The Mathematics of Music

A reading list

Items in dark red bold were recommended several times.

It is not the intent to read all these articles and books! This gives us a starting point with many materials to choose from.

The Basics: Start Here

https://en.wikipedia.org/wiki/Music_and_mathematics Music and Mathematics | Wikipedia Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. https://brilliant.org/wiki/mathematics-of-music/ Mathematics of Music | Brilliant Absolute Pitch, Frequency, and Wavelength. Relative Pitch, Interval, and Frequency Ratio. Intervals and Simple Ratios. Pythagorean and Just Intonation. https://www.simplifyingtheory.com/math-in-music/ Mathmetics and Music | Simplying Theory Pythagoras. Musical scales. Frequencies. Logarithm. https://globalmusictheory.com/music-theory-and-math-understanding-connections/ Music theory and math – understanding connections by Brandon Alsup Numeric notation. Scales and tuning. Pythagoras and modes. Equal temperament. Twelve-tone analysis. Roman numeral analysis. https://medium.com/@ciaranpconnolly/music-and-maths-a-harmony-of-numbers-and-melodies-85d5d9d432b1 Music and Maths: A Harmony of Numbers and Melodies by Ciaran Connolly | Medium Rhythm and time signatures. Pitch and frequency. Patterns. Golden ratio. Case studies. https://blog.wyzant.com/the-hidden-math-in-music/ The Hidden Math in Music | Wyzant Rhythm. Pitch. Timbre. Harmony. https://myprivateprofessor.com/math-and-music/ The Connections Between Math and Music Pythagoras. Frequency. Patterns. Fractals. https://www.icsv26.org Math in Music by Zack Hunter Fibonacci. Golden ratio. Transformational theory. Pitch. -

For Kids

https://mathematicalmysteries.org/the-mathematics-of-music/ The Mathematics of Music Pitch and frequency. Rhythm and meter. Musical form and structure. Tuning and temperament. Generative music and algorithmic composition. Musical acoustics and instrument design. https://www.kennedy-center.org/education/resources-for-educators/classroom-resources/media-and-interactives/media/music/connections/connections/math--music/ What do math and music have in common? | Kennedy Center Fractions. Ratios. Patterns. -

Temperament and Tuning

https://en.wikipedia.org/wiki/Musical_temperament Musical Temperament | Wikipedia In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. https://en.wikipedia.org/wiki/Equal_temperament Equal Temperament | Wikipedia An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same. This system yields pitch steps perceived as equal in size, due to the logarithmic changes in pitch frequency. -

People

https://en.wikipedia.org/wiki/Guerino_Mazzola +Guerino Mazzola | Wikipedia Guerino Bruno Mazzola (born 1947) is a Swiss mathematician, musicologist, and jazz pianist, as well as a writer. Mazzola is well known for his music theory book _The Topos of Music_. https://en.wikipedia.org/wiki/Leonhard_Euler#Music Leonhard Euler - Music Theory | Wikipedia One of Euler's more unusual interests was the application of mathematical ideas in music. In 1739 he wrote the Tentamen novae theoriae musicae (Attempt at a New Theory of Music), hoping to eventually incorporate musical theory as part of mathematics. This part of his work, however, did not receive wide attention and was once described as too mathematical for musicians and too musical for mathematicians. https://en.wikipedia.org/wiki/Ernst_Chladni Ernst Chladni | Wikipedia Ernst Florens Friedrich Chladni was a German physicist and musician. His most important work, for which he is sometimes labeled the father of acoustics, included research on vibrating plates and the calculation of the speed of sound for different gases. -

