BAIN MUSC 525
Post-Tonal Theory

Fall 2026

MUSC 525 | Blackboard | Listening/Analysis

C O U R S E   M O D U L E S
1.	Pitches, Intervals & Motives (Ch. 1)
	Pitch-Class Sets (Ch. 2)
3.	Set Properties & Relations (Ch. 3)
4.	Centricity & Referential Collections (Ch. 5)
5.	Advanced Topics (Ch. 4)
6.	Serialism (Ch. 6)

News

Wed., Sept. 2: T_n & T_nI

Assignments

See Blackboard

Quotable

	The normal form corresponds to one of the successive-interval arrays of a [pc set]. It represents all possible realizations of this [pc set] and its transpositions.
	– Michiel Schuijer, Analyzing Atonal Music

Required Textbook

Joseph N. Straus, Introduction to Post-Tonal Theory, 4/e (New York: Norton, 2016).
Table of Contents; E-book: VitalSource

Course Documents

1. Syllabus (pdf)
   
• Reading & Exam Schedule (pdf)
  
• Daily Schedule (pdf)
  
• Links for Students
2. Handouts
3. Worksheets
4. Straus 4/e:
   
• Quizzes (pdf)
  
• Activities
  
• Listening/Analysis
• Model Analyses
• Guided Analyses
• Musical Examples (by chapter & topic)
5. Digital Anthology
6. Mathematical Terms & Concepts
7. Bibliography
• Articles
  
  

Projects

1. Composition Project (pdf) – Due: Fri., Dec. 11, 11:59 pm
• Proposal – Due: Fri., Nov. 20, 11:59 pm
  
2. Analysis Project (pdf) – For graduate students and SCHC-option students only
   
   

Software

1. Bain, PC Polygon Assistant, v2.03 (Bain 2016)
2. Tools
• Bain, Literal Subsets, v0.14d
• Bain, Triadic Transformation Calculator, v0.13d 
3. Walters, PC Set Calculator: I Matrix, v2001
   
4. Bain, Twelve-Tone Assistant, v2.4
   
   

Chapter/Lecture Overviews

1. Chapter 1  
   • Basic Concepts of Pitch and Interval (pdf)
     
2. Chapter 2
   • Pitch-Class Sets (pdf)
     
   • Set Theory (pdf)
   • Normal Form, Set Class, and Prime Form (pdf)
     
   • Segmentation & Analysis (pdf)
   • Ch. 1 Model Analyses (pdf)
   • Ch. 2 Model Analyses (pdf)
   • Edward T. Cone, Music: A View from Delft (Cone 1961) {Overview: pdf; JSTOR}
   • Painting: Johannes Vermeer, View of Delft (c. 1659-61) {WP; WC}
3. Chapter 3
   • Some Additional Properties & Relationships (pdf)
4. Chapter 5
   • Centricity and Referential Pitch Collections (pdf)
5. Chapter 4
   • Motive, Voice Leading, and Harmony (pdf)
6. Chapter 6
• Part 1: Basic Concepts of Twelve-Tone Music (pdf)
• Part 2: Varieties of Twelve-Tone Music (pdf)
  
  

Set Class Lists

1. Under Tn/TnI
   • Bain, Set Class List, v2.3 (pdf) (Kostka & Payne 2004)
   • Straus, List of Set Classes, pp. 378-381 (Straus 2016)
   • Walters, Table of pc set classes {www.mta.ca}
     
2. Under Tn
   • Nuño, A Detailed List and a Periodic Table of Set Classes {HarmonicWheel.com; TCL} (Nuño 2020)
3. Under TnM/TnMI
   • Morris, Set-Class Table {ECMC}  (Morris 1987)
4. Other
   • Hanson, The Projection and Interrelation of Sonorities in ET {Archive.org} (Hanson 1960)
   • Forte, Appendix 1: Prime Forms and Vectors of PC Sets {GB} (Forte 1973)
   • Carter, Catalogue I: Catalogue of Intervals and Chords, from The Harmony Book {GB} (Carter 2002)
     
