Update Title: 33BF1741-481D-4CBF-99EB-B9556EF1A895

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Frequently, I have been asked if I ever use mathematical models or methodologies to compose music. The answer is no. (It seems that in general, such procedures lead to bad music and bad mathematics.) However, it does happen occasionally, that after writing a piece of music, I notice a similarity between the piece and a mathematical concept I have studied. This occurred while perusing my quartet "Carolina Reveille."

There is a concept in algebra known as a 'group presentation' in which a specific number of elements (generators) are given, and a relation between them is defined. For example, the presentation (a,b: a5=1, b2=2, ba=a4b) defines what is known to algebraists as D5, the dihedral group with ten elements. I started with the generators (i.e. musical motives) of the widely known tune, "Carolina in the Morning," and formulated various relationships between them. This in turn generated new musical elements, and from this aggregate, all the material--melody, rhythm, harmony, and counterlines--emanated. Of course the process is hardly new. One could argue that the same technique is often found in classical Sonata-Allegro movements, and most likely, it shows the ubiquitousness of the group-theoretic concept, which has relevance in so many diverse fields.

The source material (i.e. "Carolina in the Morning") is presented in its entirety only near the end of the work. However, apart from this detour, "Carolina Reveille" follows what is probably the most common classical variation procedure. That is there is a gradual increase in tempo from one variation to the next, up to the penultimate one, which is written in a somewhat stuffy and scholastic style. this is followed by a lively finale, here a tarantella, which brings the work to a clamorous and joyful conclusion.

"Carolina Reveille" was commissioned as a tribute to Dick and Maryan Schall-- friends of the Hoeschlers, the commissioning family. Discussing the content of the work, a list of songs significant to the Schalls was proposed. From the list I chose "Carolina in the Morning," which seemed particularly well suited to extended elaboration and development. --Paul Schoenfield

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