DIRECTORY / SANDBOXES / EUCLIDEAN.RHYTHMS

EUCLIDEAN POLYRHYTHM WHEEL

Ancient Euclidean algorithm E(k, n) distributing hit pulses evenly across polyrhythmic rings.

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// PRESET WORLD POLYRHYTHMS

🔴 KICK

Hits: 4 Steps: 16

🔵 SNARE

Hits: 3 Steps: 8

🟡 HIHAT

Hits: 7 Steps: 16

🟢 BASS

Hits: 5 Steps: 12

TEMPO (BPM) 128

VOLUME 50%

💡 TIP: Adjust hits and step counts on concentric rings to generate E(k, n) algorithms.

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RESEARCH & LEARNING VAULT // Bjorklund's Euclidean Polyrhythms

Nuclear physics timing algorithms generating world traditional musical rhythms.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

E. Bjorklund developed the algorithm in 2003 for neutron spallation timing at nuclear reactors. Godfried Toussaint discovered in 2005 that it generated almost all traditional world rhythms.

// GOVERNING EQUATIONS

E(k, n) = \text{Bjorklund}(k \text{ pulses}, n \text{ steps})

// BROWSER IMPLEMENTATION

Evenly distributes `k` pulses over `n` time slots using repeated Euclidean remainder division.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOXNORMAL

1Cuban Tresillo vs Bossa Nova

🎯 Action:Set KICK to E(3, 8) (3 Hits / 8 Steps) and SNARE to E(5, 16).

✨ Observe:Hear the polyrhythmic syncopation of Afro-Cuban and Brazilian samba grooves.

// CURATED PAPERS, RFCS & RESOURCES

The Euclidean Algorithm Generates Traditional Musical Rhythmspaper

By Godfried Toussaint (McGill University, 2005)

The seminal ethnomusicological paper connecting Euclid's algorithm to world music.

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EUCLIDEAN POLYRHYTHM WHEEL

RESEARCH & LEARNING VAULT // Bjorklund's Euclidean Polyrhythms