An Honors Seminar in Music

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An Honors Seminar in Music MathematicsMathfest
2009
Alien Musical Scores a drawing by Robert Mueller.
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• HONORS 151 Music Math
• Freshman level
• Accepted for general education requirement
• Six students (two music majors)
• Math backgrounds from algebra to calculus
• All played an instrument (most often guitar)
• Two could not read music!

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• Five broad themes
• Sound
• Pitch
• Rhythm
• Melody
• Theory

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• My general approach
• Five reading assignments with reaction form
• In-class discussion
• Occasional lecture (mostly on math)
• Five homework assignments
• Two exams
• Final project

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Sound

• Frequency, Harmonics, Acoustic spectrum
• Consonance and dissonance (Euclid, Galileo,
  Helmholtz)
• Sine curves
• Fouriers Theorem
• Reading Kline, The Sine of G Major, Chapter
  XIX from Mathematics in Western Culture

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Pitch

• Ratios for musical intervals
• Pythagorean tuning and its flaws
• Just intonation and its flaws
• Equal temperament
• (An aside cents and logarithms)
• Reading Bibby, Tuning and Temperament Closing
  the Spiral, in Music and Mathematics from
  Pythagoras to Fractals

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Boom Whackers(part of Pitch)
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Rhythm

• Time signatures
• Filling measures with notes (combinatorics)
• Permutations cycle notation, composition,
  order, inverses
• Readings Haack, The Mathematics of Steve
  Reich's Clapping MusicToussaint, The Euclidean
  Algorithm Generates Traditional Musical Rhythms

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Melody

• Transposition, retrograde, inversion, retrograde
  inversion
• Translation, reflection, rotation
• Composition, group properties
• Twelve-tone music (Babbitt square)
• Reading Harkleroad, How to Vary a Theme
  Mathematically, Chapter 4 from The Math Behind
  the Music

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Theory

• Circle diagrams for intervals, chords, scales
• Maximally even (mathematical definition)
• The Cardinality Variety property of diatonic
  and pentatonic scales
• Readings Johnson, Spatial Relations and Musical
  Structures and Interval Patterns and Musical
  Structures, Chapters 1 and 2 from Foundations of
  Diatonic Theory

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• Assessment
• Five homework assignments, 7-9 problems each
• Two exams
• Final project and presentation

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• Next time?
• Better musical examples for Melody
• Alternative representations for melodies (Rachel
  Hall)
• More with Boom Whackers
• Practice Clapping Music
• Create our own variations with permutations
• Recruit more students!

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Thanks for listening!