The curves, as functions

Every band is a stated function of frequency, so anyone with a sweep can reproduce the numbers on the product page. Write s = j·f/f0 for a frequency f against the band’s frequency f0, G = 10^(gain/20) for the band’s gain, and A = √G. The curve a band draws is the magnitude of H(s) below. Each mode holds it within the bound in the specifications, measured through a real DAW at each sample rate against these same forms. Exact Curve holds the phase of H(s) as well; Zero Latency holds the magnitude alone, because a zero-delay filter cannot carry the analog phase at the top of the band; Linear Phase holds the magnitude with no phase shift, or a band’s own analog timing when its Phase is Natural. This page is checked against the reference the release tests use, so it cannot drift from what is measured.

• Bell: H = (1 + s·A/Q + s²) / (1 + s/(A·Q) + s²). Unity at the ends, exactly gain at f0; Q is f0 over the bandwidth between the two frequencies where the band has half its gain in decibels, for a boost or a cut alike, not the −3 dB points.
• Low Shelf: H = A · (A + s·√A/Q + s²) / (1 + s·√A/Q + A·s²). The full gain at the bottom, unity at the top, and exactly half the gain at f0 at every Q; Q = 0.707 is the plain slope, higher values put a resonance at the corner.
• High Shelf: the same shelf mirrored, H = A · (1 + s·√A/Q + A·s²) / (A + s·√A/Q + s²). Unity at the bottom, the full gain at the top, half at f0.
• Tilt Shelf: the high shelf spanning the full gain from bottom to top, scaled by 1/A so it passes exactly through 0 dB at f0: −gain/2 at the bottom, +gain/2 at the top.
• Notch: H = (1 + s²) / (1 + s/Q + s²). Unity at the ends, infinite rejection at f0.
• Band Pass: H = (s/Q) / (1 + s/Q + s²). Unity at f0, falling either side.
• Low Cut and High Cut: a Butterworth cascade of the slope’s order N (6 dB per octave per order). Each pair of poles has its textbook Q_k = 1 / (2·sin((2k+1)·π/(2N))), an odd order adds one first-order section, and the band’s own Q scales only the most resonant pair against 0.707, so Q = 0.707 is the flat Butterworth curve at every slope and a higher Q puts a peak at the corner. A high cut’s magnitude squared is the product over its sections of 1 / ((1 − x²)² + (x/Q_k)²) with x = f/f0, a low cut’s of x⁴ / ((1 − x²)² + (x/Q_k)²), and the first-order section is 1/(1 + x²) or x²/(1 + x²). The corner sits at −3.01 dB at every order.

Gain-Q Interaction, when on, replaces Q with Q · √(10^((|gain| − 12)/20)), clamped to the Q range, before the band is built. Gain Scale multiplies every band’s gain and range first.