Physical Sciences and Mathematics Commons^™

Mathematical Structure Of Musical Tuning Systems, Shay Joel Francis Spitzer

Senior Projects Spring 2023

Over the course of history, western music has created a unique mathematical problem for itself. From acoustics, we know that two notes sound good together when they are related by simple ratios consisting of low primes. The problem arises when we try to build a finite set of pitches, like the 12 notes on a piano, that are all related by such ratios. We approach the problem by laying out definitions and axioms that seek to identify and generalize desirable properties. We can then apply these ideas to a broadened algebraic framework. Rings in which low prime integers can be …

A New Way To Make Music: Processing Digital Audio In Virtual Reality, Gavin E. Payne

Senior Projects Spring 2022

The work of this project attempts to provide new methods of creating music with technology. The product, Fields, is a functional piece of virtual reality software, providing users an immersive and interactive set of tools used to build and design instruments in a modular manner. Each virtual tool is analogous to musical hardware such as guitar pedals, synthesizers, or samplers, and can be thought of as an effect or instrument on its own. Specific configurations of these virtual audio effects can then be played to produce music, and then even saved by the user to load up and play with …

The Spiral Model For Generative Harmony, Jackson Guy Spargur

Senior Projects Spring 2020

Generative music is a broad and well-explored field, in which researchers have attempted various approaches at creating algorithmic models for the creation of music. Researchers may attempt to model the composition of melody, or of musical phrase structure, or, as is the focus of this paper, the harmonization of multiple voices. I use as the core of my model Elaine Chew’s “Spiral Array”, outlined in her 2000 thesis “Towards a Mathematical Model Of Tonality”. Chew’s applications for this model were all analytical, gaining insights about human-composed pieces of music by running them through her model. My project is comprised of …

A Machine Learning Approach To The Perception Of Phrase Boundaries In Music, Evan Matthew Petratos

Senior Projects Fall 2020

Segmentation is a well-studied area of research for speech, but the segmentation of music has typically been treated as a separate domain, even though the same acoustic cues that constitute information in speech (e.g., intensity, timbre, and rhythm) are present in music. This study aims to sew the gap in research of speech and music segmentation. Musicians can discern where musical phrases are segmented. In this study, these boundaries are predicted using an algorithmic, machine learning approach to audio processing of acoustic features. The acoustic features of musical sounds have localized patterns within sections of the music that create aurally …

The Impact Of Live Coding Within An Educational And Performance Setting, Alexus Renee Foster

Senior Projects Spring 2020

For the past three semesters at Bard, live coding has become my newest form of creative expression and performance. This method of coding involves either creating on the spot from scratch or editing pre-existing code in a real time manner. There is no real set structure or steps that must be followed, however, one rule must always be followed: show your code. In the classroom, live coding occurs when the professor demonstrates some algorithm by displaying the program on a projector for the entire class to observe. During musical performances, the same improvisational nature of live coding is also present, …

Practice Room Acoustics: What Matters To Musicians About The Practice Space, Yu-Tien Chou

Senior Projects Spring 2019

Why do people always prefer the practice room in the corner on the second floor than the others? What’s the reason why string players often go for the “dryer” room than the wind players? Wondering why brass players often occupy the resonant room? This paper is here to decipher all the mysteries behind all of the questions above by the acoustic analysis suggested by Bonnelo and the other supplying papers on sound absorbing materials. The question to be answered is how the rooms are different from each other in terms of their dimensions and damping surfaces. Eventually, construct a criteria …

Algorithmic Music Composition And Accompaniment Using Neural Networks, Daniel Wilton Risdon

Senior Projects Spring 2016

The goal of this project was to use neural networks as a tool for live music performance. Specifically, the intention was to adapt a preexisting neural network code library to work in Max, a visual programming language commonly used to create instruments and effects for electronic music and audio processing. This was done using ConvNetJS, a JavaScript library created by Andrej Karpathy.

Several neural network models were trained using a range of different training data, including music from various genres. The resulting neural network-based instruments were used to play brief pieces of music, which they used as input to create …