University Courses, Theses, and Articles

https://www.math.wustl.edu/~wright/Math109/00Book.pdf +Mathematics and Music by David Wright | Washington University at St. Louis [PDF] Harmony. Musical intervals. Logarithms. Chromatic scales. Octave identification. Properties of integers. Timbre and periodic functions. Rational numbers as intervals. Rational tuning. 140 pages. https://www.math.wustl.edu/~wright/new_mathmusic_class.html +Mathematics and Music by David Wright | Course Materials Scales. ntervals. Rhythm. Meter. Form. Melody. Chords. Progressions. Temperament. Groups. Rings. Modular arithmetic. Periodic functions. Harmonic analysis. https://logosfoundation.org/kursus/music_math.pdf +Music: A Mathematical Offering by Dave Benson | University of Aberdeen [PDF] Waves and harmonics. Fourier theory. Wave equations for strings, wind instruments, drum, horn, etc. Consonance and dissonance. Scales and temperaments. Digital music. Synthesis. Symmetry in music. 500 pages. https://www.gresham.ac.uk/watch-now/series/maths-music Mathematics in Music and Writing | Gresham College Music, with its rhythms and structures, is almost by definition mathematical in flavour. Mathematics in composition. Creating musical instruments. Analyse and create patterns. https://www.ams.jhu.edu/dan-mathofmusic/ Mathematics of Music | Johns Hopkins University Some examples of connections between music and mathematics. Number theory. Sound waves. Intervals, exponents, logarithms. Stochastic processes. https://www-personal.umd.umich.edu/~tmfiore/1/musictotal.pdf Music and Mathematics by Thomas M. Fiore | University of Michigan [PDF] Transposition and inversion. The integer model of pitch. The PLR group. Topology and the torus. 36 pages. http://www-personal.umd.umich.edu/~tmfiore/1/FioreWhatIsMathMusTheoryBasicSlides.pdf What is Mathematical Music Theory? by Thomas M. Fiore | University of Michigan [PDF] Pitch class. Transposition and inversion. Triads. P, L, R operations. Diatonic scale. Sturmian morphisms. Conjugates and dividers. Christoffel duality. Presentation 20 pages. https://guides.tricolib.brynmawr.edu/music-math MUSI 009A: Music and Mathematics (SC) | Bryn Mawr Short reviews of some suggested books. http://www.stat.yale.edu/~zf59/MathematicsOfMusic.pdf Seminar Notes: The Mathematics of Music by Zhou Fan | Yale University [PDF] Understanding musical sound. Human ear. Sine wave. Timbre. Harmonics. Fourier series. Consonance and dissonance. Scales and temperament. Symmetries and transformations. Groups, generators, and relations. Transformations of motifs. The geometry of chords. 33 pages. https://eprints.maths.manchester.ac.uk/1548/1/Saloni2010.pdf An Exploration of the Relationship between Mathematics and Music by Shah, Saloni | University of Manchester [PDF] Historical conneections. Pythagoras. Rameau. Fibonacci. Circle of fifths. Transposition. Rhythms. Religious symbolism. Mathematical periods vs. Musical periods. 100 pages. https://scholarsjunction.msstate.edu/cgi/viewcontent.cgi?article=6428&context=td The mathematical foundation of the musical scales and overtones by Michaela DuBose-Schmitt | Mississippi State University [PDF] Musical scales. Pythagorean diatonic scale. Just intonation. Equal temperament. Fourier series. The wave equation. 40 pages. http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf The Euclidean Algorithm Generates Traditional Musical Rhythms by Godfried Toussaint | McGill University [PDF] Mathematics and music have been intimately intertwined since the days of Pythagoras. However, most of this interaction has been in the domain of pitch and scales. Rhythm, on the other hand has been historically mostly ignored. Here we make some mathematical connections between musical rhythm and other areas of knowledge such as nuclear physics and computer science. 10 pages. https://www.science.org/doi/10.1126/sciadv.aav8490 The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory | Science Here, I present a theoretical formalism that aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems. I first apply the mean field approximation to demonstrate that phase transitions occur in this model from disordered sound to discrete sets of pitches, including the 12-fold octave division used in Western music. https://www.uwlax.edu/globalassets/offices-services/urc/jur-online/pdf/2011/hammond.mth.pdf Mathematics of Music by Janelle K. Hammond | University of Wisconsin La Crosse [PDF] Fourier analysis. Sound basics. Harmonics and the harmonic series. Fourier series and modeling music. Tuning systems. Practical applications. 11 pages. https://www.gresham.ac.uk/sites/default/files/2020-10-13_Hart-MusicalComp-T.pdf The Mathematics of Musical Composition by Professor Sarah Hart | Gresham College [PDF] Musical notation. Theme and variations. Repetition. Translation. Inversion. Retrogression. Rotation. Musical groups. Tone rows. Conscious use of mathematical forms in music. Sets and groups. Magic squares. Infinite sequences. Fractals. Probability and randomness. 14 pages. https://amath.colorado.edu/pub/matlab/music/MathMusic.pdf Mathematical Harmonies by Mark Petersen | University of Colorado [PDF] Sine wave. Pitch and volume. Octaves and harmonics. Harmonics of different instruments. Beats and intervals. Just and equal temperament. 12 pages. https://archive.bridgesmathart.org/2004/bridges2004-273.pdf The Mathematics of Jazz by W. Douglas Maurer | The George Washington University [PDF] Duration of notes in symphonic music vs. jazz and swing. Number of bars in a passage. Jazz notes. Symphonic chords vs. jazz chords. Jazz keys and instrumentation. The mathematics of rock. 8 pages. https://scholarship.claremont.edu/jhm/vol4/iss1/5/ An Introduction to Fourier Analysis with Applications to Music Discrete Fourier Transform. Analyze a musical signal for chord structure. -

