metrical structure. A Long Short-term Memory Recurrent Neural Network (LSTM) models longer-term temporal relations based on the GFNN output.
The output of the system is a prediction of when in time the next rhythmic event is likely to occur. These predictions can be used to produce new rhythms, forming a generative model.
We have trained the system on a dataset of expressively performed piano solos and evaluated its ability to accurately predict rhythmic events. Based on the encouraging results, we conclude that the GFNN-LSTM model has great potential to add the ability to follow and generate expressive rhythmic structures to real-time interactive system
Generation of folk song melodies using Bayes transforms
The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models
Interactive real-time musical systems
PhDThis thesis focuses on the development of automatic accompaniment systems.
We investigate previous systems and look at a range of approaches
that have been attempted for the problem of beat tracking. Most beat
trackers are intended for the purposes of music information retrieval where
a `black box' approach is tested on a wide variety of music genres. We
highlight some of the diffculties facing offline beat trackers and design a
new approach for the problem of real-time drum tracking, developing a
system, B-Keeper, which makes reasonable assumptions on the nature of
the signal and is provided with useful prior knowledge.
Having developed the system with offline studio recordings, we look to
test the system with human players. Existing offline evaluation methods
seem less suitable for a performance system, since we also wish to evaluate
the interaction between musician and machine. Although statistical data
may reveal quantifiable measurements of the system's predictions and behaviour,
we also want to test how well it functions within the context of a
live performance. To do so, we devise an evaluation strategy to contrast
a machine-controlled accompaniment with one controlled by a human.
We also present recent work on a real-time multiple pitch tracking,
which is then extended to provide automatic accompaniment for harmonic
instruments such as guitar. By aligning salient notes in the output from
a dual pitch tracking process, we make changes to the tempo of the
accompaniment in order to align it with a live stream. By demonstrating
the system's ability to align offline tracks, we can show that under
restricted initial conditions, the algorithm works well as an alignment tool
The Butterfly Schema as a Product of the Tendency for Congruence and Hierarchical Selection in the Instrumental Musical Grammar of the Classical Period
Diverging explanations of local multiparametric schemata are found in music of the common practice period (c. 1600–c. 1900). Associative statistical theories describe schemata as situated structures in particular times and places, whereas generative theories present these constructions as features formed through stability in universal and general rule systems. Associative-statistical theories of schemata elucidate the culturally conditioned relationships between features (distinctive attributes commonly used in grammars and schemata), but do not show the influence of universal psychological constraints; generative theories reveal the implicit structure of music, but do not formalise particular grammatical features and contexts. A synthesis of generative and associative-statistical approaches is necessary to model the interaction between universal and particular constraints of grammars and schemata. This dissertation focuses on a novel localised schema formed in the Classical instrumental grammar, termed the butterfly schema. It is posited that the butterfly schema is generated by a tendency for congruence that is manifest in and between the particular features of this grammar.
Computational musicology and psychology provide interdisciplinary insight on the formal possibilities and limitations of grammatical structure. Computational models of schemata and grammars show how the congruent features of musical structure can be represented and formalised. However, they also highlight the difficulties found in the automatic analyses of multiparametric relationships, and may be limited on account of their inductive frameworks. Psychological approaches are important for establishing universal laws of cognition, but are limited in their potential to account for the diversity of musical structuring in grammars. The synthesis of associative-statistical and generative approaches in the present dissertation permits modelling the combination of the universal and particular attributes of butterfly schemata. Butterfly schemata are dependent on the particular grammars of periods of history, but are constrained by the tendency for congruence, which is proposed to be a cognitive universal. The features of the butterfly schema and the Classical instrumental grammar are examined and compared against the features of the Baroque and Romantic grammars, showing how they are formed from diverse types of congruent structuring. The butterfly schema is a congruent grammatical category of the Classical instrumental grammar that comprises: chords that are close to the tonic in pitch space (with a chiastic tension curve starting and ending on the tonic); a textural and metrical structure that is regular and forms a regular duple hierarchy at the level of regular functional harmonic change and at two immediately higher levels; and simple harmonic-rhythm ratios (1:1 and 3:1).
A survey conducted using arbitrary corpora in European instrumental music, c. 1750–c.1850, shows the distribution of butterfly schemata. Butterfly schemata are more common in the Classical-period sample (c. 1750–c. 1800) than in the Romantic-period sample (c. 1800–c.1850), suggesting that the tendency for congruence manifest in and between the features common in the Classical grammar generates butterfly schemata. A second component to the statistical analysis concerns the type of schemata observed, since the tendency for congruence is presumed to also apply to the type of features that form in butterfly schemata. Maximally congruent features are generated more commonly than minimally congruent features, indicating the influence of the tendency for congruence. This dissertation presents a formulation of the Classical instrumental grammar as a multiparametrically congruent system, and a novel explanation and integration of the concepts of grammars and schemata. A final component to the dissertation poses that the features of the Classical instrumental grammar and butterfly schema follow a distinct order of dependency, governed by the mechanism of selection in culture. Although the tendency for congruence governs all features of a grammar, features are also formed by the top-down action of culture which selects those features. Thus, a top-down hierarchical selection model is presented which describes how the butterfly schema is formed through the order of selection of features in the Classical instrumental grammar
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