     

Research Tools

Online Resources

1. Arnold Schoenberg Center {ASC; YouTube Channel}
   
• Compositions: A complete works list {ASC}
  
2. Digital Scores: Explore 20th- and 21st-century music literature
   
3. London, Row Forms in the Serial Works of Schoenberg, Berg, and Webern (2000) {Carleton.edu}
   
4. Morris, Downloadable pdf Files of Texts by Robert Morris {ECMC}
   
5. Schoenberg, Style and Idea (Schoenberg 1975)
   • Composition with Twelve Tones 1 (1941) {GB}
   • Composition with Twelve Tones 2 (1948)
     
6. SMT-V: The Society for Music Theory Videocast Journal {SMT-V}
• Mailman, Babbitt's Beguiling Surfaces, Improvised Inside (2019): Part 1 {SMT-V}; Part 2 {SMT-V}: Part 3 {SMT-V}
7. Socratica, Abstract Algebra/Group Theory (2020), video course {Website: YouTube Playlist}
   
8. Straus, Analytical Media {Website}
   
• Analyzing Modernist Music {YouTube Channel}
  
• The Art of Post-Tonal Analysis {Videos: Website; YouTube Playlist; OUP} (Straus 2022)
• Broken Beauty {Videos: Website; YouTube Playlist; OUP} (Straus 2018)
• The Music of Igor Stravinsky
  
• The Music of Igor Stravinsky (2024) {Videos: Website; YouTube Playlist}
• Twenty Stravinsky Analyses, podcast {Website}
• The Rite of Spring
• Analyzing Stravinsky's Rite of Spring (2022) {Website; YouTube Channel}
  
• The Melodic Organization of The Rite of Spring, Music Theory Online 28/4  {MTO} (Straus 2022)
• Harmony and Voice Leading in the Music of Stravinsky, Music Theory Spectrum 36/1 {JSTOR} (Straus 2014)
• Three Stravinsky Analyses, Music Theory Online 18/4 (Dec. 2012)  {MTO} (Straus 2012)
• Twelve-Tone and Serial Composition: The First 100 Years {Website}
9. Webern, The Path to New Music (1932-33) {Archive.org} (Webern 1963)
   
   

History

Schuijer, Michiel. 2008. Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts. Rochester: University of Rochester Press. {GB}

Taruskin, Richard. 2010. Music in the Early Twentieth Century. New York: Oxford University Press. {GB; Full text: TCL}

______________. 2010. Music in the Late Twentieth Century. New York: Oxford University Press. {GB; Full text: TCL}

Bibliographies

1. BAIN MUSC 525 Bibliography & Articles
• Mathematics and the Twelve-Tone System
• Teaching Post-Tonal Theory
  
2. Séminaire MaMuX
• Andreatta, Set Theory Bibliography {IRCAM}
  
  

Main 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}

Forte, Allen. 1973. The Structure of Atonal Music. New Haven: Yale University Press. {GB}

Lewin, David. 2007/1987. Generalized Musical Intervals and Transformations. New York: Oxford University Press. {GB; Full text: TCL}

Morris, Robert. 1987. Composition with Pitch Classes: A Theory of Compositional Design. New Haven: Yale University Press. {GB}

Rahn, John. 1980. Basic Atonal Theory. New York: Longman. {GB}

Straus, Joseph N. 2022. The Art of Post-Tonal Analysis: Thirty-Three Graphic Music Analyses. New York: Oxford University Press. {GB; Full text: TCL; Videos: Website; YouTube Playlist; OUP}

______________ 2018. Broken Beauty: Musical Modernism and the Representation of Disability. New York: Norton. {GB; Full text: TCL; Videos: Website; YouTube Playlist; Oxford}

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

Legend
ASC - Arnold Schoenberg Center (Vienna)
ETS -  Explore the Score (Klavier-Festival Ruhr)
GB - Google Books
IRCAM - Institut de recherche et coordination acoustique/musique (Paris)
MTO - Music Theory Online
TCL - Thomas Cooper Library (Find It @ USC Libraries)