Australian Music Centre | Breaking sound barriers

Work Overview

Hypatia's Circle was commissioned by Tom Petsinis with funds provided by Arts Victoria for performance as a song cycle for the full-length play Hypatia's Circle. The work serves as an exploration of Jewish historian and general Flavius Josephus's historical órganon trígonon enarmónion scale, originally presented in his 93 C.E. publication of Jewish Antiquities, and subsequently transformed within the context of a contemporary adaptation of this ancient Egyptian harp tuning. Rhythm and meter on the other hand has been organized in accordance to the musical properties of the Euclidean algorithm, as presented by Godfried Toussaint in The Euclidean Algorithm Generates Traditional Musical Rhythms - a publication of the Centre for Interdisciplinary Research in Music Media and Technology (CIRMMT), The Schulich School of Music, McGill University, Montréal, Québec, Canada. According to Toussaint, "The Euclidean algorithm (which comes down to us from Euclid's Elements) computes the greatest common divisor of two given integers. It is shown here that the structure of the Euclidean algorithm may be used to automatically generate, very efficiently, a large family of rhythms used as timelines (rhythmic ostinatos), in traditional world music. These rhythms, here dubbed Euclidean rhythms, have the property that their onset patterns are distributed as evenly as possible in a mathematically precise sense, and optimal manner."

Hypatia's Circle, within its contemporary adaptation of an ancient Egyptian harp tuning, takes the ascending form of Flavius Josephus's historical scale (A, F, E, C and B) and transposes it to C, which presents the pitches (in ascending order): C, Db, F, Gb and Bb. This scale, which features two conjunct 'enharmonic' tetrachords (two consecutive sets of minor second and major third intervals, followed by a major second to complete the octave) is then juxtaposed with its retrograded intervallic ordering in the second octave (two consecutive sets of major third intervals and minor second intervals, followed by a major second to complete the octave) to create an essentially two-octave pentatonic scale with additional auxiliary tones. This new hybrid two-octave scale forms the structural basis for four unique two-octave scales generated from the four possible combinations of conjunct (juxtaposed) tetrachords based on the diatonic and chromatic genus: diatonic (the juxtaposition of two diatonic tetrachords), chromatic (the juxtaposition of two chromatic tetrachords), diatonic-chromatic (the juxtaposition of a diatonic and chromatic tetrachord), chromatic-diatonic (the juxtaposition of a chromatic and diatonic tetrachord). The four two-octave scales generate a further 7 modes each, or 28 modes in total (28 representing a 'perfect number', or "a positive integer that is equal to the sum of its proper positive divisors" - the first 8 perfect numbers being 6, 28, 496, 8128, 33550336, 8589869056, 137438691328 and 2305843008139952128). The resulting pitch material is utilized in the work not only as way of unifying all melodic and harmonic development via a modal structural scheme, but also as a musical characterization of the respective characters in the play: diatonic, chromatic, diatonic-chromatic and chromatic-diatonic modes number 1 and 2 (Zeno: No. 1, Alexandrian by Birth, No. 3, Gather Around Me / No. 5, More than Our Winning, No. 8, My Subject is a String, and No. 12, Union of Zero and One); diatonic, chromatic, diatonic-chromatic and chromatic-diatonic modes number 3 and 4 (Thalia: No. 2, Music and Mathematics, No. 6, Where Three Dances with Seven, No. 7, Let's Consummate Our Affair, and No. 10, Praise the Golden Mean); diatonic, chromatic, diatonic-chromatic and chromatic-diatonic modes number 5, 6 and 7 (Hypatia: No. 4, Swept Out by the Seventh Wave and No. 9, All Multiplied by Three, and in this case, both diatonic-chromatic and chromatic-diatonic modes number 7 have been utilized in No. 11, Nothing Purer than a Prime).

Work Details

Year: 2012

Instrumentation: Soprano, contralto, tenor, flute, viola, harp.

Duration: 25 min.

Difficulty: Advanced

Contents note: No. 1 Alexandrian by Birth -- No. 2 Music and Mathematics -- No. 3 Gather Around Me -- No. 4 Swept Out by the Seventh Wave -- No. 5 More than Our Winning -- No. 6 Where Three Dances with Seven -- No. 7 Let’s Consummate Our Affair -- No. 8 My Subject is a String -- No. 9 All Multiplied by Three -- No. 10 Praise the Golden Mean -- No. 11 Nothing Purer than a Prime -- No. 12 Union of Zero and One.

Commission note: Commissioned by Tom Petsinis with funds provided by Arts Victoria.

Winner of the 2013 Boston Metro Opera ‘Mainstage Award’ (Boston, MA, USA).