University of South Carolina
School of Music

Duke TIP Academic Adventure
Music, Math & Computers

Saturday, April 16, 2016

School of Music, R210 and
Music Technology Center (R209)

Duke TIP | SCHC | School of Music

Workshop 1: Middle School
1. Music and Sound Activities
2. Music and Number Activities
3. Hands-on Explorations
in the Music Technology Center
Workshop 2: High School
1. Everything is Number
2. The Music of the Spheres
3. The Elements of Music
4. Mathematical Models of
Pitch and Rhythm

Musical Programming


What is Sound?


The Harmonic Series & Tuning


Gödel, Escher, Bach


Selected Math & Music Topics


Composing with Computers


Dr. Reginald Bain
Professor of Composition & Theory
School of Music
University of South Carolina
(803) 777-8183


Did you know that composers use math and computers to compose music? Have you ever imagined making your own music using computers? In this workshop, you will discover how the mathematical concepts you are learning in school are related to sound. You will also have the opportunity to work in pairs in USCís Music Technology Center (MTC) to create computer-generated music. No math or music prerequisite is required for this workshop.

Workshop Flyer & Schedule

  1. Flyer (pdf)
  2. Schedule (pdf)

Instructional Approaches

Demonstrations, hands-on activities, group discussion, group listening, group performance,
group composition and pair programming

Reference Materials

  1. Music Terminology
  2. Math Terminology
  3. Acoustics Primers
  4. Online Introductions to Computer Music

Online Media

  1. Nigel Stanford, CYMATICS: Science Vs. Music {YouTube}
  2. Science of Music: Accidental Scientist {}
  3. Science and Music: How music and science connect {The Kennedy Center}
  4. Ted Talks related to this course
  5. World Science Festival Videos related to this course
  6. American Mathematical Society, Math and Music Samplings {AMS}
  7. Sante Fe Videos
    • Music + Math: The Majesty of Music + Math {SFI}
  8. Marcus du Sautoy {Oxford}
  9. Vi Hart {YouTube Channel}
  10. Rachel Hall, Sounding Number: Music and Mathematics from Ancient to Modern Times {Saint Joseph’s}
  11. Discovery Channel Videos: How Stuff Works, Assignment Discovery Video Clips

Books & Articles

  1. Plus Magazine articles that are related to this course
  2. Wooden Books that are related to this course
  3. Books by Theoni Pappas that are related to this course


  1. Music & Math
  2. Math
  3. Music & Computers
    • Berklee, Introduction to Music Production {Coursera}
    • CalArts, Introduction to Programming for Musicians and Digital Artists {Coursera}
    • Georgia Institute of Technology, Survey of Music Technology {Coursera}
  4. Computer Science
  5. Physics
  6. Gödel, Escher, Bach


  1. Music Notation
    • MakeMusic's Finale – A professional music notation program {MakeMusic}
    • MuseScore – A free music notation program {}
  2. Musical Instrument Digital Interface (MIDI)
    • What is MIDI? {}
    • GM Instrument List {}
    • MIDI Yodi {}
      A MIDI Editor that allows examination, playback, editing and conversion of MIDI files
    • J.S. Bach (1685-1750) {WP}
      • Chorales
        • Major Key: Ich bin's, ich sollte bussen (Tis I, I must be sorry) {Naxos}
        • Minor Key: Jesu, meine Freude (Jesus, my joy) {Naxos}
      • Standard MIDI Files (SMFs)
  3. Sequencing
    • Apple's GarageBand – Music creation software for Mac OS X and iOS {Apple}
      Play, mix, record and share your own songs at the touch of a button
    • The Music Radar Team, Digital Audio Workstation (DAW) software apps {Music Radar}
  4. Audio Editing & Transformation
  5. Oscilloscope and FFT
  6. Metronones
    • Metronome – A browser-based metronome with w/ meter settings {Flash Player}
    • Tap Metronome – Tap out a tempo using your computer keyboard's space bar {}
  7. Sequencers that run in your Web browser
  8. Other Useful and Fun Applications
    • Drumbot Tools for Musicians {}
    • Bamberger, Impromptu Study melody, rhythm and form using musical tuneblocks (primatives) {Website}
    • Hicks & White, PulseBoy A Gameboy-like tracker that uses classic 8-bit sounds and samples {Website}
  9. Algorithmic Composition
  10. Visualization
  11. Sonification
  12. Speech Synthesis
  13. Math Tools
  14. Programming Music & Media

