Filters: carving the recipe

A filter removes harmonics you already have. Cutoff chooses where the cut starts; resonance and slope decide what its edge sounds like.

Lesson 2 left you with a stack of harmonics. A filter turns part of that stack down and leaves the rest where it was. It has no way to add anything: run a sine through a filter and almost nothing happens, because there is only the fundamental to touch. Give it a sawtooth at 110 Hz instead — fundamental at 110 Hz, harmonics at 220, 330, 440 Hz and on upward — and the filter has around 180 partials inside the audible range to work on. Cut at 800 Hz and seven of them survive; the woody tone left behind was sitting inside the raw wave the whole time. The classic method is named after the move: subtractive synthesis starts bright and removes until a character appears.

Three directions of the cut

• Low-pass (LP) — passes everything below the cutoff and removes what sits above. The most used filter in electronic music. On that 110 Hz saw, a cutoff at 5 kHz is barely audible, 1 kHz rounds the sound off, and 300 Hz leaves only the first two harmonics.
• High-pass (HP) — removes everything below the cutoff. At 40–100 Hz it clears rumble and leaves the note alone, its everyday job on every part that is not the bass. At 800 Hz on a 110 Hz bass it deletes the fundamental; the ear rebuilds a thin version of the pitch from the surviving harmonics and the part turns papery.
• Band-pass (BP) — keeps a band around the cutoff and removes both sides. Set near 1.5 kHz it lands close to what a telephone line does to a voice; sweeping one with resonance up is how the radio-tuning effect is made.

Cutoff and resonance

Cutoff is the frequency where the filter starts working, in Hz, on the same axis as the harmonics from lesson 2. Four points cover most of what the knob does to a low-pass. At 8 kHz almost nothing changes. At 2 kHz the sound loses its edge. At 500 Hz it is clearly muffled. Below 150 Hz little survives but the fundamental. Like pitch, cutoff sits on a logarithmic scale, so equal travel changes the tone by equal amounts anywhere in the range.

Resonance feeds a little of the filter output back into its input, which lifts a narrow peak at the cutoff and steepens the fall just above it. The toy shows resonance as a bare number, the filter's Q, and the peak follows it directly: 0.7 is flat through the passband and 3 dB down at the cutoff, 2 gives a 6 dB peak, 6 gives 15 dB and a definite pitch at the cutoff, 18 gives 25 dB and a filter close to ringing on its own.

Push a well-modeled filter past that last point and it self-oscillates: the feedback loop sustains a sine at the cutoff frequency with nothing fed in, which is why a resonant filter can be played as an oscillator. High resonance also costs low end, because the feedback path drains energy below the peak. On bass, resonance past about half travel usually needs the level pushed back up.

Slope: how fast the cut arrives

Cutoff sets where the fall begins. Slope sets how steep it is, measured in dB per octave. A 2-pole filter falls 12 dB for every doubling of frequency: with the cutoff at 1 kHz, 2 kHz comes out 12 dB down and 4 kHz 24 dB down. A 4-pole filter falls 24 dB per octave, so the same 2 kHz is already 24 dB down and 4 kHz is 48 dB down, which is quiet enough to count as gone.

The two do different jobs. A 12 dB slope leaves material alive above the cutoff, so sweeps feel gradual and the sound keeps its air; it is the usual choice for high-pass duty and gentle tone shaping. A 24 dB slope removes the top decisively and is what most people picture when they hear the phrase “synth filter”. One famous design sits between them: the TB-303 rolls off at 18 dB per octave, and a fair share of the acid sound comes from that middle ground.