Novel Synthesis Method VII · 2026 · Kuramoto Network

Coupled Micro-Oscillator
Network Synthesis

N phase oscillators, each with a slightly different natural frequency, coupled through a network. At critical coupling Kc a textured static tone crystallises from collective synchronisation — the texture is intrinsic to the equilibrium, not modulation.

INCOHERENT
ONSET
CRITICAL Kc
PARTIAL
LOCKED
0.000
Order r
0°
Mean phase ψ
2.00
Coupling K
—
Est. Kc
0
Locked osc.
128
N oscillators
Network · hue = phase · bright = locked · gold arrow = order parameter r
Waveform · Σᵢ cos(φᵢ) / N
Spectral density
Order parameter r(t)
Oscillator Parameters
Network Topology
Presets
Kuramoto Parameters
Micro-Oscillator Waveform
Audio Output
Mode
Sound Shaping
Sub-Oscillator · Micro-Beating
Reverb
Delay
Kuramoto Model · Coupled Phase Oscillators
dφᵢ/dt = ωᵢ + (K/N)·Σⱼ sin(φⱼ − φᵢ) + ηᵢ(t)
r·e^{iψ} = (1/N)·Σⱼ e^{iφⱼ} — order parameter r∈[0,1]
Kc ≈ 2·(Δω+η) — critical coupling · below: noise · above: tone
audio = (1/N)·Σᵢ cos(φᵢ) — real part of order parameter