Week 2 (Jun 10): Techniques for Atonal Music (Su19)

Last modified on August 4, 2023

This week, you will learn about set theory and segmentation. You’ll analyze music using set theory, apply set theory terminology, and critique the usefulness of set theory.

Set theory

Introductory reading

The reading makes use of some standard atonal theory terminology. First, pitches and pitch classes will be discussed using integers, where C=0, C#=1, etc. Second, calculating intervals will use what’s called mod-12 arithmetic, which is essentially math on the clock—6+8 = 2, like how if you work for eight hours beginning at 6AM, you get off at 2PM. Third, there are different types of intervals in atonal theory that help us describe different intervallic relationships, the most unfamiliar of which is interval classes. If any of this is unfamiliar to you, follow the links above (all from ) to learn about them. These concepts should not be difficult for you to comprehend after a bit of reading.

Locate the scan of Chapter 2 of . This textbook is the go-to text for atonal music theory. For this reason I’ve placed the whole thing on reserve at the library.

Read pages 43–71 of Chapter 2 to get introduced to set theory.


As a supplement, you may also wish to watch my tutorial that explains how to use clock faces to calculate normal form and prime form. I have another video that explains transposition and inversion, too. For a sheet of blank clockfaces to download, click here.

Note: This video uses interactive technology. The picture-in-picture can be swapped or even viewed side-by-side. The video also uses a menu so you can quickly navigate to certain portions of the video. For more explanation, see this video from Kaltura.

download normal/prime form slides – download normal/prime form captions/transcript

download transformations slides – download transformations captions/transcript

Concept check

Complete the Concept Check quiz on Blackboard to see if you are understanding the set theory concepts properly.

Due Wednesday: Example analysis reading and response

Listen to the first movement of Bartok’s String Quartet No. 4.


Then, read Straus’s analysis of the opening of this movement, which is in Chapter 2, pages 81–86.

Write a response essay (NB: NOT a summary!) to Straus’s analysis of Bartok, at least 700 words long.

More on response essays
A response essay is your personal take on the readings, and thus you shouldn’t be trying to write the “right answer,” but rather your opinion and reaction to what you’ve read. Remember that these are graded pass/fail, so anything you write is valuable in that sense. Feel free to use I/me pronouns and to freely express yourself (while remaining professional) and your opinion of the reading.

Below are some questions to inspire you, which you may choose to answer (you do not have to answer all, or any, of them!):

  • In the last paragraph on page 83, Straus describes neighbor notes in the texture. This is interesting! What is a neighbor note in tonal music? How do you recognize neighbor tones in tonal music? How can we recognize them in post-tonal music?
  • What are some differences in our interpretation of neighbor notes in tonal vs. atonal music?
  • At the top of page 76, Straus notes why one particular arrival on Bb-C-D-E sounds cadential. Think about cadences more broadly and generally. How do we know what a cadence is in tonal music? How else could something sound cadential in post-tonal music?
  • How aurally salient (i.e., hearable) are the structures that Straus creates?

Submit this by posting in your group’s “blog” on Blackboard.

Due Friday: Peer response

Respond to the members of your peer group by clicking the “comment” button under their blog post and typing your response directly into the text box, rather than uploading an attachment.

Due Sunday: Analysis assignment


  • On page 86 of the Straus Chapter 2 reading, you will find Guided Analysis 2.1: Ruth Crawford Seeger, Piano Prelude No. 9, mm. 19–24. Read through the questions given.
  • Listen to the recording of the excerpt (found in the Recordings folder).
  • Analyze this excerpt according to the prompts. You may wish to use a combination of score annotation and verbal responses—do whatever you need to get your point across efficiently.


  • You will be assessed on the following concepts
    • Understanding of interval types (interval classes, pitch intervals)
    • Understanding of set classes
    • Understanding of transformations (Tn and TnI)
    • Interpretation
  • You will be given detailed feedback through the rubric. Click “View rubric” in the gradebook to access this.
  • Assignments are always graded pass/fail, with a threshold of 70% to pass.


  • Submit your assignment on Canvas.
  • Upload your assignment as a .pdf attachment. Please do not use other file types.



If articles are not available online, you should be able to find them in the Readings folder on Teams.

Shaffer, Kris, Bryn Hughes, and Brian Moseley. 2018. Open Music Theory. http://openmusictheory.com/.
Straus, Joseph Nathan. 2016. Introduction to Post-Tonal Theory. 4th ed. Upper Saddle River, NJ: Prentice Hall.