University Popular Articles

https://dornsife.usc.edu/news/stories/relationship-between-music-and-math/ Musical numbers: Math and music nurture a deep and complex relationship | USC When famed jazz saxophonist, composer and bandleader John Coltrane wanted to illustrate his understanding of music, he turned to mathematics. https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100%3A_Liberal_Arts_Mathematics_(Saburo_Matsumoto)/07%3A_Mathematics_and_the_Arts/7.03%3A_Musical_Scales Musical Scales | College of the Canyons Vibrations. Pythagoras. Numbers and Music. Harmony. https://news.uchicago.edu/story/combining-math-and-music Combining math and music | University of Chicago Leaders in disparate fields explain what unites them https://www.jstor.org/stable/27957839 Music and Mathematics by H. S. M. Coxeter | The Mathematics Teacher JSTOR The Mathematics Teacher (MT), an official journal of the National Council of Teachers of Mathematics, is devoted to improving mathematics instruction from grade 8-14 and supporting teacher education programs. It provides a forum for sharing activities and pedagogical strategies, deepening understanding of mathematical ideas, and linking mathematics education research to practice. https://www.montclair.edu/newscenter/2023/12/06/musical-numbers-understanding-how-math-and-music-merge/ Musical Numbers: Understanding How Math and Music Merge | Montclair State University In building a thongophone for mathematical analysis of its pipes for pitch, Montclair students find the connection between music and math https://physicalsciences.ucsd.edu/media-events/articles/2023/math-music.html Rhythm and Proofs: Finding Music in the Math by Michelle Franklin | UC San Diego Three professors in UC San Diego’s Department of Mathematics share their own connections. https://www.researchgate.net/publication/368845853_MATHEMATICS_BEHIND_THE_MUSIC_-_2_MATHEMATICAL_FOUNDATION_IN_MUSIC MATHEMATICS BEHIND THE MUSIC - 2: MATHEMATICAL FOUNDATION IN MUSIC | Loyola College (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. https://www.jstor.org/stable/2322282 Musical Scales and the Generalized Circle of Fifths by John Clough and Gerald Myerson | American Mathematical Monthly JSTOR This paper deals with the way the diatonic set (the white keys on the piano) is embedded in the chromatic scale (all the keys on the piano). -

