harmonic_shaper

NODE

Adds the 2nd to 5th harmonics in proportions you set, rather than whatever a saturation curve happens to produce.

Parameters

FIELD	WHAT IT DECIDES	RANGE	REQUIRED
h2_pct	2nd harmonic percentage [%].	0 〜 20	no
h3_pct	3rd harmonic percentage [%].	0 〜 20	no
h4_pct	4th harmonic percentage [%].	0 〜 20	no
h5_pct	5th harmonic percentage [%].	0 〜 20	no

{
  "h2_pct": 1.5,
  "h3_pct": 0.3,
  "type": "harmonic_shaper"
}

How it is computed

u = x / A_ref                    A_ref is the reference amplitude (-20 dBFS RMS)

T̂2(u) = 2u²                      a sine gives 1 - cos(2ωt): 2nd harmonic and DC
T̂3(u) = 4u³ - 3u                 gives -sin(3ωt)
T̂4(u) = 8u⁴ - 8u²                gives -1 + cos(4ωt): 4th harmonic and DC
T̂5(u) = 16u⁵ - 20u³ + 5u         gives sin(5ωt)

u is clamped to ±2 so the polynomials cannot run away on a large input.
At the reference level the clamp never engages and the percentages hold exactly.

Chebyshev polynomials corrected so that they pass through the origin: at silence the node emits neither offset nor DC, and at the reference level each order appears at exactly the percentage you asked for.

Using it

Even orders need a DC blocker after them.
The 2nd and the 4th produce a DC component as a property of the polynomial. If either percentage is above zero, put a dc_blocker downstream.
The percentages are defined at the reference level.
They are exact for a signal at -20 dBFS RMS. Quieter or louder material sits at a different point on the polynomial, so the ratios move, which is also true of every real circuit.
It is deterministic, unlike a saturator.
A waveshaper gives you whatever spectrum its curve produces. This node lets you ask for a spectrum directly, which is the difference between colouring by ear and colouring by specification.