Symmetric Sounds

Jonathan L. Friedmann, Ph.D.

According to science writer Philip Ball, roughly ninety-four percent of music lasting more than a few seconds contains verbatim repeats. This is true of music-cultures scattered throughout the globe. Indeed, despite the astonishing variety of expressive sounds culturally defined as music, repetition appears to be a unifying characteristic. On the micro scale, repetition derives from alternating longer and shorter note values, sometimes with pauses in between. If extended, these temporally balanced blocks merge into macro patterns: ostinati, verse-chorus form, sonata form (exposition, development, recapitulation), thirty-two bar form (AABA), and so on. Repeated rhythms and melodic/harmonic lines are also heard in through-composed works, flowing ecclesiastical chants, and patchwork songs, such as “Fingertips” by They Might Be Giants, comprising twenty-one short songs of five to twenty seconds apiece.

On the small and large scale, repetition yields symmetry: a sense of pleasing proportions. Symmetry is a fundamental aspect of beauty. Biologically, left-to-right symmetry in the face and/or body is a generalized indicator of physiological and psychological health. Thus, the most symmetrical people are considered the most beautiful (eye-of-the beholder arguments notwithstanding). Likewise, we are attracted to well-proportioned patterns of nature—flora, fauna, and geological—and repelled by their opposite.

To a significant extent, art is indebted to the mathematical symmetry present in nature. Nature-imitative patterns are woven into pottery, poetry, architecture, and musical repetition. Contrastingly, modernist movements that intentionally frustrate our pattern-seeking brains tend to provoke negative responses. (In the works of Pierre Boulez, for instance, references to other music are expunged as far as possible.)

However, over-redundancy has its own problems. Occasional deviations can be welcome and gratifying surprises, so long as the pattern is quickly retrieved. Agreeable breaks are typically achieved through truncation (subtraction of metrical units), prolongation (addition of metrical units), or elision (overlapping of two symmetrical units). It can also result accidentally. For example, during a performance “Perdido” at Carnegie Hall on January 19, 1974, Charles Mingus and his band of all-stars (George Adams, Hamiet Bluiett, Jon Faddis, John Handy, Rahsaan Roland Kirk, Charles McPherson, Don Pullen, and Dannie Richmond) botched the AABA form under Bluiett’s baritone sax solo. The musicians played three A sections in a row in one chorus, and just one A section in the next. In Montréal, these gaffes are known as a “three-headed monster” and a “one-eyed beauty,” respectively. The “three-headed monster” emerges again in the last chorus of Pullen’s piano solo. These errors, hardly unusual during jam sessions, rarely spoil the music. They are (usually) amusing anomalies, which temporarily rupture, but never dismantle, the predictable pattern.

The attraction of symmetry in music is self-evident. All human cultures have music, virtually all of that music contains repetition, repetition creates symmetry, and all cultures consider music aesthetically rewarding. Moreover, music that discards symmetry is often called “ugly,” with some challenging its very musical-ness.

Visit Jonathan’s website to keep up on his latest endeavors, browse his book and article archives, and listen to sample compositions.

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