The Inequality Factor: Internal-Similarity and Internal-Distinctiveness Within Abstract Sets David Lefkowitz

In this study (co-written with Kristin Taavola of Sarah Lawrence College), we develop a new measure for determining the degree to which an abstract set class exhibits regularity or irregularity in the interval-class relationships found between the individual member tones–in effect, a similarity measurement applied to a single set-class. For each member of a pitch-class set, an individual interval-class vector–one that tabulates its relationships with other member tones–can be generated; the individual IC vector is then compared with the other tones’ vectors. This leads to two simple questions: How similar are these individual interval vectors? At the same time, how distinct are they? The degree of tension between these two features (termed Interval-Similarity and Interval-Distinctiveness) generates the Inequality Factor, which, within cardinalities, can be used to compare sets. A low Inequality Factor (or "IF") value is associated with fairly equal IC relationships and a resulting high degree of Internal Cohesion, while higher IF values are associated with less equal IC relationships, resulting in a greater degree of IC "angularity" and a lower degree of Internal Cohesion. The measure has potential relevance to composition, analysis, and performance, and to questions of the psychology of perception.

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Mixing the Vernacular with the Abstract: Bien Serré for Big Band James Harley

After a decade away from the jazz scene, in the past few years I have begun a fruitful collaboration with the director of a big band jazz ensemble. He has been interested in exploring new territory with this ensemble. He performed a couple of my early (experimental) big band pieces with great dedication, and on the basis of that experience, commissioned a new piece. I was reluctant at first, given my removal from the jazz domain. However, the power and range of such an ensemble, together with the possibility of incorporating strongly rhythmic elements, drew my interest. In addition, these would be musicians who would be open to new experiences, and would be at ease with various forms of improvisation.

My approach to writing a new work, from a perspective strongly shaped by my experiences in the realm of "classical" or "notated" contemporary composition, began with the idea of creating a collage of styles. My aim was to establish a network of materials that could be combined and layered in various ways over the course of the work. The guiding considerations were primarily structural. The music was organized around variations of textural density (number of elements occuring simultaneously), rhythmic structure, pitch organization (separated into horizontal and vertical elements), and presence and type/degree of improvisation.

Guidelines were implemented in order to draw upon more explicitly "jazz" stylistic features, such as the rhythmic "feel" (Latin, swing, funk, etc.), the use of a "walking bass," circular harmonic progressions, and so forth. The result, I have been told, is rather Ivesian, in the layering of different kinds of material and the explicit mixture of more "popular" elements with more "esoteric" ones.