Filter stage character: the four nonlinear stages the instruments are known by, and what the tree has instead #136

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opened 2026-10-06 00:13:39 +00:00 by bcox · 0 comments

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2026-10-06 00:13:39 +00:00

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bcox asked on 2026-10-05 for one ticket covering the filter-stage characters that moregaps.md names and that no row of its feature table can hold. Engine claims are from reading the tree at f6aa8eba on main. Instrument claims are from that document's research, read from manuals, datasheets, Electric Druid, Stinchcombe's MS-20 study and the DAFx 2022 Wasp paper by research agents and not re-checked; the sources are listed there. Nothing here is built, measured or listened to.

What the tree has

The ladder: saturation between stages, LadderSaturate(input - LadderSaturate(k * previous_y4)), then a linear one-pole (dsp/ladder.h:296, :546); the feedback is one tick late at 4x, and a zero-delay solve is ruled out on fabric cost (:6-12).
The SVF: linear, rounding toward zero so a decaying state reaches zero; resonance deliberately short of self-oscillation (dsp/va_filter.h:23-27).
The driven SVF: the same SVF with a saturating drive at its input only (dsp/va_filter.h:90-96).
The low-pass gate and the ladder gate.

So every nonlinearity sits between stages or at the input. None sits inside an integrator, in a feedback diode, or in the amplifier of a Sallen-Key.

The four characters

CEM3320 (Prophet-5 Rev 3, Pro-One, OB-Xa, Synthex, SH-101's relative IR3109 is a different chip). Saturation sits inside each integrator, on input minus output, so a loud signal slew-limits the stage; the overdrive dulls where the ladder clips. Resonance feedback is instantaneous. The moregaps.md Curtis section's "To get it": a new topology over the same loop, taps and pole mixing, with the one-pole made implicit so it reads the previous state as the feedback path does. The instantaneous feedback stays out, by the zero-delay ruling.
Korg35 and its successor (MS-20). A 6 dB highpass into a 12 dB lowpass, each with a peak control and diodes limiting the feedback; the early version a Sallen-Key, the later one two cascaded first-order OTA sections; both self-oscillate. Stinchcombe's study is the thing to test against. Two ladder slots in series reach the structure, but each is the four-stage loop read at an earlier tap, not a two-pole with a clipped feedback path.
The GX-1's potted modules (and, by Vintage Synth Explorer, the SY-1's). A diode-ring Sallen-Key that distorts at high resonance and does not self-oscillate, by Old Crow's teardown and the Gearspace restoration thread; slope 12 dB per octave by three sources and 9 by one. No slot here is a Sallen-Key; the driven SVF is the nearest.
The Wasp (and Gnat). A 12 dB state-variable filter built from CA3080 transconductance amplifiers and CD4069 inverters run as amplifiers: distortion rising gradually with level, more resonance adding nonlinear feedback through diodes, full Q on the verge of oscillation. Köper, Holters, Esqueda and Parker's DAFx 2022 paper is a virtual-analog model with measurements.

Two more the research touched and did not characterize: the SSM2044 (Mono/Poly, Polysix) and the diode ladder (the SH-5's lowpass, "a ladder type network of diode chain transistors", and the TB-303's; patches/tb303_line.h is built on the transistor ladder).

The work, as a sketch

One new topology at a time, each a value of the filter slot's topology enum beside kSvfDriven, so a patch chooses it and the oversample derivation prices it from the topology field alone, as it does today.
Start where there is a model to test against: the Wasp (a paper with measurements) or the MS-20 (a study with schematics). The 3320 needs a bench measurement of a modern AS3320, which Electric Druid cites as available.
Each is a fixed-point question first: the saturation inside an integrator is a nonlinearity inside the recursion, which forces oversampling as the ladder's does, and the rounding mode has to keep the loop a contraction.

