Abstract
Tonal melody can imply vertical harmony through a sequence of tones. Current methods for automatic chord estimation commonly use chroma-based features extracted from audio signals. However, the implied harmony of unaccompanied melodies can be difficult to estimate on the basis of chroma content in the presence of frequent nonchord tones. Here we present a novel approach to automatic chord estimation based on the human perception of pitch sequences. We use cohesion and inhibition between pitches in auditory short-term memory to differentiate chord tones and nonchord tones in tonal melodies. We model short-term pitch memory as a gradient frequency neural network, which is a biologically realistic model of auditory neural processing. The model is a dynamical system consisting of a network of tonotopically tuned nonlinear oscillators driven by audio signals. The oscillators interact with each other through nonlinear resonance and lateral inhibition, and the pattern of oscillatory traces emerging from the interactions is taken as a measure of pitch salience. We test the model with a collection of unaccompanied tonal melodies to evaluate it as a feature extractor for chord estimation. We show that chord tones are selectively enhanced in the response of the model, thereby increasing the accuracy of implied harmony estimation. We also find that, like other existing features for chord estimation, the performance of the model can be improved by using segmented input signals. We discuss possible ways to expand the present model into a full chord estimation system within the dynamical systems framework.
Highlights
Melody is a succession of pitched sounds arranged to form a coherent musical pattern (Bingham, 1910; Apel, 1969)
The model is driven by audio signals, and acoustic frequencies are transformed into a complex pattern of oscillations which we take as a measure of pitch salience
We describe the structure and function of the shortterm pitch memory model with an example. (The differential equations governing the dynamics of the model are given below, along with the parameter values used in this study, but understanding of the mathematical details is not required to comprehend the results and implications of this study.) The model consists of two layers of nonlinear oscillators tuned to a chromatic scale (Figure 1)
Summary
Melody is a succession of pitched sounds arranged to form a coherent musical pattern (Bingham, 1910; Apel, 1969). To model the interaction of melodic pitches in auditory memory, we use a network of tonotopically tuned nonlinear oscillators. The model is driven by audio signals, and acoustic frequencies are transformed into a complex pattern of oscillations which we take as a measure of pitch salience. We use a generic mathematical form of nonlinear oscillation, called the canonical model, which describes oscillatory activities with complex-valued state variables (Kim and Large, 2015). When two Layer 2 oscillators in a simple frequency relationship have high amplitudes at the same time, the plastic connections between them quickly strengthen and let the oscillators reinforce each other through nonlinear resonance (i.e., mode-locking). Let us discuss how the pitch memory model can improve the estimation of implied harmony by selectively enhancing chord tones over nonchord tones. We are developing a GrFNN pitch estimator, and the future versions of the present model will include a pitch estimator and be able to handle signals containing complex sounds
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