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## An Honors Seminar in Music & Mathematics Mathfest 2009

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**An Honors Seminar in Music & MathematicsMathfest 2009**Alien Musical Scores; a drawing by Robert Mueller.**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!**Five broad themes:**• Sound • Pitch • Rhythm • Melody • Theory**My general approach:**Five reading assignments with reaction form In-class discussion Occasional lecture (mostly on math) Five homework assignments Two exams Final project**Sound**Frequency, Harmonics, Acoustic spectrum Consonance and dissonance (Euclid, Galileo, Helmholtz) Sine curves Fourier’s Theorem Reading: Kline, “The Sine of G Major,” Chapter XIX from Mathematics in Western Culture**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**Rhythm**Time signatures Filling measures with notes (combinatorics) Permutations: cycle notation, composition, order, inverses Readings: Haack, The Mathematics of Steve Reich'sClapping MusicToussaint, The Euclidean Algorithm Generates Traditional Musical Rhythms**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**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**Assessment:**Five homework assignments, 7-9 problems each Two exams Final project and presentation**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!