Music Theory Commons^™

Music: Numbers In Motion, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Music develops and appears as we allow numbers to acquire a dynamical aspect and create, through their growth, the various keys that permit the richness of the musical texture. This idea was simply adumbrated in Plato’s work, but its importance to his philosophical worldview cannot be underestimated. In this paper we begin by discussing what is probably the first written record of an attempt to create a good temperament and then follow the Pythagoreans approach, whose problems forced musicians, over the next several centuries up to the Renaissance and early modern times, to come up with many different variations.

Liquid Tab, Nathan Hulet

Williams Honors College, Honors Research Projects

Guitar transcription is a complex task requiring significant time, skill, and musical knowledge to achieve accurate results. Since most music is recorded and processed digitally, it would seem like many tools to digitally analyze and transcribe the audio would be available. However, the problem of automatic transcription presents many more difficulties than are initially evident. There are multiple ways to play a guitar, many diverse styles of playing, and every guitar sounds different. These problems become even more difficult considering the varying qualities of recordings and levels of background noise.

Machine learning has proven itself to be a flexible tool …

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 …

Wordmuse, John M. Nelson

Computer Science and Software Engineering

Wordmuse is an application that allows users to enter a song and a list of keywords to create a new song. Built on Spotify's API, this project showcases the fusion of music composition and artificial intelligence. This paper also discusses the motivation, design, and creation of Wordmuse.

The Significance Of Sonic Branding To Strategically Stimulate Consumer Behavior: Content Analysis Of Four Interviews From Jeanna Isham’S “Sound In Marketing” Podcast, Ina Beilina

Student Theses and Dissertations

Purpose:
Sonic branding is not just about composing jingles like McDonald’s “I’m Lovin’ It.” Sonic branding is an industry that strategically designs a cohesive auditory component of a brand’s corporate identity. This paper examines the psychological impact of music and sound on consumer behavior reviewing studies from the past 40 years and investigates the significance of stimulating auditory perception by infusing sound in consumer experience in the modern 2020s.

Design/methodology/approach:
Qualitative content analysis of audio media was used to test two hypotheses. Four archival oral interview recordings from Jeanna Isham’s podcast “Sound in Marketing” featuring the sonic branding experts …

The Mathematical Foundation Of The Musical Scales And Overtones, Michaela Dubose-Schmitt

Theses and Dissertations

This thesis addresses the question of mathematical involvement in music, a topic long discussed going all the way back to Plato. It details the mathematical construction of the three main tuning systems (Pythagorean, just intonation, and equal temperament), the methods by which they were built and the mathematics that drives them through the lens of a historical perspective. It also briefly touches on the philosophical aspects of the tuning systems and whether their differences affect listeners. It further details the invention of the Fourier Series and their relation to the sound wave to explain the concept of overtones within the …

The International Conference On Creative Mathematical Sciences Communication: Online Event (Cmsc'20) And Cmsc'21, Frances Rosamond

Journal of Humanistic Mathematics

You are warmly invited to register now for the 5th International Conference on Creative Mathematical Sciences Communication (CMSC’21) which will be held at Adam Mickiewicz University in Poznań, Poland, 2–6 July, 2021.

The International Conference on Creative Mathematical Sciences Communication (CMSC) is a unique gathering of computer scientists and mathematicians, teachers, musicians, dancers, dramatists, game designers, educators and communicators of all sorts.

