A Temporal Basis for Acousmatic Rhythm

In an attempt to begin to redress the relative lack of literature focused on rhythm in acousmatic music, this article is intended as a brief look at the acousmatic perspective on rhythm. This begins with a quick overview of discussion around rhythm in electroacoustic music more broadly, then contrasts this with some of Pierre Schaeffer's views on rhythm, and finally compares the perceptual temporal levels identified by Schaeffer with similar levels drawn from electroacoustic music, contemporary music, and cognitive psychology

Perceiving and predicting expressive rhythm with recurrent neural networks

Automatically following rhythms by beat tracking is by no means a solved problem, especially when dealing with varying tempo and expressive timing. This paper presents a connectionist machine learning approach to expressive rhythm prediction, based on cognitive and neurological models. We detail a multi-layered recurrent neural network combining two complementary network models as hidden layers within one system. The first layer is a Gradient Frequency Neural Network (GFNN), a network of nonlinear oscillators which acts as an entraining and learning resonant filter to an audio signal. The GFNN resonances are used as inputs to a second layer, a Long Short-term Memory Recurrent Neural Network (LSTM). The LSTM learns the long-term temporal structures present in the GFNN's output, the metrical structure implicit within it. From these inferences, the LSTM predicts when the next rhythmic event is likely to occur. We train the system on a dataset selected for its expressive timing qualities and evaluate the system on its ability to predict rhythmic events. We show that our GFNN-LSTM model performs as well as state-of-the art beat trackers and has the potential to be used in real-time interactive systems, following and generating expressive rhythmic structures

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

Modelling metrical flux: an adaptive frequency neural network for expressive rhythmic perception and prediction

Beat induction is the perceptual and cognitive process by which humans listen to music and perceive a steady pulse. Computationally modelling beat induction is important for many Music Information Retrieval (MIR) methods and is in general an open problem, especially when processing expressive timing, e.g. tempo changes or rubato. A neuro-cognitive model has been proposed, the Gradient Frequency Neural Network (GFNN), which can model the perception of pulse and metre. GFNNs have been applied successfully to a range of ‘difficult’ music perception problems such as polyrhythms and syncopation. This thesis explores the use of GFNNs for expressive rhythm perception and modelling, addressing the current gap in knowledge for how to deal with varying tempo and expressive timing in automated and interactive music systems. The cannonical oscillators contained in a GFNN have entrainment properties, allowing phase shifts and resulting in changes to the observed frequencies. This makes them good candidates for solving the expressive timing problem. It is found that modelling a metrical perception with GFNNs can improve a machine learning music model. However, it is also discovered that GFNNs perform poorly when dealing with tempo changes in the stimulus. Therefore, a novel Adaptive Frequency Neural Network (AFNN) is introduced; extending the GFNN with a Hebbian learning rule on oscillator frequencies. Two new adaptive behaviours (attraction and elasticity) increase entrainment in the oscillators, and increase the computational efficiency of the model by allowing for a great reduction in the size of the network. The AFNN is evaluated over a series of experiments on sets of symbolic and audio rhythms both from the literature and created specifically for this research. Where previous work with GFNNs has focused on frequency and amplitude responses, this thesis considers phase information as critical for pulse perception. Evaluating the time-based output, it was found that AFNNs behave differently to GFNNs: responses to symbolic stimuli with both steady and varying pulses are significantly improved, and on audio data the AFNNs performance matches the GFNN, despite its lower density. The thesis argues that AFNNs could replace the linear filtering methods commonly used in beat tracking and tempo estimation systems, and lead to more accurate methods