Music and Mathematics: Resources

Lecture notes and Books:

• Tom Fiore, Music and Mathematics, ---- lecture notes.
• John Baez, This Week's Finds in Mathematical Physics (Week 234), ---- lecture notes (and many references).
• Dmitri Tymoczko, The Generalized Tonnetz----.
• David Wright, Mathematics and Music----.
• Dave Benson, Music: a Mathematical Offering----.

Some papers:

• Alissa S. Crans, Thomas M. Fiore, and Ramon Satyendra, Musical Actions of Dihedral Groups..
• Konstanze Rietsch, Generalisations of Euler's Tonnetz on triangulated surfaces..
• Athanase Papadopoulos, Mathematics and group theory in music..
• Peter Buch, Favored cardinalities of scales.

Books or papers by subscription:

• Dmitri Tymoczko, A geometry of music harmony and counterpoint in the extended common practice.
• Clifton Callender, Ian Quinn, Dmitri Tymoczko, Generalized Voice-Leading Spaces.
• Dmitri Tymoczko, The Geometry of Musical Chords.
• Richard Cohn, Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective.

Webpages:

• music theory, in nLab.
• Mathematics and Music, AMS page.
• Xenharmonic Wiki.
• Musical Rhythm and Mathematics, collection by Godfried T. Toussaint.

Software:

• Moreno Andreatta, Corentin Guichaoua, The Tonnetz.
• Louis Bigo, HexaChord, AMS page.

Coding:

• It is ridiculously easy to generate any audio signal using Python, on The Hacker Diary.

Youtube channels:

• Gilles Baroin, MatheMusic4D, Scientific MatheMusical Animations in 2 and 4 Dimensions.
• Marc Evenstein, Marc Evanstein / music․py, videos on composing music in Python.
• Channels playing music written for xenharmonic scales: Mike Battaglia, Zheanna Erose.

Videos (examples of music based on Mathematics):

• contemporary examples:
  • Konstanze Rietsch, Elaine Chew, Juliette Majid, Fano Rainbow.
  • Moreno Andreatta The Music of Maths (seven little songs based on mathematics).
  • Mathematical Music - Numberphile Interview with Alan Stewart (+links to his compositions in the description).
• Examples from classics:
  • Mozart Kanon "der Spiegel" , video by MARIANIMUSIK.
  • J.S.Bach- Crab Canon on a Möbius Strip , video by Jos Leys.
  • Music on a Clear Möbius Strip , Numberphile video on JS Bach - by Marcus Du Sautoy.
  • Chopin - Etude Op. 25 No. 12 (Ocean) - Tonnetz visualization , by Szymon Skoneczny.
• Music theory and maths/programming:
  • TONNETZ , 1-minute video by Reuben Levine.
  • Composing lab: The Tonnetz , by Richard Millington Music.
  • Music And Measure Theory , video by 3blue1brown.
  • The Physics Of Dissonance , video by minutephysics.

More reading:

• Ernst Kurth, Grundlagen des linearen kontrapunkts; Bachs melodische polyphonie, see here for Russian translation