"Another complicated Carter piece."

That is how Aaron Copland referred to Elliott Carter's Holiday Overture, Carter's attempt to compose in the new populist style that Copland and Roy Harris had developed. Carter soon gave up this style, developing his multiple-layer forms of music as influenced by Charles Ives and Nadia Boulanger.

Reader Stephen Hicken asks what Carter pieces I will be teaching today, and what I will say. This is as good a time as any to organize my lecture notes, online. I will be covering two works by Carter, his Eight Etudes and a Fantasy (1950) for woodwind quartet (the typical quintet minus the horn), and the Eight Pieces for Timpani (1968). Both of these works illustrate Carter's development of metric modulation (Carter preferred the term 'tempo modulation'), as well as other techniques of rhythm, timbre, and pitch organization.

The Eight Etudes and a Fantasy came out of lectures Carter was giving on orchestration at Columbia University. He was disappointed with the efforts of the students, so he sketched small examples of woodwind pieces on the blackboard to illustrate different potentials of the woodwind ensemble. He explored and discovered as much as his students had, the small sketches developing into the Etudes. The final Fantasy utilizes techniques and motives from previous etudes in a quasi-fugue. Etude 7 is a great application of Schoenberg's concept of Klangfarbenmelodie. All four instruments play the same G, with all emphasis on color and dynamics. Despite the lack of pitch variation, Carter manages to create a three-part form through the variation of articulation and dynamics. He uses similar techniques in a more typical Schoenbergian sense in Etudes 3 and 6, by using a single chord in Etude 3 and different sustained chords in Etude 6.

The Fantasy starts out like a fugue, with 3 entrances of the subject that is derived from Etudes 6, 8, and 1. Using these three different motives gives a tripartite structure to the subject that Carter will develop in the fantasy. The movement starts in the tempo of the first etude (quarter = 84), modulating to the tempi of Etude 7 (quarter = 126), Etude 2 (MM 72), Etude 6 (MM 90) and Etude 4 (MM 84 in 3/4 meter). The subject is heard at the three main tempi (84, 126, and 90) and at measure 108 the subject is played at two different tempi at the same time (quarter note as the main beat for the oboe, doubly-dotted quarter note as the main beat for the flute).

So how does a tempo modulate? Metric modulation is related to pivot chord modulation in that changes are made smoothly, with little or no obvious shifts. Typically Carter will first change the meter, keeping the same beat or group of beats constant. As an example, in measure 17 of the Fantasy the meter changes from 4/4 to 6/4, with the dotted half note of the new meter held at the same rate as the half note of the previous meter. This is made very smooth by the fact that the previous two measures had quarter-note triplets, which will equal the quarter notes of the 6/4 meter. Then Carter changes the meter again, but the subdivision is kept the same in this case: one measure later, the meter changes back to 4/4, but this time the quarter note is kept constant, so the main subdivision of the 6/4 meter equals the beat of the new meter. This effectively switches the MM 84 tempo of the first 4/4 to MM 126 in the second 4/4.

In "Canaries" from the Eight Pieces for Timpani, Carter doubles the tempo through a series of modulations within the first 20 measures. He also uses a technique from the Fantasy to create multiple layers of speed occuring at the same time, though in "Canaries" one of the layers is constant and the other is accelerating! (As an aside, "Canaries" has nothing to do with the birds. The title comes from the "wildmen of the Canary Islands," and a Renaissance dance that was imported from their culture.) Canaries uses a very typical pitch organization for Carter: the timpani are tuned to E2, B2, C#3, and F3; this collection of pitches belongs to set-class (0146), one of the two all-interval tetrachords that Carter loved to use. Note that the specific pitches chosen allow some typical I - V motions, though this piece is not tonal.

That's all I have time for, as my TA is also lecturing on Messiaen today. Next, the timbral organizations of Cowell, Varèse, Ligeti, Penderecki, and Crumb. (Maybe) If you want to know more about Carter, I highly recommend David Schiff's The Music of Elliott Carter.