for harp, 2 pianos, 2 violins, 2 violas, 2 double basses, 2 flutes, 2 oboes, 2 trombones and 2 choirs positioned antiphonally. 1981. Doctoral composition for the Ph.D degree in composition. Thesis adviser: Lejaren Hiller. Available on microfilm. Copies of the complete dissertation are available from UMI, 300 N. Zeeb Road, Ann Arbor, MI 48106 USA.

Tel. 1-800-521-0600.

UMI order no. DA8214158.

The Law of One is a composition of 1 hour, 16 minutes, and 22 seconds for harp, two pianos and two identical ensembles, each consisting of mixed chorus, flute, oboe, trombone, strings (violins, violas, and basses) and percussion. To insure uniformity in stereophonic effects of motion, the recording should use one set of musicians, overdubbed for both ensembles. In this work, just tuning, semi-fixed orchestration and periodic structure are combined systematically and intuitively into a coherent whole. Here, just tuning means that all instruments play the frequencies of the harmonic partials of a fundamental C = 33 Hz., either through scordatura, alternate fingerings or alternate slide positions. As a consequence, any combination from the resulting gamut of pitches will be harmonic and will yield the least possible beating - ideally none. Semi-fixed orchestration refers to a table contained in the score of pre-compositional options. The table assigns a specific combination of instruments to each pitch in the gamut: I allowed myself to choose either all instruments from an assigned combination or just a few, but not to violate the pre-compositional restrictions. Finally, by periodic structure I mean control of both rhythm and form in the work. The rhythmic structure is derived from a table of rhythmic durations that determine a period (duration) and a frequency (a rate of repetition for each pitch in the gamut. This rhythmic structure reflects the microcosm, the timbral structure of pitch and is in turn reflected by the macrocosm, the formal structure of the work. The micro-rhythmic (harmonic) structure of just tuning reflects the rhythmic and formal structures, while semi-fixed orchestration links all notes of the same pitch as constituents of a periodic, horizontal plane. In so doing, it counters one's aural tendency to group neighboring pitches into melodic sequences. In short, the three properties of this work, just intonation, semi-fixed orchestration and periodic structure merge into a single concept: there are three facets of the same law, The Law of One.


For a more detailed analysis of this work, read the essay: The Law of One: Recursive Structures in Composition.


The Law of One is a very impressive score, both in its overall conception and in its realization. Mr. Hatzis has clearly mastered many of the important techniques of contemporary music-and developed some new ones of his own-thus demonstrating considerable originality as well as formidable skills in the craft of composition. The sonorities and textures in this piece will be quite stunning when it is given the kind of performance it deserves... I have absolutely no doubt that he has a very bright future ahead of him.

James Tenney (Outside Reader's review)

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