Signal Processing Approaches to Musical Tuning System Detection in Audio

Abstract

There are three main intonation systems musicians use––just, equal temperament, and Pythagorean. The use of any one of these particular intonation systems depends on a number of factors, most importantly musical and harmonic context. While work has been done in analyzing intonation tendencies in vocal and instrumental performance as well as temperament estimation of fixed-pitch instruments such as the harpsichord, no work has been done in detecting instances of intonation systems in audio from a signal processing perspective. For my thesis, I propose several algorithms and signal processing techniques to detect and identify intonation systems in recordings of the Third Bach Cello Suite Prelude, which I chose for its musical and harmonic complexity. I first obtained timestamps and fundamental frequency estimates utilizing CREPE, a pretrained deep convolutional neural network used for monophonic frequency estimation. Then, I implemented an algorithm that obtains an estimated classification for each note by calculating an associated probability for each tuning system and applying a centered moving average. Finally, a set of sequences of intonation systems were identified by splitting the intonation system-labeled time series at instances where consecutive labels differ and merging any consecutive equivalently-labeled sequences within a presupplied time threshold of each other. Clear overall trends in the use of just and Pythagorean intonation emerged from running the model on twelve different recordings of the Prelude. This research offers musicians a tool for understanding and assessing their intonation by providing an objective measure of intonation. It also provides a way to gain insight into the history of intonation in performance.