Springer Handbook of Systematic Musicology pp 313-328 | Cite as

# Adaptive Musical Control of Time-Frequency Representations

## Abstract

In this chapter we consider control structures and mapping in the process of deciding upon the underlying sonic algorithm for a digital musical instrument. We focus on control of timbral and textural phenomena that arise from the interaction and modulation of stationary spectral components, as well as from stochastic elements of sound. Given this observation and general design criteria, we focus on a family of sound models that parameterize the stationary and stochastic components using a spectral representation that is commonly based on an underlying short-time Fourier transform (STFT ) analysis. Using this as a fundamental approach we build a dynamic model of sound analysis and synthesis, focusing on a design that will simultaneously lead to musically interesting transformations of textural and noise-based sound features while allowing for control structures to be integrated into the sound dynamics. Building upon well-established adaptive algorithms such as the Kalman Filter, we present a recursive-exponential implementation, and exploit a fast algorithm derivation in order to process both additive data and the full underlying phase vocoder. The model is further augmented to allow for nonlinear adaptive control, pointing towards new directions for adaptive musical control of time-frequency models.

- AR
autoregressive

- ARMA
autoregressive moving average

- DFT
discrete Fourier transformation

- EKF
extended Kalman filter

- IIR
infinite impulse response

- KF
Kalman filter

- MSD
mass-spring-damper

- RESTFT
recursive exponential short-time Fourier transform

- SMS
spectral modeling synthesis

- SSR
state-space representation

- SSSPV
stochastic state-space phase vocoder

- STFT
short-term Fourier transform/short-time Fourier transform

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