Due to the pandemic, the in-person event scheduled for 2020 has been post- poned and a short CMSC Online Event was organized as a “teaser” or trailer in order to feel the spirit of the full 5th CMSC …

Gray Codes In Music Theory, Isaac L. Vaccaro

Electronic Theses and Dissertations

In the branch of Western music theory called serialism, it is desirable to construct chord progressions that use each chord in a chosen set exactly once. We view this problem through the scope of the mathematical theory of Gray codes, the notion of ordering a finite set X so that adjacent elements are related by an element of some specified set R of involutions in the permutation group of X. Using some basic results from the theory of permutation groups we translate the problem of finding Gray codes into the problem of finding Hamiltonian paths and cycles in a Schreier …

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Facuty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo

The STEAM Journal

The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of …

The Battle Between Impeccable Intonation And Maximized Modulation, Timothy M. True

Musical Offerings

Equal temperament represents a way of completing the musical circle, and systematically compensating for the Pythagorean comma. Pythagoras discovered this acoustical problem around 550 B.C., and since that time music theorists have debated how to deal with it. The problem is that no perfect solution exists—something must be compromised. As musical styles developed, specific factors and harmonic tendencies led to the gradual adoption of equal temperament. Early in music history, theorists preferred systems which kept acoustical purity relatively intact. Pythagorean intonation and just intonation serve as two examples. However, the move from modality to tonality decentralized the melody as the …

A Short Note On Pitch, Interval, And Melody Matching Assessment, Eric Hanson, Hannah Baslee, Eric Freudenthal

Departmental Technical Reports (CS)

This short note describes a metric and procedure for assessing an individual's overall simple pitch and interval matching proficiency when singing.

Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra

Alissa Crans

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Musical Sound: A Mathematical Approach To Timbre, Timothy Weiss (Class Of 2016)

Writing Across the Curriculum

What is the mathematical reasoning behind the ear’s ability to distinguish two completely different musical sounds? In answering this question, one must call to mind a fundamental term with regards to music: timbre.

The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong

Dissertations, Theses, and Capstone Projects

This interdisciplinary study explores musical-mathematical analogies in the fourth movement of Ligeti’s Piano Concerto. Its aim is to connect musical analysis with the piece’s mathematical inspiration. For this purpose, the dissertation is divided into two sections. Part I (Chapters 1-2) provides musical and mathematical context, including an explanation of ideas related to Ligeti’s mathematical inspiration. Part II (Chapters 3-5) delves into an analysis of the rhythm, form, melody / motive, and harmony. Appendix A is a reduced score of the entire movement, labeled according to my analysis.

Blending Two Automatic Playlist Generation Algorithms, James Curbow

Honors Theses

We blend two existing automatic playlist generation algorithms. One algorithm is built to smoothly transition between a start song and an end song (Start-End). The other infers song similarity based on adjacent occurrences in expertly authored streams (EAS). First, we seek to establish the effectiveness of the Start-End algorithm using the EAS algorithm to determine song similarity, then we propose two playlist generation algorithms of our own: the Unbiased Random Walk (URW) and the Biased Random Walk (BRW). Like the Start-End algorithm, both the URW algorithm and BRW algorithm transition between a start song and an end song; however, issues …

Empyreal Radiance: An Application Of Sonification In The Field Of Astrophysics, Ryan Loth

Undergraduate Distinction Papers

Broadly, this paper discusses the application of sonification and its potential for increasing knowledge. The paper is broken up into three sections: the theory of sonification, sonification for artistic purposes, and lastly an extensive look at one process of sonification dealing with solar winds in space. Concerning the theory of sonification, the paper will divulge into the process of sonification and ask questions about the limitations of it as well. The second section discusses how sonification is a way to build the curiosity of not just scientists, but also the general public. The final section addresses my composition Empyreal Radiance …

A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson

Undergraduate Honors Thesis Collection

The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …

An Introduction To Fourier Analysis With Applications To Music, Nathan Lenssen, Deanna Needell

Journal of Humanistic Mathematics

In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for …

Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra

Mathematics Faculty Works

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Mathematical Methods In Composing Melodies, Thomas Brown

Undergraduate Theses and Capstone Projects

This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …

Inside Unlv, Diane Russell, Betty Blodgett, Kevin Force, Jennifer Vaughan, Cate Weeks, Jonathan Paver

Inside UNLV

No abstract provided.

Music And Mathematics, Roxanne Kitts

Humanistic Mathematics Network Journal

No abstract provided.