TurboBass Acid Synth

Overview

TurboBass is an acid bass synthesizer with a 4-pole diode ladder filter running as an AudioWorklet. All DSP parameters are mathematically derived from circuit analysis, not arbitrary values.

Signal Chain

Main Oscillator (saw / variable-pulse) ──┐
Sub Oscillator (sine, -1 octave) ────────┤→ Pre-Filter HP (44 Hz)
Drift LFO → Main Osc frequency          │   → Drive (tanh saturation)
                                         │   → Diode Ladder Filter (4-pole AudioWorklet)
                                         │       ↑ Filter LFO (BPM-synced)
                                         │       ↑ Filter Envelope (bipolar)
                                         └→ VCA (2 ms attack)
                                              → Dry + Distortion (Rat asymmetric)
                                              → Delay (BPM-synced, HP feedback)
                                              → Bus (reverb, chorus, auto-pan, limiter)

Diode Ladder Filter

Implemented as an AudioWorklet (diode-ladder-processor.js) with 2× internal oversampling.

Mathematical Constants

Constant	Value	Derivation
VT	0.4	Thermal voltage. Geometric mean of 4 pole input levels: (0.7 · 0.49 · 0.34 · 0.24)^0.25 ≈ 0.41
K_MAX	3.07	Barkhausen: k_crit = 1/(0.894 × 0.707³) = 3.16, then × 0.97 for stability
Pole 1 scale	0.5	Half capacitance (303 mismatch — "broken 24 dB" slope)
Poles 2–4 scale	1.0	Matched capacitance

Derived Coefficients

Coefficient	Formula	Purpose
g	tan(π × fc / (2 × sampleRate))	TPT integrator gain (exact bilinear transform)
k	res² × K_MAX	Quadratic resonance curve for musical control
compGain	√(1 + k)	Resonance volume compensation

Per-Pole Transfer

s[i] += g × poleScale × (tanh(input/VT) - tanh(s[i]/VT))

Feedback from last pole: u = input - k × tanh(s[3]/VT)

tanh Approximation

Padé 3/3: x × (27 + x²) / (27 + 9x²), hard-clipped at ±3. Max error < 0.004.

Fallback

If the AudioWorklet fails to load, a BiquadFilter (2-pole lowpass) is used as fallback. Resonance maps to Q = 1 + value × 25.

Synth Parameters

Parameter Reference

ID	Default	Formula	Range
cutoff	0.5	20 × 900^x	20 Hz – 18 kHz
resonance	0.5	res² × 3.07 (in worklet)	0 – 1
envMod	0.5	cutoff × 2^(envMod × 7)	0 – 7 octaves sweep
decay	0.5	0.02 × 100^x	20 ms – 2 s
accent	0.5	VCA boost: 1 + accent × 0.8	0 – 1
tuning	0.5	(tuning - 0.5) × 24 semitones	±12 semitones
waveform	0	0 = sawtooth, > 0.5 = variable pulse	0 or 1
drive	0	tanh(k×x)/tanh(k), k = 1 + drive × 8	0 – 1
subLevel	0.3	Sub oscillator mix gain	0 – 1
drift	0.3	Drift LFO depth: drift × 2.5 Hz	0 – 1
gateLength	0.75	Gate fraction: 0.1 + x × 0.9	10% – 100%
slideTime	0.15	RC time constant: 0.005 × 60^x	5 ms – 300 ms
filterTracking	0	cutoff × 2^((midi-60) × tracking/12)	0 – 1 (off to 1:1)

Cutoff

Exponential mapping following Weber-Fechner law. Each 0.1 knob increment ≈ 1 octave.

f(x) = 20 × 900^x

x=0 → 20 Hz, x=0.5 → 600 Hz, x=1 → 18 kHz.

Decay

Exponential mapping giving fine control in the acid range (short decays).

f(x) = 0.02 × 100^x

x=0 → 20 ms, x=0.3 → 170 ms, x=0.5 → 632 ms, x=1 → 2 s.

Filter Envelope

Bipolar three-phase envelope:

1. Spike: Instant jump to envPeak = cutoff × 2^(envMod × 7 × accentBoost)
2. Decay: Exponential ramp down to undershoot = cutoff × 0.85 (15% below steady-state)
3. Recovery: setTargetAtTime back to cutoff, τ = decaySec × 0.6

The undershoot creates the characteristic pump/breathing effect.

Accent Behavior

Three independent interactions:

Interaction	Formula	Effect
Filter depth	√(1 + resonance × 3)	More resonance → deeper envelope sweep
Decay snap	0.02 + baseDec × 0.1	Forces ~20 ms decay regardless of knob
VCA boost	1 + accent × 0.8	Independent amplitude increase
Resonance boost	+0.2 absolute, decays back in decaySec × 0.4	Momentary squelch

Oscillator

Sawtooth (Default)

Standard OscillatorNode sawtooth. Sub-oscillator (sine, -1 octave) mixed via subLevel gain.

