Turing's Palette

An experiment for a larger card: a simple synth voice where every parameter is read from a Turing-Machine-style shift register.

The register is 64 bits long. In the web editor you split it into 1–8 loops (one 64-bit loop, four 16-bit loops, 20 + 12 + 16 + 16, anything that adds up to 64 or less). Each loop rotates on its own clock divider, and each has a chaos amount that scales how often the Main knob flips its bits. Then you drag each of the synth synthesis parameters onto any window of 1–16 bits and give it an output range. Windows may overlap, and may straddle two loops.

Quick start

1. Insert the card and press reset. It starts with a four-loop layout, so it plays straight away.
2. Patch Audio Out 1 to a mixer or speaker.
3. Turn Y to set the clock speed, or patch a clock into Pulse In 1.
4. Main at noon gives an ever-changing pattern. Turn Main fully clockwise, or push the switch up, to lock the loops.
5. Open the web editor in Chrome or Edge, connect with a USB-C data cable, and start dragging parameters around.

The voice

Two oscillators (morphing sine → triangle → saw → square) → mix → resonant 12 dB low-pass (state-variable, run at 96 kHz) → VCA. Osc 2 can frequency-modulate Osc 1 (through-zero FM), with its own envelope on the FM depth, and Osc 2 can be soft- or hard-synced to Osc 1. Five attack/decay envelopes, all fired together: filter, volume, FM depth, and a pitch envelope for each oscillator. All but the FM one have a curve control.

LFOs

Three LFOs, each with Rate, Shape, Sync and Depth lanes. Rate runs from about 0.02 Hz to 50 Hz; with Sync on it chooses a length in clock steps instead (1/4, 1/2, 1, 2, 3, 4, 6, 8, 12, 16, 32 or 64 steps per cycle, from the measured clock, internal or Pulse In 1) and the LFO restarts on the right step. Shape morphs sine → triangle → saw → square, and its top tenth is random: a new level held for each cycle (sample and hold). Depth 0 (the default) leaves the sound untouched.

Outputs

Audio Out 2, CV Out 1, CV Out 2 and both pulse outs each have a lane, and a Sends choice on its Parameter card:

The CV outs are calibrated; Audio Out 2 is not (about ±6 V across its range). An output's lane only matters while it sends its register; otherwise its bar greys out.

How bits become values

For each assigned parameter, the bits start … start+width−1 are read with start as the least significant bit, either

• Binary: as a binary number, normalised to 0…1, or
• Count: the number of set bits divided by the width (smoother, more "probabilistic" movement),

optionally inverted (1 − x), then scaled to Min + x × (Max − Min). Setting Min above Max also reverses the direction. An unassigned parameter is fixed at its Min value.

A held parameter keeps the value it had when you held it: the register goes on stepping, but that parameter no longer follows it. Hold is saved with the layout. When a slot loads, a held parameter takes the value the slot's saved register pattern gives, and holds that. A held Env Trigger acts like a fixed setting: held at "fire" it fires on every clock step, held at "rest" never.

How the loops move

On each clock step, every loop whose divider is due shifts its bits up by one place. The bit falling off the top of the loop goes back in at the bottom, and is flipped with probability p × chaos. p comes from the Main knob (plus CV In 2), as on the Turing Machine:

Bits outside every loop never move. Assignments can still read them, as fixed values.

Panel

Layout slots

The card keeps six layouts in flash, one per LED. Each slot holds a layout, the register pattern it was saved with, and a name (up to 16 characters).

• On the module: with the switch up the loops are locked, so Main is free to choose a slot. Its travel is split into six zones, slot 1 fully anticlockwise to slot 6 fully clockwise. Flicking the switch up only shows the playing slot on the LEDs; a layout loads once you turn Main into another slot's zone, and its LED lights for 1.5 s. An empty slot's LED blinks and nothing loads. Back in the middle, Main does nothing until it reaches its randomness setting again (pick-up), so the loops don't suddenly unlock at a different setting.
• At power-up the card plays the slot it last played. (It notes the slot in flash once it has stayed chosen for 5 s, so sweeping Main doesn't wear the flash.)
• In the editor, the Layouts on the card panel lists the six slots when the card connects, with their names and loop layouts and the one playing, and follows any change made with Main. Save here saves what is playing into a slot under the name typed above the list; Load, Rename and Clear (two clicks) do the rest. Save to card in the header saves into the slot that is playing.
• Firmware before 0.6 kept one layout; the first time 0.6 or later starts, that layout becomes slot 1, "Saved". A fresh card starts with the factory layout in slot 1.
• New firmware keeps your slots: each layout format only adds parameters at the end, so the card reads layouts saved by earlier firmware, and the parameters they lack take their factory settings (Sync off, for example).

