|
COPYRIGHT 2000 University of Washington
INTRODUCTION
IN THE LINER NOTES to the 1993 recording of Lou Harrison's Fugue Percussion (1941), the composer relates how he and John Cage met in "a good pie shop" in San Francisco to work out the "is-tos and as-tos" of employing in rhythmic form the tonal relations found in a fugue. [1] Harrison had become interested in advanced rhythmic issues during the 1930s; in particular he was concerned with cross-rhythms, which he conceived of as "transferring rhythmic patterns into other lengths of time. "[2] He identified cross-rhythms with the overtone series, a concept borrowed from his one-time teacher, Henry Cowell. [3] The task that Harrison discussed with Cage over pie, then, was the application of this correspodence between pitch and rhythm to a musical structure with established pitch or tonal associations, namely the fugue.
This paper will begin with the source of Harrison's pitch/rhythm ideas, that is with a discussion of Cowell's rhythmic innovations. By analyzing the subject and answer statements in the exposition of Harrison's Fugue for Percussion, I will then discuss how Harrison adapted Cowell's ideas, and explain precisely what he is comparing when he abbreviates the phrase "this is to this, as that is to that." An examination of the middle section of the Fugue will follow, focusing on the ways in which Harrison creates rhythmic equivalents to traditional fugal techniques. This discussion will lead to an overview of the formal structure of the piece, and I will address aspects of pitch and instrumentation. I will close with remarks about the musical effectiveness of Harrison's Fugue for Percussion.
COWELL'S RHYTHMIC INNOVATIONS
When the informally schooled Henry Cowell encountered his first music-theory textbook at the University of California in 1914, he discovered that the ratios formed by the lower partials of the overtone series corresponded to the ratios he had been using as cross-rhythms in his compositions. [4] Intrigued by this, he got together with a graduate student in physics to conduct an experiment to prove his hypothesis that there was a "demonstrable physical identity between rhythm and harmony." They tuned two simultaneous sirens in the relationship 3/2 and confirmed that the sirens sounded the interval of a perfect fifth. Then they slowed the sirens down, keeping the same 3/2 relationship, and discovered that they arrived at a rhythm of 3 against 2, "heard as gentle bumps but also visible in tiny puffs of air through the holes in the sirens." [5]
This experiment proved to Cowell that the ratios express a single physical relationship which can be heard as rhythm when slow and as pitch when fast. He went on to formalize the relationship in New Musical Resources, proposing a means by which vibration ratios of intervals derived from the overtone series can be translated into rhythmic ratios, thereby creating what Cowell called "parallel time-systems" (51). In his representation, the whole note is the basic durational unit, and the ratio of an acoustically pure interval becomes the ratio between simultaneous durational subdivisions of the whole note. For example, the interval of a perfect fifth, vibration ratio 3/2, translated into time (as Cowell expresses this process in New Musical Resources), produces a whole-note measure of three equal notes set over another measure of two equal notes, as shown in Example 1. [6]
Cowell also applied these principles compositionally. He wrote two polyphonic "rhythm-harmony" quartets, Quarter Romantic (1917) and Quartet Euphometric (1919), in which he used pitch ratios to generate aspects of the rhythmic organization. In Quartet Romantic the rhythmic content of the first movement is derived from the harmonic ratios of a precomposed harmonic theme (similar to a four-part chorale), based on the overtone series of [C.sub.2]. Each quarter-note duration of the harmonic theme generates one whole-note measure in the Quartet. Quartet Euphometric is also based on a precomposed harmonic theme, but in it the ratios are applied to simultaneous meters, not to durational subdivisions of the whole note.
An excerpt from the harmonic theme and the corresponding measures in the Quartet Romantic are reproduced in Example 2. [7] I have added annotations to the harmonic theme to indicate the ratios associated with each note, relative to the fundamental [C.sub.2]. So, for example, the E two octaves and a major third above the fundamental is the fifth overtone, vibration ratio 5/1, and...
Read the full article for free courtesy of your local library.
|
Bookmark this article
Print this article
Link to this article
Email this article
Digg It!
Add to del.icio.us
RSS
