Physical Sciences and Mathematics Commons^™

The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson

Journal of Humanistic Mathematics

In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.

The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita

Journal of Humanistic Mathematics

We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model.

A Classification Of Musical Scales Using Binary Sequences, Thomas Hillen

Journal of Humanistic Mathematics

Every beginning music student has gone through the four main musical scales: major, natural minor, harmonic minor, and melodic minor. And some might wonder, why those four and not five, or six, or just three? Here we show that a mathematical classification can be used to identify these scales as representatives of certain scale families. Moreover, the classification reveals another scale family, which is much less known: the harmonic major scale. We find that each scale family contains exactly seven scales, which include the modes (dorian, phrygian,...) and other scales such as the Romanian, …

Fourth Voices Conference On Teaching Stem With Song, Lawrence M. Lesser

Journal of Humanistic Mathematics

The fourth VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song) conference will be held September 26, 2021, with its Sunday date especially targeting those whose teaching schedule precludes attendance on a weekday. This online-only conference explores the use of song to teach STEM content at the college or secondary school level and will include reviewed interactive sessions, video-posters, and discussions of interest to both practitioners and researchers.

Markov Chains For Computer Music Generation, Ilana Shapiro, Mark Huber

Journal of Humanistic Mathematics

Random generation of music goes back at least to the 1700s with the introduction of Musical Dice Games. More recently, Markov chain models have been used as a way of extracting information from a piece of music and generating new music. We explain this approach and give Python code for using it to first draw out a model of the music and then create new music with that model.

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 …

The Emergence Of Creativity: Insights From Carnatic Raaga Improvisation And Mathematical Proof Generation, Srividhya Balaji, Sean Chorney

Journal of Humanistic Mathematics

Creativity is a broad phenomenon that scholars have interpreted in a multitude of ways. We notice that a majority of the views describe creativity as something innate. This paper aims to verge from this perspective and explore creativity in terms of the constant mutual interaction of a person and their environment. Using the theoretical framework, enactivism, and the notion of emergence, we investigate the creative processes involved in musical improvisations of south Indian classical or Carnatic music and mathematical proof generation. Interview excerpts from professional Carnatic musicians and research mathematicians on their respective creative processes during musical improvisation and proof …

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 …

Cartegory Theory: Framing Aesthetics Of Mathematics, Maria Mannone

Journal of Humanistic Mathematics

Mathematics can help investigate hidden patterns and structures in music and visual arts. Also, math in and of itself possesses an intrinsic beauty. We can explore such a specific beauty through the comparison of objects and processes in math with objects and processes in the arts. Recent experimental studies investigate the aesthetics of mathematical proofs compared to those of music. We can contextualize these studies within the framework of category theory applied to the arts (cARTegory theory), thanks to the helpfulness of categories for the analysis of transformations and transformations of transformations. This approach can be effective for the pedagogy …

A Generalised Song, Will Turner

Journal of Humanistic Mathematics

We consider parallels between words and music. We call a triple of structures, one verbal, one musical, and one mathematical, in which the mathematical structure is related to the verbal and musical structures, a generalised song. With the intention of exhibiting the potential of this form, we describe a generalised song called ‘Cube’.

Musical Missteps: The Severity Of The Sophomore Slump In The Music Industry, Shane M. Zackery

Scripps Senior Theses

This study looks at alternative models of follow-up album success in order to determine if there is a relationship between the decrease in Metascore ratings (assigned by Metacritic.com) between the first and second album for a musician or band and the 1) music genre or 2) the number of years between the first and second album release. The results support the dominant thought, which suggests that neither belonging to a certain genre of music nor waiting more or less time to drop the second album makes an artist more susceptible to the Sophomore Slump. This finding is important because it …

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 …

Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers

HMC Senior Theses

The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …

Skolem’S Paradox And Contradictory Popular Songs, Maurice Machover

Humanistic Mathematics Network Journal

No abstract provided.

Curriculum Development Via Literary And Musical Forms, Joel K. Haack

Humanistic Mathematics Network Journal

No abstract provided.

Puzzles, Patterns Drums: The Dawn Of Mathematics In Rwanda And Burundi., D. Huylebrouck

Humanistic Mathematics Network Journal

No abstract provided.

Music And Mathematics, Roxanne Kitts

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Emblems Of Mind, The Inner Life Of Music And Mathematics, By Edward Rothstein, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Emblems Of Mind, The Inner Life Of Music And Mathematics, By Edward Rothstein, Dan Fitzgerald, Joel Haack

Humanistic Mathematics Network Journal

No abstract provided.

Fibonacci Melodies, Robert Lewand

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Ethnomathematics: A Multicultural View Of Mathematical Ideas, By Marcia Ascher, Bernadette Anne Berken

Humanistic Mathematics Network Journal

No abstract provided.