Variable Duty-Cycle Pulse

When waveform > 0.5, a PeriodicWave is generated from Fourier series with pitch-dependent duty cycle:

• Low notes (55 Hz): 71% duty (fat)
• High notes (880 Hz): 45% duty (thin)
• Recomputed when octave changes (saves CPU)

Analog Drift

Sine LFO at 0.08–0.13 Hz (random per instance), modulating oscillator frequency. Depth: drift × 2.5 Hz.

Sequencer

Step Format

Each step has 7 properties:

Property	Type	Description
note	number	MIDI note (36–72 typical)
gate	boolean	Note on/off
accent	boolean	Accent flag
slide	boolean	Glide to next note
tie	boolean	Legato — gate stays open, no envelope re-trigger
up	boolean	Octave up (+12 semitones)
down	boolean	Octave down (-12 semitones)

TIE Behavior

When a step has tie=true, the previous note's gate stays open — no noteOff, no new noteOn. If slide is also active, pitch glides without re-triggering the envelope.

Gate Length

Note-off time: stepDur × (0.1 + gateLength × 0.9). Default 0.75 → ~80% of step.

Swing

Odd steps are delayed by swing × stepDur × 0.5. Range: 0 to 0.5.

Scheduling

25 ms JavaScript timer with 50 ms AudioContext look-ahead. Step duration = 60 / BPM / 4.

Pattern System

Banks

4 banks × 8 patterns = 32 factory patterns.

Bank	Style	Patterns
A	Classic Acid House	Acid Trax, Hardfloor, Wild Pitch, Pierre, Pump It Up, Sleazy, Da Funk, Mentasm
B	Techno / Industrial	Surgeon, Berghain, Regis, Monolith, EBM Grind, Warehouse, Ostgut, Schranz
C	Minimal / Deep	Plastikman, Hypnotic, Deep Space, Microglide, R. Hood, Dub Chord, Looping, Pulse
D	Experimental	Poly 7, Stutter, Chromatic, Random Feel, Octave Jump, Trance Gate, Acid Rain, Machine

Randomize

Scale-aware pattern generator. Default: minor pentatonic, root C2, density 70%.

• Accent: 35% on off-beats, 15% on beats
• Slide: 15% (only if previous step gated)
• Tie: 10% (only if previous gated, no accent, no slide)
• Octave up: 10%, down: 8%

Available scales: chromatic, minor, phrygian, minor pentatonic, blues, dorian.

Mutate

Progressive random edits. At amount=1, applies ~7 mutations:

• 35%: note shift ±1–5 semitones
• 20%: toggle gate
• 15%: toggle accent
• 15%: toggle slide
• 15%: toggle octave

Ghost Sequence

After 5 minutes of inactivity, auto-generates a new pattern. Uses the current pattern's root note (most common note class). Any user interaction cancels.

ACID Macro

Single knob controlling 4 parameters simultaneously:

Parameter	Range (macro 0→1)
Cutoff	0.3 → 0.9
Env Mod	0.2 → 0.9
Resonance	0.3 → 0.85
Decay	0.6 → 0.15 (inverted)

Bus Effects

Spring Reverb (Synthetic IR)

Comb filter reflections at 97, 233, 389, 557 samples for metallic spring character. Pre-delay: 8 ms (L), 12 ms (R). Duration: 0.5–3.0 s. Ducking: noteOn ducks to 0.15 (5 ms), noteOff releases to 1.0 (150 ms).

Chorus

Dual delay lines (12 ms + 18 ms) modulated by sine LFOs (0.7 Hz + 0.9 Hz). Rate range: 0.2–4 Hz.

Auto-Pan

Stereo panner modulated by 0.25 Hz sine LFO. Depth up to 80%.

Delay

BPM-synced dotted 8th note: (60/BPM) × 0.75. HP filter (200 Hz) in feedback loop. Feedback capped at 85%.

Distortion

Rat-style asymmetric hard clip: positive side 1.2× harder, negative 0.8×. Oversampled 4×.

Limiter

Brick-wall: -1 dB threshold, 20:1 ratio, 1 ms attack, 10 ms release.

Volume Curve

Quadratic: output = value².

UI Layout

Two-row knob layout:

Row 1: [Filter Canvas] │ CUT  RES  ENV  DEC │ GATE SLDT TRK │ ACID
         FILTER          │   SYNTH CORE       │   CONTROL      │ MACRO

Row 2: [SAW/SQR TUNE]  │ ACC  DRV  SUB  DFT │ DST DLY FB REV CHO LFO
         WAVE            │   TONE + CHARACTER  │      EFFECTS

Transport: ENGAGE, SWG, VOL, RND, MUT, CPY, PST, CLR, RST, PNC, X↔F.