Number Symbolism in the Isorhythmic Motet

Number symbolism has a long history in music, dating back not only to the music studies of the Greek philosopher Pythagoras (6th century B.C.E.) but also to his precursors in Babylonia and elsewhere in the Eastern world. One of the most highly developed and meaningful forms of number symbolism in Western music is the isorhythmic motet.

The isorhythmic motet flourished in the fourteenth and fifteenth centuries.

The medieval motet, in general, was a polyphonic choral composition in which the sacred text and melody of the tenor (at that time, the bottom voice) were based on a Gregorian chant.

An added upper melody was supplied with its own new French or Latin words, hence the naming of the upper part as motet, the diminutive of French mot ("word"). The use of the diminutive pointed to the secondary role of the commenting text. The second voice was also known by the Latin word motetus, while possible third and fourth voices were called respectively triplum and quadruplum.

Eventually the French word motet became the generic term for this type of composition.

The tenor, with its sacred text and melody, was the Word, the unifying, ever-present cantus firmus ("firm song" or "fixed song") that served as the basis for the addition of the commenting parts. In the motet, however, the free rhythm of the original plainsong was changed to a strict pattern based on ternary (triple) rhythm, a symbol of the Trinity.

Fourteenth-century composers and theorists developed a specific kind of motet involving two recurring elements in a motet tenor: a series of pitches called the color (Latin, "color, character") and a pattern of durations called the talea (Latin, "cutting, segment"). The plurals are colores and taleae.

The two elements could combine in various ways: the color and the talea could coincide, beginning and ending together repeatedly during the composition; the color could extend over two, three, or more repetitions of the talea (for example, a color of 36 notes could consist of 3 repetitions of a 12-note talea); or the color and the talea could be of such differing lengths that their endings never coincided, so that the relationship between the color and the talea constantly changed.

Composers created infinite variations on these basic structures, all based on numerical relations within a color or talea or between the two elements. A motet having a tenor constructed with a color and talea came to be called an isorhythmic ("same rhythm") motet.

An example of an isorhythmic motet is Garrit gallus-In nova fert-Neuma by Philippe de Vitry (1291-1361). (Grout, page 105)

Upper voices could also be organized isorhythmically. A motet in which all voices are isorhythmic is known as a panisorhythmic motet. Most of the twenty-three motets by Guillaume de Machaut (c. 1300-1377) are panisorhythmic. (Grout, page 107)

The isorhythmic technique was derived not from aesthetic experience but from the Pythagorean conviction that numbers are the immaterial forces behind all of cosmic order and therefore form the essence of all things, both physical and spiritual. Pythagorean mysticism and numerology greatly influenced medieval Christian music theory.

The theory behind the isorhythmic procedure was that to repeat rhythmic and melodic schemes throughout a composition was synonymous with retaining divine numerical proportions.

Medieval Christian music theorists pointed out that the cosmic importance of numbers was reinforced by the Bible. Examples: "He telleth the number of the stars; he calleth them all by their names" (Ps. 147:4); "Who hath measured the waters in the hollow of his hand, and meted out heaven with the span, and comprehended the dust of the earth in a measure, and weighed the mountains in scales, and the hills in a balance?" (Isa. 40:12); and "the very hairs of your head are all numbered" (Matt. 10:11). Some specific numbers had a recurring symbolic power, such as seven (as in Gen. 7:2-3 and Rev. 1:20).

The isorhythmic motet, through its numerical proportions, was a device for "allegorizing the universe" (Bukofzer, page 180). The recurring proportions, no matter how complex the surface textures or relationship between color and talea became, symbolized the divine unity (God's will) underlying all external multiplicity.
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Manfred F. Bukofzer. "Speculative Thinking in Mediaeval Music." Speculum: A Journal of Mediaeval Studies (April 1942).

Grout, Donald Jay, and Claude V. Palisca. A History of Western Music. 5th ed. New York: W.W. Norton, 1996.

Merriam-Webster's Collegiate Dictionary. 11th ed. Springfield, Mass.: Merriam-Webster, 2006.

The New Grove Dictionary of Music and Musicians. 2nd ed. London: Macmillan, 2001.

The Oxford English Dictionary. 2nd ed. Oxford, England: Clarendon Press, 1989.