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Teaching the Mathematics of Music

Teaching the Mathematics of Music. Rachel Hall Saint Joseph’s University rhall@sju.edu. Overview. Sophomore-level course for math majors (non-proof) Calc II and some musical experience required Topics Rhythm, meter, and combinatorics in Ancient India

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Teaching the Mathematics of Music

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  1. Teaching the Mathematics of Music Rachel Hall Saint Joseph’s University rhall@sju.edu

  2. Overview • Sophomore-level course for math majors (non-proof) • Calc II and some musical experience required • Topics • Rhythm, meter, and combinatorics in Ancient India • Acoustics, the wave equation, and Fourier series • Frequency, pitch, and intervals • Tuning theory and modular arithmetic • Scales, chords, and baby group theory • Symmetry in music

  3. Semester project Each student completed a major project that explored one aspect of the course in depth. • Topics included • the mathematics of a spectrogram; • symmetry groups, functions and Bach; • Bessel functions and talking drums; • change ringing; • building an instrument; and • lesson plans for secondary school. • Students made two short progress reports, a 15-minute final presentation, and wrote a paper about the mathematics of their topic. They were required to schedule consultations throughout the semester.

  4. Logarithms and music: A secondary school math lessonChristina Coangelo, Senior, 5 yr Math Ed program Major Math Content Covered • Functions • Linear, Exponential, Logarithmic, Sine/Cosine, Bounded, Damping • Graphing & Manipulations • Ratios

  5. Building a PVC InstrumentJim Pepper, Sophomore, History major, Music minor

  6. The Mathematics of Change RingingEmily Burks, Freshman, Math major

  7. Resources Assigned texts • David Benson, Music: A Mathematical Offering • Dan Levitin, This is Your Brain on Music Other resources • Fauvel, Flood, and Wilson, eds., Mathematics and music • Trudi Hammel Garland, Math and music: harmonious connections (for future teachers) • Lots of web resources • YouTube!

  8. Symmetry and group theory Steve Reich’s Clapping Music Performed by jugglers http://www.youtube.com/watch?v=dXhBti625_s J.S. Bach’s 14Canons on the Goldberg Ground Timothy Smith’s site: http://bach.nau.edu/BWV988/bAddendum.html

  9. Exercises (choose one) Clapping music • Describe the structure. • Write your own clapping music. • Why did Reich use this particular pattern? Groups in music • Read “Variations on a Theme.” Describe the structure of the group of translations, inversions, delay, and retrograde. Bach’s 14 Canons on the Goldberg Ground • How are canons #1-4 related to the solgetto and to each other? • Write your own canon, using the template on the back or your own template. Write your own exercise

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