Symmetry

Symmetry is a term commonly in use in musicological discourse. Surprisingly, the frequency of its use is in inverse proportion to the clarity of its definition. As of 2017, the term “symmetry” appears in more than 200 entries of the online edition of The New Grove Dictionary of Music and Musicians, but no entry in that dictionary actually defines the term. In the Oxford English Dictionary one may find several meanings attached to the noun “symmetry.” The meaning relevant to most musical references is “Due or just proportion; harmony of parts with each other and the whole; fitting, regular, or balanced arrangement and relation of parts or elements; the condition or quality of being well-proportioned or well-balanced.”

Proportional symmetry (as it will be referred to here) is often evoked through the adjective “symmetrical” attached to units of musical form such as phrases, periods, and sections. It is most clearly evident in dance movements of the Baroque suite, where double barlines divide movements into two sections whose lengths, in many cases, refer to one another in simple ratios of 1:1, 1:2, and 2:3. In many cases each section may easily be divided into halves and quarters. Both levels of symmetry are discernible in the Minuet from Purcell's Suite Z. 660 (example 4.1). In fact, here one can see another kind of “harmony of parts with each other,” in the way each strain is subdivided into three phrases of 2, 2, and 4 bars. Thus, bars 1–2 correspond with 9–10 (and are motivically connected through inversion), bars 3–4 with 11–12 (again motivically connected through inversion), and bars 5–8 with 13–16.

However, even within this specific meaning of “symmetry,” the Oxford English Dictionary leaves some space for ambiguity. According to the dictionary, “In stricter use, [symmetry is the] exact correspondence in size and position of opposite parts; equable distribution of parts about a dividing line or centre. (As an attribute either of the whole, or of the parts composing it).”

While the chain of phrase lengths 2,2,4:2,2,4 is symmetrical according to the first part of the definition, it is no longer symmetrical according to the “stricter use” of the term. In order to adhere to strict symmetry, the subdivision of the piece had to be, for example, 2,2,4:4,2,2 or 4,2,2:2,2,4.