Poincaré’s Box

Poincaré’s Box is an automated electro-mechanical instrument built by Matthew Hoare, a Sydney-based instrument builder and DJ. Hoare developed Poincaré’s Box as an exploration of Henri Poincaré’s recurrence theorem. Producing cyclical patterns of notes across sets of metal plectra, the combinations of musical patterns intertwine over the course of three days before returning to their initial starting point.

Hoare designed Poincaré’s Box as an automated electro-mechanical instrument, the musical program of which is determined by an electronic circuit largely comprised of solid-state logic microchips. It is named after Henri Poincaré, a late 19th century French physicist. In 1890 Poincaré showed with his recurrence theorem that, given vast lengths of time, the exact relationships between atoms, contained within a system with fixed total energy, will eventually repeat. His theorem showed that there is an opposing force to entropy in the universe, a constructive force. The implication of the theorem is that on a cosmic scale, across vast lengths of time, and only if the entire system were self-contained, events would also repeat. Such an idea is closely related to Nietzsche’s concept of eternal return.

The construction of Poincaré’s Box consists of a wooden resonator almost one metre long, 50 centimetres wide, and 10 centimetres tall, and is raised on columns above a wooden base. Embedded within the base is an electronic circuit board. On top of the resonator sit 36 steel tongues (or plectra). The steel tongues are plucked by electromagnetic solenoids inside the box, positioned just underneath each of the metal tongues. The solenoids receive small electrical currents to generate a small electromagnetic force which then attract and repel the steel tongues. While the attraction/repel process to pluck the metal tongues results in a strong acoustic sound, the movement of the tongues is imperceptible to the eye. The metal tongues are grouped as 9 sets of four tongues. Each set is tuned to a chord using notes of the 11th-limit just intonation tuning.

Each plectra set, or chord, is slowly arpeggiated within its own tempo. Tempos range from 80mm, around walking pace, to extremely slow, about one chord note every 22 seconds. Six of the plectra sets sound-out their chords in straight arpeggios. The remaining three plectra sets consist of a more involved pattern.

As Hoare points out ‘[Poincaré’s Box] is essentially a study on cyclical musical patterns. The smallest patterns, beyond the individual notes, are the arpeggiating chords. In a slightly larger time frame there are hundreds of repeating patterns involving combinations of notes from the various groups.’ The timescale for these many combinations varies wildly. The most repetitive pattern combinations complete one cycle within a minute, while other combinations can last for hours. The largest pattern is the combination of all of the patterns of individual groups, and is not repeated for three days.

Images: clatterbox

Audio of Poincaré’s Box will reappear here soon…