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    Pedagogical materials for twentieth-century rhythm

    edited October 2014 in Analysis

    I'm currently teaching an advanced graduate twentieth-century analysis course. We are using the Straus textbook, which is excellent, but I feel that a course like this should at least cover some theory that deals specifically with rhythm, and this is not covered in the Straus. Looking for supplementary readings, I'm struck by how little pedagogical material there is on rhythm. I currently have the chapter from Lester's textbook on the syllabus, but this is essentially a very broad survey. The same can be said about Kostka's chapter. There are pedagogically-oriented analyses of single pieces that involve largely rhythmic considerations (such as some in the Morgan anthology), but the concepts and methods are largely piece-specific. In a theory/analysis course, I think one should teach theory concepts and analytical skills that can be used more or less to gain some understanding of a range of composers and repertoire.

    In other courses, I have developed my own pedagogical approaches to periodicity, metric irregularity via additive-rhythm type processes, and polymeter. These are applicable to a relatively diverse, albeit limited, range of twentieth century music. I haven't found any readings on these topics, though, that are pedagogically appropriate and at the same time sufficiently technical for a theory course.

    So I have two questions, the first being, just, am I missing something? Does anyone have suggestions about readings I might consider?

    The second is the broader question: is this a failure of ours that we have not sufficiently developed theories of rhythm for twentieth-century repertoire? After all, many twentieth-century composers attest that rhythm takes primacy over pitch in their compositional process (Cage, Carter, etc.). Perhaps the problem really is that compositional practice concerning rhythm really is too Balkanized in the twentieth century. But the same problem has not stopped us from developing tools of pcset theory at a sufficiently abstract level to be relevant to twentieth-century composers whose non-tonal harmonic languages could hardly be more different both in method and results.

    --Jason Yust


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    • 6 Comments sorted by Votes Date Added
    • Hi Jason,

      I've been teaching a course titled "Rhythm and Temporality in 20th-Century Music" for a few years now, and, as you noted, there is no textbook that can serve as a basis for this topic. The course I teach is meant to be a survey of new developments in both musical composition and music analysis in that time period. I have structured the course around a few themes such as "early modernism,", 'free rhythm," "seriliazed time," "musique concrète," "minimalism," and "temporal multiplicity." I usually close with some treatment of "new trends," which has included popular music and non-Western influences in different offerings (usually, this is determined based on who ends up taking the course and their specific interests). Within these themes, I have focused on a few representative composers, priviledging those composers whose rhythmic language has given rise to some new analytical technique. I usually open the course with Jonathan Kramer's The Time of Music as well as a basis on rhythm perception. Each analytical technique is covered through a tutorial, and this has included cinematographic techniques/metaphors (based on Rebecca Leydon's work on Debussy), contour theory (based on Betsy Marvin's work on Varèse), serialism (multiple sources, including Boulez, Stockhausen, and Babbitt; the assignment is usually compositional rather than analytical), beat-class set theory (based on John Roeder's and Rick Cohn's work on Reich), and a few different approaches to the music of Ligeti and Carter as well as Mark Butler's work on EDM. What the course ends up achieving is familiarizing students with a set of research questions on the experience of time in music, different ways of treating temporal organization in composition, and a set of "tools" for their analytical toolbox. The final project usually requires them to pick one or more of these tools and extend them in some way to explore a work composed after 1999. The list of relevant articles is too long to put here, but I would be happy to share.

      In brief, I think that although there is no textbook, there is a wealth of materials out there to be taken advantage of, and although it might be challenging to address rhythm independently of pitch (which is my approach, for the most part in this course), students get a healthy bath of rhythmic theory.

    • I'm wondering if perhaps David Lewin's article "Cohn Functions" from Journal of Music Theory, Vol. 40, No. 2 (Autumn, 1996), pp. 181-216 would be of some use? 

      http://www.jstor.org/stable/843888 ;

      There is an interesting consideration of rhythm in there, overlapping with some transformational theory, naturally. 


      And also Harald Krebs' "Fantasy Pieces," though that isn't specifically designed for 20th century music, I think that a lot of the concepts would serve as good jumping off points.
    • Hi Jason,

      I'm not sure if the following two articles would be appropriate because I merely skimmed them after a google search, but many of Witold Lutoslawski's pieces contain sophisticated rhythmic structures.



