Document Type


Date of Degree

Spring 2014

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

David K. Gompper


My work Anisotropic Streaming is written for the University of Iowa Symphonic Orchestra. It is approximately 16 minutes in length.

The inspiration of the piece was the cosmic background radiation remaining from the Big Bang. In 1964, it was discovered that space was filled with a faint amount of radiation; a relic from the time when slight temperature variance allowed for the coalescence of particles. These particle collections soon had varying masses and therefore varying gravitational pulls, which in turn created the stars and galaxies. Since the universe expanded while the temperature variances allowed for this particle accumulation, the background radiation is patterned in a manner that is anisotropic: a nearly uniform arrangement of the radiation that appears different depending on the observer's orientation. As a formal tool, this phenomenon has suggested a compositional process focused on transition and contextualization.

The concept of anisotropy manifests itself in my composition in a number of ways. The first of three sections "collects" individual pitches until those frequencies are no longer perceptible - the listener's mind fuses the pitches into a single yet complex sonority. This fusion is encouraged further by the arrangement of pitches mimicking the overtone series. The second section features a very active and thick texture combining to make a single mass of sound. The texture gradually removes layers to reveal the individual short melodies that make up the mass. The third section rearranges these short melodies, making the high melodies low and the low melodies high. Each melody grows one note longer on each iteration, until each are so long they begin to fuse into a single, complex sonority. In these ways, I attempt to create the same kind of sound but through a shifting perspective, exposing sound's anisotropic construction.

Formally, the piece divides into three sections, each a composite sound at different levels of synchronicity and perspective. The sections are further subdivided into two parts, the first being transitional and the second being a more static exhibition of the section's conceptual purpose.

The pitch material in expositional areas is based on the mathematical overtone series (rounded to the nearest semitone). Pitch material in transitional phrases collects into aggregates, generally derived from a frequency modulation, amplitude modulation, or distortion by common fate. These pitches are not necessarily relegated to their registral frequencies, allowing for some octave equivalence.

The first section, an exposition of separate elements creating a whole sonority, begins with the accumulation of material in the middle, high, then low register. As events become more synchronized, these three disparate elements become parts of an Eb1 sonority through additive synthesis. After a brief transitional section of aggregate sonorities in a symmetrical rhythm, the fundamental switches to G1 as a pizzicato cloud texture replaces the higher overtones. The additive G1 sonority occurs repeatedly, getting more frequent towards the end of the section. Using common overtones, overtones of the G1 sonority are sustained and the harmony is displaced by Eb1.

The second section is a discovery of separate elements that exist within a sound complex, and subsequently, the germinal existences of those elements. The effect of parsing the lower pitches into imagined component pitches is the destabilization of a steady fundamental. The implied fundamentals instead fade in and out of perceivable space, creating a sonic environment of quasi-periodic harmonicity. The section begins by changing the Eb1 to a virtual Bb0 fundamental through a series of common overtones. The sustained Bb0 overtones are rhythmicized, becoming melodic fragments of varying lengths. After the surface texture of the Bb0 climaxes, the orchestration is reduced three times to solos and duets, revealing the melodies that exist in each registral area (high, middle, low). A brief transitional section of aggregate sonorities in a rhythm similar to the transitional area in section one, the implied fundamental becomes a D-1. The melodic fragments are extended through sparer orchestration, with soloists and small chamber combinations developing the ideas. The section ends with an implied C1 fundamental.

The final section is the destabilization of the quasi-periodic harmonicity of the second section. The section begins in the highest register on string harmonics that do not imply any particular fundamental. The overtones are textured, and interjections of shepherd tones and noise elements add to an active surface with an unmoored harmonic space. When the surface reaches a maximally undefined pitch space, the gesture of the completed added sonority from the first section returns, implying fundamentals of five different sonorities, moving progressively away from harmonicity. A superimposition of the solo and chamber melodies against segments of previous aggregate transitions leads the harmonic space to a C2 fundamental, played in the gesture of the completed added sonority from the first section. By holding shared common tones, the harmonic space changes to an E1 fundamental, and pitches get higher and quieter until the piece ends.


composition, music, orchestra


x, 106 pages


Copyright 2014 Brian Alexander Penkrot

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