Books

https://dokumen.pub/music-and-mathematics-from-pythagoras-to-fractals-9780199298938-0199298939-9780198511878-0198511876.html +Music and Mathematics: From Pythagoras to Fractals by John Fauvel [PDF] This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques. https://www.amazon.com/Topos-Music-Geometric-Concepts-Performance/dp/3764357312 +The Topos of Music: Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola | Amazon Topography. Musical ontology. Experiments in musicology. Denotators. Local compositions. Chords and scales. Meters and rhythms. Motives. Symmetries and morphisms. Paradigmatic classification. Orbits. Gestalt and symmetry groups. https://books.google.com/books?id=6I9U9-Rls8oC&printsec=frontcover&dq=The+Topos+of+Music:+Geometric+Logic+of+Concepts,+Theory,+and+Performance&hl=nl&ei=5YbBTuLJJNGk-gbNrJTtBA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q&f=false +The Topos of Music: Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola | Google Books Topography. Musical ontology. Experiments in musicology. Denotators. Local compositions. Chords and scales. Meters and rhythms. Motives. Symmetries and morphisms. Paradigmatic classification. Orbits. Gestalt and symmetry groups. https://www.amazon.com/Math-Behind-Music-Outlooks/dp/0521009359 +The Math Behind the Music (Outlooks) by Leon Harkleroad Acoustical basis. Compositional techniques. Overtones. Scales. Tuning systems. Twelve-tone school. Probability theory. Fourier series. Group theory. http://www.musimathics.com +Musicmathics by Dr. Gareth Loy Basic properties of sound. Notation. Pitch. Scales. Intervals. Onset and duration. Equal-tempered intervals. Just intervals and scales. The cent scale. Pythagorean diatonic scale. Microtonality. Acoustics. Vibrating systems. Fourier transform. Convolution. Filtering. Resonance. Wave equation. Electronics. Sound synthesis. https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html +Music: a Mathematical Offering by Dave Benson Waves and harmonics. Fourier theory. Wave equations for strings, wind instruments, drum, horn, etc. Consonance and dissonance. Scales and temperaments. Digital music. Synthesis. Symmetry in music. https://www.amazon.com/Cool-Math-Hot-Music-Computational/dp/3319429353 +Cool Math for Hot Music: A First Introduction to Mathematics for Music Theorists (Computational Music Science) by Guerino Mazzola This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions. https://www.tandfonline.com/journals/tmam20 +Journal of Mathematics and Music Publishes papers on mathematical approaches to musical structures and processes, including mathematical investigations of compositional issues and performances. https://www.tandfonline.com/toc/tmam20/current +Journal of Mathematics and Music - current issue (2024) Volume 18, Issue 3 (2024) https://www.amazon.com/Temperament-Became-Battleground-Western-Civilization/dp/0375703306/ Temperament: How Music Became a Battleground for the Great Minds of Western Civilization by Stuart Isacoff In this engaging and accessible account, Stuart Isacoff leads us through the battles over that scale, placing them in the context of quarrels in the worlds of art, philosophy, religion, politics and science. https://www.amazon.com/Elements-Acoustic-Phonetics-Peter-Ladefoged-dp-0226467635/dp/0226467635/ Elements of Acoustic Phonetics by Ladefoged, Peter A concise introduction to basic concepts of acoustics and digital speech processing that are important to linguists, phoneticians, and speech scientists. Assuming no background in physics or mathematics, Ladefoged explains concepts that must be understood in using modern laboratory techniques for acoustic analysis, including resonances of the vocal tract and the relation of formants to different cavities; digital speech processing and computer storage of sound waves; and Fourier analysis and Linear Predictive Coding, the equations used most frequently in the analysis of speech sounds. Incorporating recent developments