Music 202: Techniques for Analysis of Tonal and Post-Tonal Music

[ Section 01 (41896) ]

Instructor:  Ben Leeds Carson — blc at ucsc dot edu 

Meetings: Music Center 245 on Mondays, 4:00 — 7:00 PM

Office hours: Mondays 10-11:30 AM, or by appointment

Office: Music Center 148 (on the lower floor, take a right at the bottom of the stairs)

Office phone:  9-5581 (I do not check voicemail frequently!)  



Catalogue Description:

 Encompasses various forms of linear analysis, set theory, and selected topics in current analytical practice. Offered in alternate academic years.

Complete Description: 

 This course offers three techniques (see below), and some variants on them, in the analysis of modern Western music literature^1, focusing on music from the early 19th century to the mid-to-late 20th century.

Analysis—derived from Greek ana- (“back” or “away”) lysis (“loosening”), thus “to loosen up” or “to release from entanglement”—refers to any investigation that involves separating-out the parts of a perceived whole, and considering their relationships to eachother.^1

This course complements Music 201 (History of Theory), which surveys music theory from ancient Babylonian and Chinese texts through Indian and European composition manuals of the 18th century. By contrast, this course concentrates on “modern” music literature, that is, tonal idioms associated with the rise of a musically literate middle class in 19th century Europe and its colonies, and the “art” and “popular” musics that developed from that foundation.^2 This approximately 150-year period, though, is too broad, and we’ll narrow it further by concentrating on three issues: tonal coherence, motivic coherence, and pitch-class/beat-class set (pc set) coherence.

Tonal coherence is the principle that what binds a work together in Beetoven’s time (roughly) are harmonic progressions that traverse closely related keys—and that do so according to contrapuntal features like cadences and elaborations. We’ll make use of long-range counterpoint (derived from part of Schenker’s theory) to explore that principle, and we’ll briefly assess some alternative approaches.

Motivic coherence is the simpler idea that music, including some highly chromatic music (music that might lack tonal coherence) can be held together by what Carl Dahlhaus calls a compositional economy, in which larger forms arise from a minimum of motivic materials. A motivic orientation to the unity of musical forms is nearly household parlance in discussions of Berlioz and Wagner; a step along the way from what is conventionally “absolute music” toward a culture of visceral musical pleasure: “structure” in late-19th-c. music sometimes arises not through tonal procedures but through invocation and aural connection between immediate sonic experiences, signals that connect and structure experience concretely and iconically, i.e. by how they resemble one another or how they form a dramatic rhetoric in reference to the extramusical.

Pc-set coherence will offer us an introduction to revolutionary and emancipatory conceptions of pitch and time that, in T. W. Adorno’s view, the historical consequence the tension between tonal coherence and its alternatives in subject and musical idea. Because intervals labeled by numbers are abstract values, they’re ideal schema in which to understand music that resists the subordinations of modal and tonal organization, but offers a basis for order uncoupled from small-scale Gestalts. These methods, in turn, offer a foundation for “serial” organization that sets forth one of two overarching polemics of ‘art’ music in mid-20th-c. American and European composers.

The best music analyses are descriptions of what someone hears, and suggestions of what can be heard, in music. The music analyses you complete in this course will attempt to offer insight into the parts of musical experience—not just chunks of time filled with chords and phrases, but also perceptual orientations, modes of listening—as they relate to some kind of whole piece or performance, or maybe (even/just) a whole musical life. I hope this course will also accomplish something for you in your sense of a genealogy of musical ideas that cradle some of our own dialogues and impulses as music-listeners and music-makers today.


^1. A little blogging on definitions of, and reminders about, common terms for intellectual endeavors: analysis/synthesis, theory/practice, theory/observation, and practice/criticism, and even a little bit about ideology.

