Author ORCID Identifier
0009-0001-3056-6422
Document Type
Dissertation
Date of Award
12-31-2024
Degree Name
Doctor of Philosophy in Mathematical Sciences - (Ph.D.)
Department
Mathematical Sciences
First Advisor
Amitabha Koshal Bose
Second Advisor
Casey Diekman
Third Advisor
Victor Victorovich Matveev
Fourth Advisor
James MacLaurin
Fifth Advisor
Horacio G. Rotstein
Abstract
Humans possess an inherent ability to recognize evenly-spaced rhythms, known as isochronous rhythms, owing to the brain's predisposition to entrain to external auditory stimuli with regular temporal intervals. The central focus of this research is to understand how the brain learns and retains rhythmic time intervals in the context of music. This dissertation studies rhythm detection and generation through mathematical models, biophysical networks, and artificial neural networks, addressing both isochronous and non-isochronous patterns.
A primary focus of the thesis is on isochronous rhythms. In particular, given a perturbation to an isochronous rhythm such as a tempo change or phase shift of the rhythm, novel decision-making strategies for how a human resynchronizes to the new rhythm are developed. Using an existing biophysical model, the Beat Generator (BG) model, it is shown that immediate error-correction independent of the perturbation minimizes average resynchronization time. The BG model is further utilized in conjunction with beat tracking software Librosa to learn the beat of real-world auditory stimuli. Specifically, a framework to extract the beat from tabla rhythms of North Indian Classical Music is developed. The BG model is shown to maintain precise temporal tracking even under natural acoustic variations and noise conditions, effectively simulating human-like adaptability to diverse musical inputs.
For non-isochronous rhythms, a hybrid architecture combining biophysical oscillators with Deep Neural Networks is constructed to simulate the Clave pattern, a cyclic rhythmic pattern found in Afro-Cuban music. Statistical analysis is performed to classify Clave types and compute cycle lengths. The framework is then extended to Indian Classical Music to analyze tabla rhythms. Building on this rhythmic analysis, the focus pivots to pitch classification. By categorizing distinct pitch classes, characteristic features of different taals are classified. Finally, a Recurrent Neural Network architecture is developed for generating written Tabla compositions while preserving traditional metric structures and musical rules.
The research spans the spectrum from theoretical modeling to practical applications, bridging the gap between biophysical understanding and machine learning approaches in rhythm analysis. The methodologies developed show the effectiveness of combining traditional mathematical models with modern computational techniques for understanding and generating complex rhythmic patterns.
Recommended Citation
Bose, Prianka, "Learning paradigms for rhythm detection and generation using mathematical models, biophysical and artificial neural networks" (2024). Dissertations. 1803.
https://digitalcommons.njit.edu/dissertations/1803
Included in
Applied Mathematics Commons, Music Theory Commons, Neurosciences Commons, Quantitative Psychology Commons
