Figure 3: FFT Spectral Analysis of K Residuals (Standing Wave Frequency)
Frequency (cycles per window doubling)
Spectral Power (arbitrary units)
0.0
0.25
0.5
0.75
1.0
1.25
1.5
0.0
0.2
0.4
0.6
0.8
1.0
f₀ = 0.6667 cycles/window
(Period = 1.5 doublings)
f = 1.0
(performance wave)
3:2 frequency ratio
(perfect fifth in musical terms)
Dominant frequency (f₀ = 0.6667, p < 0.0001)
Secondary harmonic (performance oscillation, f = 1.0)
Noise floor
Statistical Significance
f₀ = 0.6667 ± 0.02 cycles/window
p-value < 0.0001
R² = 0.994 (FFT model fit)