ONE sample through the BIASED knee — omx_drive_sample, exactly (§4b as amended 2026-09-15).
y = (f(u + b) − f(b)) / (1 + f(b)), b = w · DRIVE_BIAS_MAX.
BOUNDED BY CONSTRUCTION. Every knee has ceiling 1, so f(u + b) − f(b) lies inside
[−1 − f(b), 1 − f(b)], whose widest magnitude is 1 + f(b) — which is the divisor. |y| < 1
for every u, every w and every curve. The superseded residue blend
(u + (1−w)(f(u)−u) + w(|f(u)|−|u|)) had slope −2 and no floor on the negative half at w > 0;
a full-scale sample at 36 dB of drive computed to ≈ −125.
At w = 0 this IS the bare knee: b = 0, f(0) = 0, y = f(u). The pure-odd end is
unchanged from the shipped stage. At w = 1 it is EVEN-DOMINANT, not pure even — H2 leads H3
by 8.5 dB at 12 dB of drive and 26.2 dB at 6 dB, and past ~15 dB the clipping's odd harmonics
take over (§4b writes the crossover down). The knob's effect is on BOTH halves: the upper one
compresses toward (1 − f(b))/(1 + f(b)) and the lower expands toward −1, which is why the
picture's domain is bipolar (amendment §10).
ONE sample through the BIASED knee —
omx_drive_sample, exactly (§4b as amended 2026-09-15).y = (f(u + b) − f(b)) / (1 + f(b)),b = w · DRIVE_BIAS_MAX.BOUNDED BY CONSTRUCTION. Every knee has ceiling 1, so
f(u + b) − f(b)lies inside[−1 − f(b), 1 − f(b)], whose widest magnitude is1 + f(b)— which is the divisor.|y| < 1for everyu, everywand every curve. The superseded residue blend (u + (1−w)(f(u)−u) + w(|f(u)|−|u|)) had slope −2 and no floor on the negative half atw > 0; a full-scale sample at 36 dB of drive computed to ≈ −125.At
w = 0this IS the bare knee:b = 0,f(0) = 0,y = f(u). The pure-odd end is unchanged from the shipped stage. Atw = 1it is EVEN-DOMINANT, not pure even — H2 leads H3 by 8.5 dB at 12 dB of drive and 26.2 dB at 6 dB, and past ~15 dB the clipping's odd harmonics take over (§4b writes the crossover down). The knob's effect is on BOTH halves: the upper one compresses toward(1 − f(b))/(1 + f(b))and the lower expands toward −1, which is why the picture's domain is bipolar (amendment §10).