^2. “Modern Western music literature”, in this case, refers to musics in “modernity” (not to be confused with modernism); for our purposes, defined by the rise of literate middle-class consumers who were consumers of sheet music in the 1800s, and who participated in cultures of notated “popular” and “art” music in the 19th and early 20th centuries. Until the rise of the Third Reich in the 1930s, composers ranging from Wagner to Offenbach, and from Puccini to Duke Ellington, typically saw art and popular music as part of a continuum, rather than as the two separate streams that structure our thinking today. All of the repertoire arises in “Western” notation, and as such reflects a potentially “colonizing” and subjugating force when it occurs in non-European musics. However, popular culture doesn’t belong to the West. (Resist any assumption that musical traditions of Latin America, East Asia, the Middle East, etc. are caught between Western influence and an “authentic” pre-modern past; rather, their traditions are living, and can retain that life in the face of foriegn influence just as readily as Western tradition can.)


Learning Outcomes:

1.          Clarify and distinguish aspects of harmonic and contrapuntal listening that are evident and prevalent in 19th-century European (“art” and “popular”) music literature.
2.          Grasp the basics of linear and voice-structure analysis, and an introduction to Schenkerian Analysis, as a set of tools common to contemporary scholarly analysis of tonal music.
3.          Grasp the basics of set-theoretic approaches to post-tonal music.

4.       Explore and challenge conventional approaches to music analysis as a means of introspection about musical experience.

Assignment format:

Except where a diagram specifically benefits from letter-orientation, please use landscape-oriented staves:

4-system sheet for “surface” graphs of complete works [REVISED 1/21/18]. These staves give you a maximum ability to diagram 8-12 bars of relativey dense music, or 16 bars of simpler music, on a single system without line breaks.

3-system sheet for sketching and drafting graphs when it is not necessary to show the continuity of a longer musical sentence.

2-system sheet with double-grand-staff systems, for foreground and middleground, or middleground and background graphs. Use these later in the quarter when you wish to show the complex surface of a piece (normally on the bottom grand staff), in parallel with a simpler description of structure, unencumbered by detail (normally on the top staff).

Coursework & evaluation:

Participants in the seminar are expected on a weekly basis to prepare materials for submission or quesitons for discussion, and materials for formal presentation approximately every two weeks. We will establish, impromptu, in each week, which seminarians are slated to present for discussion in the following week. Those slated for discussion are required to bring recordings, scores, and 4-5 photocopies of their graphs or written work, as visual aids to their presentation. Many of the assignments in the course are “accumulative,” that is, your success in the course depends on your ability in one assignment to respond to feedback on the last.

Analysis, in this course, consists of the use of established symbols and conventions of representation, to express a way of hearing a musical work. Your grade in the course will be a reflection of your ability to express such a way of hearing imaginatively, persuasively, and economically. Students will also submit two full analyses, one exhibiting tonal principles and the second exhibiting post-tonal principles, and will choose one of those two projects as the foundation for a more thoroughly developed final project.

1/4 of the grade will reflect your abilities in week-to-week exercises and analysis drafts

1/6 will reflect the strength and preparedness of your in-class discussion

1/3 will reflect your success in the two preliminary analyses (one tonal and one post-tonal)

1/4 will reflect the success of your final project.


Seminar Calendar and Readings

Primary readings

Cadwallader, Allen and David Gagne. Analysis of Tonal Music: A Schenkerian Approach. London: Oxford U Press, 1997.

Dahlhaus, Carl. Between Romanticism to Modernism. Translated by Mary Whitall. Berkeley: University of California Press, 1980.

Lerdahl, Fred and Ray Jackendoff. Generative Theory of Tonal Music. Cambridge: MIT Press, 1983.

Forte, Allen and Steven E. Gilbert. Introduction to Schenkerian Analysis. New York: Norton, 1982.

Straus, Joseph. Introduction to Post-Tonal Theory. Englewood Cliffs, New Jersey: Prentice Hall, 1990.

Nauert, Paul. Notes on PC-Set Theory. Unpublished.



WEEK 1 [January 8]

DUE: To do well in this course, you need basic music literacy, and competency in Roman-numeral analysis, including analysis involving secondary or temporary tonics. (You may have used the term “modulation” or “tonicization” for these situations in previous study.) You will also need experience in freely composing a melody above a figured bass line.


(Optional) — If you are not as confident in Roman-numeral analysis as you would like to be, please seek my feedback by completing exercises D, F, and G in the free online web resource for Chapter 19 of Laitz, Stephen G. The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening. (Cambridge/New York: Oxford University Press, 2011).


