ABSTRACT
Creating music, listening to music, and dancing to the rhythms of music are prac-tices cherished in cultures all over the world. Although the function of music as a survival strategy in the evolution of the human species is a hotly debated topic, there is little doubt that music satises a deep human need.* To the ancient philosopher Confucius, good music symbolized the harmony between heaven and earth.† e nineteenth-century philosopher Friedrich Nietzsche put it this way: “without music life would be a mistake.”‡ And the Blackfoot people roaming the North American prairies “traditionally believed that they could not live without their songs.”§
Of the many components that make up music, two stand tall above all others: rhythm and melody. Rhythm is associated with time and the horizontal direction in a typical Western music score. Melody, on the other hand, is associated with pitch and the vertical direction. Although rhythm and melody may be studied independently, in music, they generally interact together, and in uence each other in complex ways.¶ Of these two properties, rhythm is considered by many scholars to be the most fundamental of the two, and it has been argued that the development of rhythm predates that of melody in evolutionary terms.** e ancient Greeks maintained that without rhythm melody lacked strength and form. Martin L. West writes: “rhythm is the vital soul of music,”†† the philosopher Andy Hamilton notes that “rhythm is the one indispensable element of all music,”‡‡ and Ton de Leeuw considers that “rhythm is the highest and most autonomous expression of time-consciousness.”§§
Joseph Schillinger writes: “e temporal ow of music is primarily a matter of rhythm.” Christopher Hasty oers a concise universal denition of music as the “rhythmization of sound.”† From the scientic perspective, psychological experiments designed to assess the dimensional features of the music space, based on similarity judgments of pairs of melodic fragments, suggest that the major dimensions are rhythmic rather than melodic.‡ e American composer George Gershwin believed that the public loved his music because of its rhythm, and in analyzing his rhythms, Isabel Morse Jones writes: “Gershwin has found denite laws of rhythm as mathematical and precise as any science.”§
What is rhythm? ere is no simple answer to this question. Hasty cautions that “rhythm is o en regarded as one of the most problematic and least understood aspects of music.”¶ James Beament echoes this sentiment when he writes: “Rhythm is o en considered the most di cult feature of music to understand.”** For Robert Kauman, “e di culties of dealing with rhythm are immense.”†† Wallace Berry writes: “e awesome complexity of problems of rhythmic structure and analysis can be seen when one appreciates that rhythm is a generic factor.”‡‡ Berry goes on to note that another consideration that makes studying rhythm di cult is the fact that meanings ascribed to terms such as “rhythm,” “meter,” “accent,” “duration,” and “syncopation” are vague and used inconsistently. Elsewhere, he writes more concisely: “Rhythm is: everything.”§§ In spite of some of these di culties, or perhaps because of them, many denitions of rhythm have been oered throughout the centuries. Already in 1973, Kolinski wrote that more than 50 denitions of rhythm could be found in the music literature.¶¶ Before diving into the geometric intricacies of rhythm that are explored in this book, it is instructive to review a few examples of denitions and characterizations of rhythm, both ancient and modern.
