Euler Lattice Spirals Scenery (2011)

Marc Sabat


  • 1. Preludio: Les Quintes Justes
  • 2. Pythagoras Drawing (I)
  • 3. Harmonium for Claude Vivier
  • 4. Harmonium for Ben Johnston
  • 5. Pythagoras Drawing (II)

Notes de programme

[traduction française non disponible]

Euler Lattice Spirals Scenery was composed in Rome during a one-year residency at the Villa Massimo, and premiered by the Sonar Quartett on 20 October 2011. It is the third work in a continuing cycle of string quartets where musical forms follow from explicitly notating intonations. I am interested in how experiences perceived in musical listening emerge directly from the materiality of sound and its inner structure based on time.

The title refers to Leonhard Euler’s two-dimensional model of triadic harmonic space. A portion of his lattice, comprising 99 distinct pitch-classes organised as a progression of major and minor triads in Just Intonation, forms the basis of the quartet’s penultimate section, Harmonium for Ben Johnston. From the central pitch of our notation system, D, the chords spiral outward, each occurring only once, ordered so that all possible common-tone progressions between triad pairs are sounded. In the middle of the movement, a small enharmonic seam allows a retrograde inversion of the sequence to return back to D.

Recurring mottos construct microtonal pitches directly from natural harmonics and open strings, which are precisely tuned in untempered 3:2 frequency ratios. Setting this tonal scaffolding is a theme of the quartet’s other movements. The opening Preludio is a written-out tuning sequence, testing comma distinctions and partial unisons between the instruments’ 16 open strings. This is followed by Pythagoras Drawing based on fifths, fourths, seconds and their octave transpositions, and the Harmonium for Claude Vivier, in which all the natural harmonics up to 9 sing a sustained ecstatic melody.

The five parts are played attacca.