BAIN MUSC 525
Post-Tonal Theory

Mathematics and the Twelve-Tone System

Return to: MUSC 525

Introduction

For an introduction to mathematics and the twelve-tone system, see Morris 2007:

Robert Morris, "Mathematics and the Twelve-Tone System: Past, Present, and Future," Perspectives of New Music 45/2 {JSTOR}

For a brief introduction, see this 4-page talk on the author's website.

Twelve-Tone Theory & Analysis

In addition to our textbook (Straus 2016), I have found the following sources to be especially helpful in learning twelve-tone theory, analysis and composition:

Perle 1996/1977; Wuorinen 1979; Rahn 1980; Morris 1987; Mead 1994; Straus 2001 & 2009; Pearsall 2012

See also: MUSC 525 Bibliography; Morris 1991a/b; Jedrzejewski 2006; Ilomäki 2008

I also recommend you read the following three articles by Milton Babbitt (in Babbitt 2003):

Some Aspects of Twelve-Tone Composition (1955), pp. 38-47

Twelve-Tone Invariants as Compositional Determinants (1960), pp. 55-69

Twelve-Tone Rhythmic Structure and the Electronic Medium (1962), pp. 109-140

Journal of Music and Mathematics: Special Issue

In 2015, the Journal of Mathematics and Music (JM&M) dedicated a special issue to this topic:

1. Hook & Peck, "Introduction to the Special Issue on Tone Rows and Tropes" {JM&M; DOI}  (Hook & Peck 2015)
2. Fripertinger & Lackner, "Tone Rows and Tropes" {JM&M; DOI} (Fripertinger & Lackner 2015)
3. Morris, Review of "Tone Rows and Tropes" {JM&M; DOI} (Morris 2015)
4. Mead, Remarks on "Tone Rows and Tropes" {JM&M; DOI} (Mead 2015)

Links

Journal of Mathematics and Music (JM&M) {UofSC Login}

Perspectives of New Music (PNM) {UofSC Login}

References

Babbitt, Milton. 2003. The Collected Essays of Milton Babbitt, edited by Stephen Peles, Stephen Dembski, Andrew Mead, and Joseph N. Straus. Princeton, NJ: Princeton University Press. {GB; JSTOR}

Hook, Julian and Robert Peck. 2015. "Editorial: Introduction to the Special Issue on Tone Rows and Tropes." Journal of Mathematics and Music 9/2: 109-110. {JM&M; DOI}

Fripertinger, Harald & Peter Lackner. 2015. "Tone Rows and Tropes." Journal of Mathematics and Music 9/2: 111-172. {JM&M; DOI}

Ilomäki, Tuukka. 2008. On the Similarity of Twelve-tone Rows. Helsinki: Sibelius Academy. {GB}

Jedrzejewski, Frank. 2006. Mathematical Theory of Music. IRCAM Musique/Sciences Series. Paris, Delatour. {GBd}

Mead, Andrew. 2015. "Remarks on 'Tone Rows and Tropes' by Harald Fripertinger and Peter Lackner." Journal of Mathematics and Music 9/2: 173-178. {JM&M; DO}

Mead, Andrew. 1994. An Introduction to the Music of Milton Babbitt. Princeton, NJ: Princeton University Press. {GB}

Morris, Robert. 2007. "Mathematics and the Twelve-Tone System: Past, Present, and Future." Perspectives of New Music 45/2 (Summer, 2007), pp. 76-107 {JSTOR}

___________. 2015. "Review of 'Tone Rows and Tropes' by Harald Fripertinger and Peter Lackner." Journal of Mathematics and Music 9/2: 179-195. {JM&M; DOI}

____________. 1991a. Class Notes for Atonal Theory. Lebanon, NH: Frog Peak {GBd}

____________. 1991b. Class Notes for Advanced Atonal Theory. Lebanon, NH: Frog Peak. {GBd}

Morris, Robert. 1987. Composition with Pitch Classes: A Theory of Compositional Design. New Haven: Yale University Press. {Full text: JSTOR; GBd}

Pearsall, Edward. 2012. Twentieth-Century Music Theory and Practice. New York: Routledge. {GB; Full text: E-book Central}

Perle, George. 1996/1977. Twelve-Tone Tonality. Berkeley: University of California Press. {2/e: GB; 1/e: GB}

___________. 1991/1962. Serial Composition and Atonality, 6th ed. Berkeley: University of California Press. {GB}

Schoenberg, Arnold. 1984. Style and Idea: Selected Writings of Arnold Schoenberg, edited by Leonard Stein, ed, and translated by Leo Black. Berkeley: University of California Press. {GB}

Straus, Joseph N. 2016. Introduction to Post-Tonal Theory, 4th ed. New York: Norton. {GB}

_____________. 2009. Twelve-Tone Music in America. New York: Cambridge University Press. {GBd}

_____________. 2001. Stravinsky's Late Music. New York: Cambridge University Press. {GB}

Wuorinen, Charles. 1994/1979. Simple Composition. New York: C.F. Peters. {GBd}