(Required) — Instrumental Counterpoint Exercise — Compose melodies conforming to stylistic characteristics of short 18th-c instrumental compositions, over each of the two given figured bass lines in the assignment above. To help, my own overview of typical guidelines for instrumental counterpoint might be helpful:


1. Two-part writing and Note-to-note guidelines: adapted from the early chapters of Kent Kennan’s Counterpoint Based on Eighteenth-Century Practice (Saddle River, NJ: Prentice Hall, 1999; see esp. these excerpts from Kennan’s Chapter 4, and Chapter 6), and the Mitchell translation of C.P.E. Bach’s [1759] Essay on the True Art of Playing Keyboard Instruments (London: Eulenburg, 1974). 


2. Whole melody (/well-formedness) guidelines, also adapted from Kennan (ibid.) and from Reicha’s [1814] Treatise on Melody, trans. E.S Metcalf. London: E.S. Metcalf, 1896.



WEEK 2 [(Tuesday) January 16] 
(1) Forte & Gilbert Ch. 1 “Melodic Diminutions”. Choose two of these five exercises: Ex. 3, 4, 6, 7, and 9 (pp 38-40) to complete.
(2) London, Justin (1990). Riepel and Absatz: Poetic and Prosaic Aspects of Phrase Structure in 18th-c Theory.” In Journal of Musicology, Vol. 8 No. 4, pp. 505-519. Prepare 2-3 questions and lead discussion on at least one. [use UCSC Libraries’ Off Campus Access login instructions to access this article when not on eduroam or cruznet).]

(1) Complete a “rhythmic reduction”*, graph, and formal description on one of the following two songs by Stephen FosterLaura Lee or Beautiful Dreamer.

*To make a rhythmic reduction of the melody, follow the methods described in Forte & Gilbert Ch. 1. For our course, the melodic reduction should be “stems up,” so that you can then write additional noteheads (without stems) beneath the melody to express the harmonic progression. Here is a model graph & description (of Foster’s “Jeanie with the Light Brown Hair”) that you may follow. Here is a sample of the score.

(2—for discussion, no submission) Please *begin* your analysis of a Sonatina movement, assigned in class 1/8; due 1/22. By 1/15, complete a Roman-numeral harmonic analysis, identify cadences, and sketch a reduction, noting areas of ambiguity or confusion.


{ Week 2 — in-seminar examples, lecture notes + model for completion of week 3 sonatina analysis }

WEEK 3 [January 22]

(1) Read: Cadwallader & Gagne Ch. 2 “Melody and Counterpoint” (pp 15-24). Complete Two additional exercises among those listed in week 1 for Forte & Gilbert Ch. 1 “Melodic Diminutions”; with additional notations of “PD” (predominant), and elaborations discussed in class.

Optional exercises: Cadwallader & Gagne Ch. 3Forte & Gilbert Ch. 6 “Some Common Secondary Structural Features”.

(3) Complete a foreground graph of a Mozart Sonatina movement

 Sign up for a movement here

Assignment guidelines: Analysis of a Sonatina Movement, Step I.



WEEKS 4 & 5 [January 29 & February 5] 

(Due January 29) Forte & Gilbert Ch. 8 “The concept of prolongation”; revise your foreground graph due Jan 20, and complete Step II of the Sonatina Analysis. (That links to both steps; scroll down for step II.)

(1) Read: Cone, Edward T. “Analysis Today” In The Musical Quarterly 46/2 (Special Issue: Problems of Modern Music (Apr., 1960), pp. 172-188.) Prepare 2-3 questions and lead discussion on at least one. Along with the Dahlhaus excerpts below, this article is meant to introduce and frame our “big picture” transition between inquiries into tonality (weeks 1-5) and into atonality (weeks 6-10).


(Due February 5) Excerpts from Carl Dahlhaus’s “Issues in Composition” in Between Romanticism to Modernism. Translated by Mary Whitall. Berkeley: University of California Press, 1980.

To read the Dahlhaus effectively, please listen to, and read, examples from the literature discussed within the text. Bring to seminar (to turn in) a 1-2 paragraph description of harmonic or thematic issues you find in at least one work relevant to Dahlhaus’ argument. This is an open-ended assignment, but you should attempt to describe a passage of music in order to clarify, or dispute, a claim that Dahlhaus makes.