Web editor

web/index.html is a single static page, styled and connected the same way as the CVSeq and WaveSeq editors. It works without a card: it simulates the register so you can design layouts and watch the parameter values move. With a card connected over USB (WebMIDI SysEx, Chrome/Edge on desktop or Android; not iOS) the card is the source of truth: the page reads the card's layout when it connects, then shows the card's register, knobs and switch about 30 times a second.

• Knobs & clock shows Main, X and Y as the card is using them, and the switch position. Move a slider to set that value on the card: the module's knob then picks up (soft takeover). It does nothing until it is turned to, or past, the new value, so nothing jumps. While a knob is waiting, its box has a dotted outline, an orange line shows where the knob is, and LED 5 on the module blinks fast.
• The dashed box above the grid (the tray) holds any unassigned parameters, as small chips: drag one onto the grid to give it bits, or drag a bar into the tray to unassign it. Drag a bar to move it, or its ends to resize it. Drag on an empty lane to draw a range.
• Lanes come in groups: Notes, Oscillators, FM, Filter, Volume, Pitch envelopes, LFOs and Outputs. Click a group's name to fold it to one row (its bars stay visible, in miniature), or use Fold all / Unfold all. The editor remembers which groups are folded.
• The pause button, beside each parameter's name, holds it at its current value; its bar greys out. Click again to let the register move it. The parameter panel has the same Hold button.
• Click a parameter's name to select it. The Parameter card beside the grid shows its own bits live, in the grid's order with their bit numbers, what they read as (the binary number, or how many are set in Count mode) and the value that gives. It stays in view while you scroll down the grid: it and the cards below it form one column that stays beside the grid as the page scrolls, and scrolls on its own (mouse wheel over it) when it's taller than the window. Below the bits are its range, mode, Invert, Hold, and where it sits.
• Drag the handles on the loop strip to move loop boundaries. The Loops table sets length, clock divider and chaos per loop, and can split, merge or remove loops.
• Click a state bit to flip it (on the card too, when connected).
• Every edit goes to a connected card straight away. Save to card stores the layout and the current register pattern in the slot that is playing, so they come back after power-off; the Layouts on the card panel saves into, loads, renames and clears any of the six slots.
• Layouts can be exported and imported as JSON.

SysEx protocol

Documented in full in sysex.h. Every message is F0 7D 50 <cmd> … F7 (50 is 'P'); the card shows up as a MIDI device named Turing's Palette.

Layout byte layout (CONFIG_FORMAT 6): [0] format, [1] number of loops, [2..25] 8 × (length, divider, chaos), [26..27] scale mask (bit n = n semitones above root), [28] root MIDI note, [29..404] 47 × (enabled, start, width, flags, min lo, min hi, max lo, max hi) with flags bit 0 = count mode, bit 1 = invert, bit 2 = hold, bits 3–7 = source (output lanes), and min/max as signed 16-bit little endian.

Building

mkdir build && cd build
cmake .. -DPICO_SDK_PATH=/path/to/pico-sdk
make

Builds against Pico SDK 2.1.1.

ProcessSample must finish inside ~20 µs (about 3000 cycles at 144 MHz) on every sample, or the Computer's knob and CV readings get mixed up. So no sample does a burst of work: after a clock step the loops shift one per sample and the parameters are re-read one per sample; a layout from the editor is prepared on the USB core and swapped in by pointer; pitch, smoothing, pitch envelopes, LFOs, outputs, knobs, LEDs and the editor snapshot each run on their own staggered samples. Measured in an emulated Cortex-M (QEMU, instruction counts, hardware divider modelled) the worst sample is about 1,650 instructions and the average about 1,150, with FM at full depth, hard sync, both pitch envelopes, all three LFOs and quantised outputs running. It has not yet been timed on hardware; if you change the audio path, check it with a scope on a spare GPIO.

Credits

Firmware and editor written with AI assistance (Claude). The USB/SysEx link, knob pick-up and editor style follow the CVSeq and WaveSeq cards. MIT licence.