      If you might explore the relationship between form and duration, then perhaps Lutoslawski's Jeux Venitiens would be appropriate. If so, then I could recommend Roig-Francoli's analysis from Understanding Post-Tonal Music (2008), pp 287-291

    • [Sorry about the images not coming out. The package SMTDiscuss is using seems to have a glitch that isn't showing how to upload an image from my computer - so I've given URLs to link to while I figure out how to re-size a download from a URL.]

      Beside teaching from a textbook/anthology, which will unavoidably have the biases as well as expertise  of the author/anthologist built in, there is also the option of teaching from sources -- not just scores, but sketches which would introduce compositional process into the pedagogical equation. This wasn't possible 10-15 years ago, but today there is an increasing number of source documents available on line -- and making more use of them this way would also encourage institutions to digitize and make more of these available on the web. To illustrate, here's one of my favorites from the Carter collection at LoC that speaks directly to one of Jason Yust's questions. I laughed out loud when I first came across this.

      I don't think many are aware that the birth of metric/tempo modulation took place in a hotel room in Baltimore - specifically the Hotel Stafford, "Baltimore's quiet hotel" (I believe it's now an apartment building), close to Peabody where Carter was teaching at the time, commuting from NYC by train. It begins on the front of a sheet of the hotel's stationery:



      When I first noticed this I just sort of shrugged. Then I turned it over to find this on the back:



      This is a draft of the rhythmic plan for the entire cello sonata. We can never know exactly what metaphors (if any) were in Carter's head when he sketched this out, but, if we let go of preconceptions and squint just a little, doesn't it look like a diagram for the way classic sonata form used to be presented, but with harmonic relationships replaced by rhythmic ones: exposition-development-recapitulation. The "tonic tempo" is quarter note = 112 which is returned to at the end of the "exposition" before an extended excursion of tempos in the "development" & finally the "home tempo" 112 is returned to at the end of the "recapitulation." This way of looking at it wraps metric modulation & harmonic modulation into the same package, which in turn results in some hard questions -- which is a good thing. 


      Returning to Jason's question, perhaps it's time to introduce original source material into curricula (even/especially for undergraduates) to increase awareness (keyed to textbooks & scores) of where/how compositional practices may have originated (especially in the knotty C20) & the creative process generally. This isn't to suggest that such an idea could replace basic textbooks - but it might introduce a little more freedom for the instructor and a little more excitement for the student.

    • Hi Jason,

      I think I understand what you are looking for with regard to 20th century meter. We can have theories of meter that are separate from tonal pitch structures as Lerdahl does in GTTM. The common hierarchical foundation of tonal pitch and rhythmic theories, however, allows them to work together or independently. Meter/rhythm has its own independent hierarchical structure, so formulating theories about its structure that are not dependent on pitch is possible. Likewise pc-set theory structures pc-sets and properties independent of any particular piece, but 20th century rhythmic theories are almost always linked to the pitch-structures of composers.

      I think David Lewin’s article “Some Investigations into Foreground Rhythmic and Metric Patterning” presents a formal rhythmic theory independent of any particular pitch-class theory. He demonstrates the analytical application with Schoenberg’s piano piece Op. 19, No. 6.

      Elizabeth Marvin has adapted contour theory to musical spaces besides pitch, such as rhythm (“A Generalization of Contour Theory to diverse Musical Spaces: Analytical Application to the Music of Dallapiccola and Stockhausen, Concert Music, Rock, and Jazz Since 1945.)

      These rhythmic theories might provide the general, abstract, and level of independence you want, but ultimately, for me, how a composer structures rhythm is inextricably tied to how a composer contextually structures the pitch-class material. For example, the rhythms in Schoenberg’s fourth quartet movement 1 seem to me to be the product of his hexachordal and trichordal combinatorial thinking, especially in measures 27 and 28.

      All the best,

      Ciro Scotto  

    • Hi Jason, I've been pondering this for the last few days and came up with some suggestions - why not look at real repertoire?  Maybe something not so large scale like Bartok's Mikrokosmos series or violin duets?  Or some of Schoenberg's piano pieces, maybe some of the Sonata's For Prepared Piano by Cage - doesn't get much more rhythmic than that!  I also like "An Anthology of Piano Music The Twentieth Century" Volume IV, Yorktown Music Press, Inc.  Just thought I'd make a suggestion - nothing like the real thing for teaching materials.