Sample Scores for Week 4-5 Project (Full graph due February 12): Brahms, Wolf, Strauss, and Mahler.



WEEK 6 [February 12]

Nauert notes pp. 1-13

Straus Ch. 2 “Pitch-class Sets”

Although there is overlap between these two readings, complete them both. After reading the Nauert, make sure you have grasped the concept of “Tn prime form” as applied to 4-5 common pitch sets, including some chords with which you’re familiar from tonal or vernacular traditions. Consider finding your own words for the distinction between “Tn” and “TnI” prime form, and come to class with at least a preliminary, intuitive understanding of how the terms relate to one another.

When reading the Straus, note that he uses the term “Prime form” in place of Nauert’s (more precise) term “TnI prime form.” (Nauert’s tutorial presumes that in some cases “Tn” set classes—smaller classes of sets transpositionally but not inversionally related—are a relevant distinction in the structure of a work.)  

Complete the Straus exercises on pp 44-45.



WEEK 7 & 8 [extended office hours Feb. 20, February 26]

Nauert notes pp. 14-26

Richard Bass (1991), “Sets, Scales, and Symmetries: The Pitch-Structural Basis of George Crumb’s “Makrokosmos” I and II,” in Music Theory Spectrum  Vol. 13, No. 1

Post-tonal analysis project, step 1 [due February 23]: Listen attentively to several songs from these two collections (scores are linked to the cycle titles; recordings following):

 Arnold Schoenberg’s Op. 15 (1908/9) “Das Buch der Hängenden Gärten,” (here’s a strong live performance by Elizabeth Smith & Josef Jungen at Eastman; there are others on youtube)

 and Anton Webern’s 6 Lieder Op. 14 (1917-22) settings of poems by (Gedichte von) Georg Trakl (recording by  Heather Harper; Pierre Boulez cond.).


Choose one song, and after more careful listening, identify 3-5 pc sets that you consider salient as a group. The group should not only be connected perceptually somehow, but perceptually distinct, in at least one way, from any events that you don’t include.

Identify each group as a pc set (using the “normal form” label), as a Tn set class, and as a TnI set class.

For each pc set, write all 11 transpositions, and all 11 indices of its inversion.

Write all of the pitch classes in the work—tedius, but it will start to go quickly once momentum sets in. (You can either label the score with clear ink, or simply write the pc-intergers on a blank sheet, in spatial arrangements resembling the score, so that you can easily connect the two.

Scanning your pc-set description of the piece, identify any occurrences of transformation or variation of the original 3-5 sets that you identified. Come to class prepared to discuss either the invariance, or variation, of pc-sets in the work.



WEEK 9 [March 5]

Presentation previews (optional — you may choose to present a portion of your work in advance, in order to “prepare” the seminar with listening, or questions and problems to consider. Some analytical claims are better made to an audience familiar with fundamental claims, and that familiarity is easier to establish when a presentation is split between meetings a week apart.)

1. Nauert notes pp. 27-32

2. J. Daniel Jenkins (2009), “After the Harvest: Carter’s Fifth String Quartet and the Late Late Style,” in Music Theory Online Volume 16, Number 3.

3. Straus Ch. 5 “Basic Twelve-tone Operations”



WEEK 10 [March 12]

Presentations + Joseph Straus’ “Analytical Misreadings” (Ch. 2 of Remaking the Past)

Optional reading: Carson, Ben Leeds. [zip file 2.3 MB] “Schoenberg’s Ambivalent Thought: subjectivity in ‘Du lehnest wider eine Silberweide…” In Cox, Biro, Takesugi, & Sigman, eds., The Second Century of New Music. New York: Edwin Mellen Press, 2011.



FINALS-WEEK MEETING [Thursday, March 22 — 12:00 noon - 3:00 PM]

Presentations +

Kofi Agawu, “How We Got out of Analysis, and How to Get Back in Again,” in Music Analysis, Vol. 23, No. 2/3 (Jul. - Oct., 2004), pp. 267-286.