in our knowledge of the nature of speech, Ladefoged also discusses the basic properties of sound waves; variations in loudness, pitch, and quality of speech sounds; wave analysis; and the hearing and production of speech. https://www.brepols.net/products/IS-9782503585703-1 Twentieth-Century Music and Mathematics by Roberto Illiano (ed) Music and math in the music of Messiaen, Xenakis, Boulez, Part, Reich, Glass. Neo-Riemannian theory, diatonic set theory, theory of musical kaleidocycles. https://www.press.jhu.edu/books/title/11245/music-mathematics From Music to Mathematics: Exploring the Connections by Gareth E. Roberts | Johns Hopkins U Press Geometric sequences. Phase-shifting techniques. Twelve-tone music. Fibonacci numbers. Golden ratio. Magic squares. https://www.worldscientific.com/worldscibooks/10.1142/10858#t=aboutBook Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological and Applied Approaches to Understanding Musical Phenomena (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. https://link.springer.com/chapter/10.1007/978-3-030-39709-8_10 Mathematical Music Theory Mathematical Music Theory offers a new view on musical conceptualization, in particular the power of generalization of models and theorems for musical phenomena. We stress the creative power of this approach, as opposed to traditional conservative music theories. https://www.wfmt.com/math-in-music/ Math in Music | WFMT Communtativy of multiplication. Finding clarity in music. Composition techniques. Symmetry. Fractions. Musical machines. Math can sound bad. Harmonics. Doing math unconsciously. The devil interval. https://www.amazon.com/Musical-Mathematics-Science-Acoustic-Instruments/dp/0811874079 Musical Mathematics: On the Art and Science of Acoustic Instruments by Cris Forster Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world. https://cup.columbia.edu/book/music-math-and-mind/9780231193795 Music, Math, and Mind: The Physics and Neuroscience of Music by David Sulzer This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. https://link.springer.com/book/10.1007/978-3-031-34440-4 The Mathematics of Music and Art | by Arturo Portnoy The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each other’s advancement. https://www.amazon.com/dp/0199759944 Generalized Musical Intervals and Transformations by David Lewin David Lewin's Generalized Musical Intervals and Transformations is recognized as the seminal work paving the way for current studies in mathematical and systematic approaches to music analysis. Lewin, one of the 20th century's most prominent figures in music theory, pushes the boundaries of the study of pitch-structure beyond its conception as a static system for classifying and inter-relating chords and sets. https://www.amazon.com/dp/1439867097 Mathematics and Music: Composition, Perception, and Performance by James S. Walker, Gary W. Don In an accessible way, the text teaches the basics of reading music and explains how various patterns in music can be described with mathematics. The authors extensively use the powerful time-frequency method of spectrograms to analyze the sounds created in musical performance. Numerous examples of music notation assist students in understanding basic musical scores. The text also provides mathematical explanations for musical scales, harmony, and rhythm and includes a concise introduction to digital audio synthesis. https://www.amazon.com/Geometry-Music-Counterpoint-Extended-Practice/dp/0195336674/ A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) by Dmitri Tymoczko Describes a new framework for thinking about music that emphasizes the commonalities among styles from medieval polyphony to contemporary rock. Tymoczko identifies five basic musical features that jointly contribute to the sense of tonality, and shows how these features recur throughout the history of Western music. In the process he sheds new light on an age-old question: what makes music sound good? -

