Paul Purgas

Discovered by Godfried Toussaint, a researcher at Harvard in 2004, the Euclidean Rhythm was deciphered using a skillset developed from a background in computational geometrics and discrete mathematics. The algorithm, which first appears in Euclid’s Elements around 300 BC, is a fundamental tool for identifying the greatest common divisor of two whole numbers. Through his research, Toussaint found that when this algorithm was applied to computer-based distribution patterns of musical notes, it formed the structural foundation for most known world music systems, through a mathematical spreading of beats and silence. His discovery was a landmark turning point in considering the relationship between musical time and computing, unlocking a hermetic system and extrapolating it into a calculable formula. In effect, Toussaint’s skeleton key opened up a new approach to the representation and communication of time into an event-based structure, a vision of repeating iterations in a constantly returning pattern. A staccato of beats and rests, compression and rarefaction, and a diagram of pure on/off binary data.

— Extract from Divide & Fracture by Paul Purgas commissioned for REPETITIONER #4 by Hannah Sawtell/Foundling Court 2013

MFile 0 1 96
MTrk
0 Meta SeqName "\0"
0 TimeSig 4/4 36 8
0 TimeSig 4/4 36 8
0 On ch=1 n=62 v=100
1 Off ch=1 n=62 v=64
1 On ch=1 n=62 v=100
3 Off ch=1 n=62 v=64
3 On ch=1 n=62 v=100
4 Off ch=1 n=62 v=64
4 On ch=1 n=62 v=100
6 Off ch=1 n=62 v=64
6 On ch=1 n=62 v=100
7 Off ch=1 n=62 v=64
7 On ch=1 n=62 v=100
9 Off ch=1 n=62 v=64
9 On ch=1 n=62 v=100
10 Off ch=1 n=62 v=64
10 On ch=1 n=62 v=100
12 Off ch=1 n=62 v=64
12 On ch=1 n=62 v=100
13 Off ch=1 n=62 v=64
13 On ch=1 n=62 v=100
15 Off ch=1 n=62 v=64
15 On ch=1 n=62 v=100
16 Off ch=1 n=62 v=64
16 On ch=1 n=62 v=100
18 Off ch=1 n=62 v=64
18 On ch=1 n=62 v=100
19 Off ch=1 n=62 v=64
19 On ch=1 n=62 v=100
21 Off ch=1 n=62 v=64
21 On ch=1 n=62 v=100
22 Off ch=1 n=62 v=64
22 On ch=1 n=62 v=100
24 Off ch=1 n=62 v=64
24 On ch=1 n=62 v=100
25 Off ch=1 n=62 v=64
25 On ch=1 n=62 v=100
27 Off ch=1 n=62 v=64
27 On ch=1 n=62 v=100
28 Off ch=1 n=62 v=64
28 On ch=1 n=62 v=100
30 Off ch=1 n=62 v=64
30 On ch=1 n=62 v=100
31 Off ch=1 n=62 v=64
31 On ch=1 n=62 v=100
33 Off ch=1 n=62 v=64
33 On ch=1 n=62 v=100
34 Off ch=1 n=62 v=64
34 On ch=1 n=62 v=100
36 Off ch=1 n=62 v=64
36 On ch=1 n=62 v=100
37 Off ch=1 n=62 v=64
37 On ch=1 n=62 v=100
39 Off ch=1 n=62 v=64
39 On ch=1 n=62 v=100
40 Off ch=1 n=62 v=64
40 On ch=1 n=62 v=100
42 Off ch=1 n=62 v=64
42 On ch=1 n=62 v=100
43 Off ch=1 n=62 v=64
43 On ch=1 n=62 v=100
45 Off ch=1 n=62 v=64
45 On ch=1 n=62 v=100
46 Off ch=1 n=62 v=64
46 On ch=1 n=62 v=100
48 Off ch=1 n=62 v=64
48 On ch=1 n=62 v=100
49 Off ch=1 n=62 v=64
49 On ch=1 n=62 v=100
51 Off ch=1 n=62 v=64
51 On ch=1 n=62 v=100
52 Off ch=1 n=62 v=64
52 On ch=1 n=62 v=100
54 Off ch=1 n=62 v=64
54 On ch=1 n=62 v=100
55 Off ch=1 n=62 v=64
55 On ch=1 n=62 v=100
57 Off ch=1 n=62 v=64
57 On ch=1 n=62 v=100
58 Off ch=1 n=62 v=64
58 On ch=1 n=62 v=100
60 Off ch=1 n=62 v=64
60 On ch=1 n=62 v=100
61 Off ch=1 n=62 v=64
61 On ch=1 n=62 v=100
63 Off ch=1 n=62 v=64
63 On ch=1 n=62 v=100
64 Off ch=1 n=62 v=64
64 On ch=1 n=62 v=100
66 Off ch=1 n=62 v=64
66 On ch=1 n=62 v=100
67 Off ch=1 n=62 v=64
67 On ch=1 n=62 v=100
69 Off ch=1 n=62 v=64
69 Meta TrkEnd
TrkEnd

—Euclidean sequence test pattern – MIDI text format

Paul Purgas trained as an architect and graduated from the Royal College of Art. He has presented performances and installations with Spike Island, Tate Britain, Bergen Konsthall, the Whitechapel gallery and Whitstable Biennale, and written work has been presented at Focal Point Gallery, Banner Repeater and Transmediale. He is a 2015 participant in Wysing Arts Centre’s Multiverse residency programme.