Open

Whether the SVF's "no self-oscillation" ruling extends to new two-pole topologies, or whether the MS-20's clipped feedback is the case that earns one, since its self-oscillation is bounded by the diodes rather than by resonance.

bcox asked on 2026-10-05 for one ticket covering the filter-stage characters that `moregaps.md` names and that no row of its feature table can hold. Engine claims are from reading the tree at `f6aa8eba` on `main`. Instrument claims are from that document's research, read from manuals, datasheets, Electric Druid, Stinchcombe's MS-20 study and the DAFx 2022 Wasp paper by research agents and not re-checked; the sources are listed there. **Nothing here is built, measured or listened to.** ## What the tree has - The ladder: saturation between stages, `LadderSaturate(input - LadderSaturate(k * previous_y4))`, then a linear one-pole (`dsp/ladder.h:296`, `:546`); the feedback is one tick late at 4x, and a zero-delay solve is ruled out on fabric cost (`:6-12`). - The SVF: linear, rounding toward zero so a decaying state reaches zero; resonance deliberately short of self-oscillation (`dsp/va_filter.h:23-27`). - The driven SVF: the same SVF with a saturating drive at its input only (`dsp/va_filter.h:90-96`). - The low-pass gate and the ladder gate. So every nonlinearity sits between stages or at the input. None sits inside an integrator, in a feedback diode, or in the amplifier of a Sallen-Key. ## The four characters 1. **CEM3320** (Prophet-5 Rev 3, Pro-One, OB-Xa, Synthex, SH-101's relative IR3109 is a different chip). Saturation sits inside each integrator, on input minus output, so a loud signal slew-limits the stage; the overdrive dulls where the ladder clips. Resonance feedback is instantaneous. The `moregaps.md` Curtis section's "To get it": a new topology over the same loop, taps and pole mixing, with the one-pole made implicit so it reads the previous state as the feedback path does. The instantaneous feedback stays out, by the zero-delay ruling. 2. **Korg35 and its successor** (MS-20). A 6 dB highpass into a 12 dB lowpass, each with a peak control and diodes limiting the feedback; the early version a Sallen-Key, the later one two cascaded first-order OTA sections; both self-oscillate. Stinchcombe's study is the thing to test against. Two ladder slots in series reach the structure, but each is the four-stage loop read at an earlier tap, not a two-pole with a clipped feedback path. 3. **The GX-1's potted modules** (and, by Vintage Synth Explorer, the SY-1's). A diode-ring Sallen-Key that distorts at high resonance and does not self-oscillate, by Old Crow's teardown and the Gearspace restoration thread; slope 12 dB per octave by three sources and 9 by one. No slot here is a Sallen-Key; the driven SVF is the nearest. 4. **The Wasp** (and Gnat). A 12 dB state-variable filter built from CA3080 transconductance amplifiers and CD4069 inverters run as amplifiers: distortion rising gradually with level, more resonance adding nonlinear feedback through diodes, full Q on the verge of oscillation. Köper, Holters, Esqueda and Parker's DAFx 2022 paper is a virtual-analog model with measurements. Two more the research touched and did not characterize: the SSM2044 (Mono/Poly, Polysix) and the diode ladder (the SH-5's lowpass, "a ladder type network of diode chain transistors", and the TB-303's; `patches/tb303_line.h` is built on the transistor ladder). ## The work, as a sketch - One new topology at a time, each a value of the filter slot's topology enum beside `kSvfDriven`, so a patch chooses it and the oversample derivation prices it from the topology field alone, as it does today. - Start where there is a model to test against: the Wasp (a paper with measurements) or the MS-20 (a study with schematics). The 3320 needs a bench measurement of a modern AS3320, which Electric Druid cites as available. - Each is a fixed-point question first: the saturation inside an integrator is a nonlinearity inside the recursion, which forces oversampling as the ladder's does, and the rounding mode has to keep the loop a contraction. ## Open - Whether the SVF's "no self-oscillation" ruling extends to new two-pole topologies, or whether the MS-20's clipped feedback is the case that earns one, since its self-oscillation is bounded by the diodes rather than by resonance.