<em>Clapping Music:</em> Complexity and Information in Reich's Rhythm Space

CLAPPING MUSIC: COMPLEXITY AND INFORMATION IN REICH’S RHYTHM SPACE ADOLFO MAIA, JR.1 An idea can never perish. —Arnold Schoenberg (Style and Idea) 1. INTRODUCTION NCE IN WHILE THERE APPEAR MUSICAL WORKS which seem to have been designed to demonstrate a particular musical idea, effect, or process. For example, Schoenberg’s Farben, Scelsi’s Quatre Pezzi Orchestrale, and Ligeti’s Continuum explore the orchestration of timbre; Cage’s 4’33” enacts Cage’s revolutionary concept of music; Ligeti’s Poème Symphonique pour 100 Métronomes and Reich’s Clapping Music provide examples of how simple processes can generate interesting and engrossing musical experiences. In this paper, we are interested in Clapping Music, and the consequences of the idea behind it. Consider the rhythmic motive in Example 1. It was Steve Reich’s idea—not the rhythm pattern itself but what to do with it. Minimalist to the extreme, deprived of any sophistication of timbre or pitch, the O 92 Perspectives of New Music piece is easily performable with some practice by almost anyone; it requires only two performers just clapping their hands. The rst performer keeps the rhythm in Example 1 in ostinato through thirteen measures, repeating each measure twelve times. The second performer starts clapping the rst measure in unison, iterating it twelve times with the rst performer. Next, the second performer shifts the rhythmic pattern cyclically one beat to the left, clapping it also twelve times. After twelve left one-step shifts—each one de ning a new rhythmic motive for the second performer—the process returns to the initial unison situation, and the piece ends. Since each measure is indicated to be performed twelve times, the piece has a total of 13 × 12 = 156 measures. In fact, its score is short (one page), clear and ef ciently composed: just the thirteen notated measures and instructions. Nevertheless, in spite of its presumed simplicity, Clapping Music attracts us with its evolution of perceptually captivating superimposed rhythmic patterns, especially during a live performance. The effectiveness of this work is an amazing surprise considering its economy of musical resources. It belongs to the group of works using gradual phase shifting processes that Reich ceased composing after 1972 since “it was time for something new” (Reich 2002). The frugal resources of Clapping Music can be used to investigate the theoretical and perceptual analysis of rhythm as well as provide a good example of “economic” music composition. Of course, in performance the piece is not absolutely (or mathematically) economical since each measure is repeated twelve times. But it should be noted that these repetitions—or pattern loops—induce a state of perceptual accommodation in the listener to guarantee appreciation of the abrupt rhythmic transition from a measure (or loop) to the next one. Reich himself observes that “the sudden changes here create the sensation of a series of variations of two different patterns with their downbeats coinciding” (Reich 2002). Clapping Music is therefore an interesting artistic application of perceptual features of human hearing such as the accommodation of repeated musical segments and the perception of transition patterns, speci cally at signi cant changes of information. In fact, at least for sound communications, information ux transitions are more perceptible than the information quantity itself; for example, white noise, which EXAMPLE 1: CLAPPING MUSIC RHYTHMIC MOTIF Clapping Music: Complexity and Information in Reich's Rhythm Space 93 has theoretically maximal information, gets boring, in the absence of any expectations, after some seconds of hearing. In this regard, Clapping Music has some characteristics of “ordered noise,” precluding weariness But its information transitions and associated complexity measures can be not only perceived but also be formally evaluated. From Example 1 we see that Clapping Music motive has eight notes and four rests. A simple combinatorial calculation shows that the number of rhythmic motives having the same numbers of notes and rests is exactly 495. The Clapping Music motive is just one of them and its performance it just a twelve step path in this set of 495 rhythm patterns. Since we have hundreds of possibilities, the immediate question is: what makes Reich’s rhythm pattern a singular one? Well, besides those characteristics mentioned above, it...