Music Theory


  1. Duke TIP
  2. Duke TIP Academic Adventures at USC
  3. USC School of Music
  4. USC Honors College
  5. Dartmouth's Math Across the Curriculum
  6. STEM Education Coalition
  7. Exploring Computer Science


The Music of the Spheres
Calter, Paul A. 2008. "Pythagoras & Music of the Spheres," in Squaring the Circle: Geometry in Art and Architecture.
      New York: John Wiley & Sons Inc. {Website}

Music and Sound
Backus, John. 1977. The Acoustical Foundations of Music. New York: Norton. {GBd}
Traig, Jennifer, ed. 2015. "Chapter 6 Making Waves," STEM to Story: Enthralling and Effective Lesson Plans for Grades 5-8.
      San Francisco: Wiley. {Wiley | YouTube}

Music and Math

Fauvel, John, Raymond Flood, and Robin J. Wilson, ed. 2006. Music and Mathematics: From Pythagoras to Fractals.
      New York: Oxford University Press. {GB}
Garland, T. H., & Kahn, C. V. 1995. Math and Music: Harmonious Connections. Palo Alto, CA: Dale Seymour Publications.

Hofstadter, Douglas. 1979. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books. {WP}
_______________. 1985. Metamagical Themas: Questing for the Essence of Mind and Pattern. New York: Basic Books. {GB}

Johnson, Tim. 2003/2008. Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals.
      Lanham, MD: Scarecrow Press. {GB}
Kung, David. 2013. How Music and Mathematics Relate. DVD. Chantilly, VA: The Great Courses. {Website}

Mathieu, W.A. 1997. Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression. Inner Traditions. {GBd}
Lundy, Miranda, Anthony Ashton, et al. 2010. Quadrivium: The Four Classical Libreral Arts of Number, Geometry, Music & Cosmology.
     Bloomsbury, NY: Wooden Books.
Pappas, Theoni. 1999. Mathematical Footprints: Discovering Mathematical Impressions All Around Us.
      San Carlos, CA: Wide World Publishing/Tetra.

Stewart, Ian. 2003. Another Fine Math You've Got Me Into. Mineola, NY: Dover.

Music and Computers
Burg, Jennifer, et al. 2016. Digital Sound & Music: Concepts, Applications, & Science. {Wake Forest}
Burk, Phil, Larry Polansky, Douglas Repetto, Mary Roberts and Dan Rockmore. 2011. Music and Computers: A Theoretical and Historical Approach,
     Archival Version. {Website}
Manzo, V.J. 2015. Foundations of Music Technology. New York: Oxford. {GBd | Website | Video Intro.: YouTube}
Watson, Scott. 2011. Using Technology to Unlock Musical Creativity. New York: Oxford University Press. {GB}

Music Theory

Bamberger, Jeanne. 1999. Developing Musical Intuitions: A Project-Based Introduction
      to Making and Understanding Music. New York: Oxford. {Website}

Bernstein, Leonard. 1976. The Unanswered Question. Cambridge, Harvard University Press. {GB | Norton Lectures}
Nowlin, Ryan and Bruce Pearson. 2010. Excellence in Theory: Music Theory, Ear Training and History Workbook.
      San Diego, CA: Neil A. Kios Music Company.

Scoggin, Nancy. 2010. Barron's AP Music Theory. Hauppauge, NY: Barrons Educational Series. {GB}

Sererance, Charles. Programming for Everybody (Getting Started with Python). Coursera MOOC.
      Available online at: <>.
Manaris, Bill and Andrew R. Brown. 2014. Making Music with Computers: Creative Programming in Python.
      Boca Raton, FL: CRC Press. {GB}
Manzo, V.J. 2011. Max/MSP/Jitter for Music: A Practical Guide to Developing Interactive Music Systems for Education and More.
      New York, Oxford. {GB | Website | EAMIR}

GB - Google Books; WP - Wikipedia

Updated: Februrary 25, 2018

Reginald Bain | University of South Carolina | School of Music