Videos

https://www.youtube.com/watch?v=1Hqm0dYKUx4 Why it's impossible to tune a piano | YouTube 4:19. Harmonics. Equal tempered. Equal tuning. https://www.youtube.com/watch?v=nK2jYk37Rlg +The Mathematical Problem with Music, and How to Solve It | YouTube 31:44. There is a serious mathematical problem with the tuning of musical instruments. A problem that even Galileo, Newton, and Euler tried to solve. Melodies. Harmonics. Intervals. Choosing frequencies. Pitch class. Pythagorean tuning. Just intonation. Meantone temperament. Equal temperament. Other temperaments. https://www.youtube.com/watch?v=Y7TesKMSE74 The Math Behind Music and Sound Synthesis | YouTube 13:25. Pitch vs. frequency. Chromatic scale. Consonance and dissonance. Harmonic series. Tonality. Instrument timbre. Wave shapes. Sound design. https://www.youtube.com/watch?v=O5G_XD434Qs Music Theory EP01a: Maths Behind The Music 10:28. Art or science? Frequency and Pitch. Fundamental frequency and harmonics. Harmonics of A440. Harmonics in the gaps. Re-ordering harmonics. Why do harmonics matter? https://www.youtube.com/watch?v=K0jkbaJqL1s&t=6s The Beauty of Math and Music | Marcus Miller | TEDxOttawa 20:26. Cardinality. Fractions. Infinity times infinity is infinity. Prestiditation. The Mozart Effect. https://www.simonsfoundation.org/2013/08/12/mathematical-impressions-making-music-with-a-mobius-strip/ Mathematical Impressions: Making Music With a Möbius Strip 6:44. Musical chords naturally inhabit various topological spaces, which show all the possible paths that a composer can use to move between chords. Surprisingly, the space of two-note chords is a Möbius strip, and the space of three-note chords is a kind of twisted triangular torus. https://thecodingtrain.com/challenges/130-drawing-with-fourier-transform-and-epicycles Drawing with Fourier Transform and Epicycles 46:09. Visualize a Fourier series for a square wave in JavaScript using p5.js. https://www.youtube.com/watch?v=n9nfTxp_APM Coding Challenge: Fourier Transform User Drawing 9:20. Discrete Fourier Transform algorithm in JavaScript and render a drawing using epicycles derived from the transform. https://www.youtube.com/watch?v=FgKKA9sdfs4 Music from Mathematics 26:54. 60's Abstract, Electronic, Experimental Music Compilation IBM 7090. LP,Vinyl, Mono. 1962. -

Miscellaneous Web Pages

https://en.wikipedia.org/wiki/Math_rock Math Rock | Wikipedia Math rock is a style of alternative and indie rock. It is characterized by complex, atypical rhythmic structures (including irregular stopping and starting), counterpoint, odd time signatures, and extended chords https://www.woodpecker.com/writing/essays/math+music.html On Mathematics and Music Pythagorean scale. Octave. Interval. Chord. Temperings. https://www.insmi.cnrs.fr/en/cnrsinfo/maths-music-1-maths-music-music-maths-reflections-mathemusical-dynamics-moreno-andreatta Maths & Music #1: Maths in music, the music of maths: reflections on "mathemusical dynamics," by Moreno Andreatta The flexibility and generality of mathematical concepts and constructs have suggested to artists the value of formalising and modelling the theoretical problems posed by music. The identification of such musical problems is the starting point for a veritable "mathematical-musical dynamic". https://www.scientificamerican.com/article/secret-mathematical-patterns-revealed-in-bachs-music/ Secret Mathematical Patterns Revealed in Bach’s Music | Scientific American By representing scores as simple networks of dots, called nodes, connected by lines, called edges, scientists quantified the information conveyed by hundreds of Bach’s compositions. An analysis of these musical networks published in Physical Review Research revealed that Bach’s many musical styles, such as chorales and toccatas, differed markedly in how much information they communicated—and that the musical networks contained structures that could make their messages easier for human listeners to understand. https://www.ams.org/publicoutreach/math-and-music Mathematics & Music | American Mathematical Society A long list of videos, podcasts, and articles. - https://www.smcm-net.info Society for Mathematics and Computation in Music Publishers of the Journal of Mathematics and Music -

Recommended books (lists)

https://www.reddit.com/r/math/comments/pnrbug/is_there_really_a_deep_connection_between_math/?rdt=55139 Is there a deep connection between math and music? | Reddit Recommendations from the Reddit community. https://mathoverflow.net/questions/263202/books-on-music-theory-intended-for-mathematicians Books on music theory intended for mathematicians | Math Overflow Recommendations from the Math Overflow community. -