Music
2007 Chicago REU Lectures on Mathematical Music Theory
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Lecture 1: Introduction to Mathematical Music Theory, Scale Theory.
July 16th, 2007.
Slides pdf. (Some figures from Rahn, Carey, Clampitt, McCartin)
Problems pdf.
Musical Examples: Schumann, Album for the Young, Numbers 8 and 10, 1848 (Rico Gulda).
Bartok, Mikrokosmos, Volume IV, Number 101, Diminished Fifth, 1926-1939 (Jenö Jando).
Debussy, Preludes, Book 1, Number 2, Sails, 1910 (Paul Jacobs).
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Lecture 2: Set Theory.
July 17th, 2007.
Slides pdf.
Problems pdf.
Musical Examples: Schoenberg, Five Piano Pieces, Opus 23, Number 1, 1920-1923 (Paul Jacobs).
Schoenberg, Six Little Piano Pieces, Opus 19, Number 6, 1911 (Paul Jacobs).
Wagner, Tristan and Isolde, Prelude, 1859 (Daniel Barenboim).
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Lectures 3, 4: The Topos of Triads.
July 18th, July 19th 2007.
Noll, Thomas. The Topos of Triads. Colloquium on Mathematical Music Theory, 103--135,
Grazer Math. Ber., 347, Karl-Franzens-Univ. Graz, Graz, 2005.
Lecture Notes.
Special Characteristic Morphisms and Subobjects.
Summary.
Problems pdf.
Musical Example: Skrjabin (1872-1915), Opus 65, Number 3(Nikita Magaloff).
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Lectures 6, 7: Transformational Theory
July 24th, 26th, 2007.
Slides pdf and pdf.
Problems pdf and pdf.
Musical Examples: Hindemith, Ludus Tonalis, Fugue in G, 1942 (Siglind Bruhn).
The Beatles, Abbey Road Album, Oh! Darling, 1969. Chords.
Beethoven, Ninth Symphony, Second Movement, 1822-1824 (Alberto Lizzio).
2006 Chicago REU Lectures on Mathematical Music Theory
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Lecture 1: Introduction to Mathematical Music Theory, Scale Theory.
July 5th, 2006.
Slides pdf. (Some figures from Rahn, Carey, Clampitt, McCartin)
Problems pdf.
Musical Examples: Schumann, Album for the Young, Numbers 8 and 10, 1848 (Rico Gulda).
Bartok, Mikrokosmos, Volume IV, Number 101, Diminished Fifth, 1926-1939 (Jenö Jando).
Debussy, Preludes, Book 1, Number 2, Sails, 1910 (Paul Jacobs).
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Lecture 2: Set Theory.
July 7th, 2006.
Slides pdf.
Problems pdf.
Musical Examples: Schoenberg, Five Piano Pieces, Opus 23, Number 1, 1920-1923 (Paul Jacobs).
Schoenberg, Six Little Piano Pieces, Opus 19, Number 6, 1911 (Paul Jacobs).
Wagner, Tristan and Isolde, Prelude, 1859 (Daniel Barenboim).
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Lectures 3, 4: Transformational Theory
July 11th, 13th, 2007.
Slides pdf and pdf.
Problems pdf and pdf.
Musical Examples: Hindemith, Ludus Tonalis, Fugue in G, 1942 (Siglind Bruhn).
The Beatles, Abbey Road Album, Oh! Darling, 1969. Chords.
Beethoven, Ninth Symphony, Second Movement, 1822-1824 (Alberto Lizzio).
Undergraduate Lectures on Transformational Theory at Michigan
The links below were created from a series of lectures I gave in Math 107 on applications of group theory to music theory as part of my VIGRE project at the University of Michigan. It was inspired by the work of music theorist David Lewin. These ideas
are further developed in a joint paper with Ramon Satyendra, which has appeared in Music Theory Online.
I also gave a talk on these topics in the Undergraduate Math Club at the University of Michigan.
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Start Here! The examples below pertain to this text: Music and Mathematics ps, pdf
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Handouts and Musical Examples we did in class:
Bach's Fugue in d minor from the Well-Tempered Clavier
Wagner's Tristan Prelude, taken from John Rahn, Basic Atonal Theory. New York: Schirmer Books, 1980.
Hindemith's Fugue in G major from Ludus Tonalis
Handout for Lecture 2
Beethoven's Symphony 9, Movement 2
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In class we listened to:
Bach's Fugue in d minor from the Well-Tempered Clavier, performed by Glenn Gould
Wagner's Tristan Prelude, performed by the Berlin Philharmonic under Daniel Barenboim
Hindemith's Fugue in G major from Ludus Tonalis, performed by Siglind Bruhn
The Beatles' "Oh! Darling"
Beethoven's Symphony 9, Movement 2, performed by Great Festival Orchestra under Alberto Lizzio