tesserae
README
Tesserae — Arpeggiated Harmonic Generator
A variable-voice arpeggiated chord generator for the Workshop Computer. Inspired by Laurie Spiegel's Music Mouse (1986) and Patchwork (1977).
In mosaic art, a tessera (plural: tesserae) is an individual piece of stone or glass that, combined with others, forms a larger pattern. This card weaves individual harmonic voices — tesserae — into arpeggiated patterns across a scale-aware harmonic space.
Concept
Tesserae maps the three Workshop Computer knobs to the X/Y chord grid concept from Laurie Spiegel's Music Mouse. Knob X selects a melody position in the scale, Knob Y spreads voices apart, and the Z switch controls root note, pattern, scale, voice count, and tempo. Where Music Mouse used mouse position on a 2D grid, this card uses knobs and CV to navigate the same harmonic territory — but with variable voice count (2–8), multiple arpeggio patterns, tap tempo, andCV/audio transpose inputs.
Controls
| Control | Function |
|---|---|
| Knob X | Melody position — selects base note in the current scale across 3 octaves |
| Knob Y | Chord spacing — how many scale degrees apart each voice is (1–5). Also sets voice count when Z Down held (2–8). |
| Knob Main | Function depends on Z switch position (see below) |
Z Switch Modes
| Position | Mode | Knob Main | Knob Y |
|---|---|---|---|
| Up | Pattern select | Choose arpeggio pattern (5 patterns) | — |
| Centre | Root octave | Select root note (C1–C7, logarithmic) | — |
| Down (tap < 300ms) | Tap tempo | — | — |
| Down (hold >= 300ms) | Scale & voice select | Choose scale (10 scales) | Choose voice count (2–8) |
- Pattern select (Z Up): Knob Main sweeps through 5 arp patterns. The selected pattern persists when the switch returns to Centre.
- Root octave (Z Centre): Knob Main sets the root note with a logarithmic curve — even spacing across C1 to C7. Default is C3 (MIDI 48) when in Pattern select mode.
- Tap tempo (Z Down quick tap): Each tap resets the beat phase so the next step fires one beat after the tap. The interval between two consecutive taps (within 2 seconds) sets the internal clock BPM. First tap after a gap just resets phase without changing tempo. Tap tempo is ignored when an external clock is connected.
- Scale & voice select (Z Down hold): Hold Z Down for 300ms or longer. Knob Main selects a scale (0–9), Knob Y selects voice count (2–8, default 4). Both update in real-time while held. LED 4 lights up to indicate this mode.
Voice Count
The arpeggio can use 2–8 voices (default 4). More voices = a wider chord spread across the same scale. Set via Knob Y while Z Down is held. The chord is built as:
Voice 0: degree + 0
Voice 1: degree + spacing
Voice 2: degree + 2×spacing
...
Voice N-1: degree + (N-1)×spacing
Arpeggio Patterns
Patterns work with any voice count N. Cycle lengths adapt automatically.
| # | Pattern | Behaviour |
|---|---|---|
| 0 | Up | 0 → 1 → … → N-1 → 0 … |
| 1 | Down | N-1 → … → 1 → 0 → N-1 … |
| 2 | Up-Down | 0 → 1 → … → N-1 → N-2 → … → 1 (2N-2 step cycle) |
| 3 | Down-Up | N-1 → N-2 → … → 0 → 1 → … → N-2 (2N-2 step cycle) |
| 4 | Random | XOR-shift PRNG, equal probability for all N voices |
Inputs
| Input | Function |
|---|---|
| Audio In 1 | Pitch transpose — shifts the arpeggiated voice (CV Out 1, Audio Out 1 & 2) by semitones when connected. 1V/oct: +1V = +12 semitones. |
| Audio In 2 | Root transpose — shifts the entire chord (root + all voices) by semitones when connected. 1V/oct: +1V = +12 semitones. |
| CV In 1 | Offsets melody position (Knob X) when connected |
| CV In 2 | Offsets chord spacing (Knob Y) when connected |
| Pulse In 1 | External clock — each rising edge advances one arpeggio step (overrides internal clock when connected) |
| Pulse In 2 | Reset — restarts arpeggio from step 0 |
Outputs
| Output | Function |
|---|---|
| CV Out 1 | Current arpeggiated chord note, calibrated 1V/oct |
| CV Out 2 | Root note (base melody pitch), always present, calibrated 1V/oct |
| Audio Out 1 | Same as CV Out 1 — current arpeggiated note, approximate 1V/oct (uncalibrated audio DAC) |
| Audio Out 2 | Previous arpeggiated note (the note before the current step), approximate 1V/oct |
| Pulse Out 1 | Gate — high while the current arpeggio note is active (~50ms) |
| Pulse Out 2 | Trigger — short pulse (~10ms) at the start of each arpeggio step |
Audio outputs use the 12-bit audio DAC without per-channel calibration, so pitch is approximate (~10–20 cents deviation possible). This is good enough for patching into V/Oct inputs on other modules.
LEDs
| LED | Function |
|---|---|
| LEDs 0–3 | Shows current voice index modulo 4 (one LED on at a time) |
| LED 4 | On when scale/voice select mode is active (Z Switch Down held) |
| LED 5 | On when external clock is connected (Pulse In 1) |
Scales
10 scales, selected by holding Z Switch Down and turning Knob Main:
| # | Scale | Intervals |
|---|---|---|
| 0 | Major | 0, 2, 4, 5, 7, 9, 11 |
| 1 | Minor | 0, 2, 3, 5, 7, 8, 10 |
| 2 | Pentatonic Major | 0, 2, 4, 7, 9 |
| 3 | Pentatonic Minor | 0, 3, 5, 7, 10 |
| 4 | Dorian | 0, 2, 3, 5, 7, 9, 10 |
| 5 | Phrygian | 0, 1, 3, 5, 7, 8, 10 |
| 6 | Lydian | 0, 2, 4, 6, 7, 9, 11 |
| 7 | Mixolydian | 0, 2, 4, 5, 7, 9, 10 |
| 8 | Whole Tone | 0, 2, 4, 6, 8, 10 |
| 9 | Chromatic | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 |
How It Works
Chord Generation
Knob X maps to a scale degree across 3 octaves. With Knob Y setting the spacing, the chord is built by adding spacing scale degrees for each successive voice (2–8 voices).
For example, with Major scale (7 notes), 4 voices, and spacing=2:
- Knob X at degree 2 (D in C major)
- Chord: D, F#, A, C (D minor 7)
With 6 voices and spacing=1:
- Knob X at degree 0 (C in C major)
- Chord: C, D, E, F, G, A (6 notes of the scale)
Arpeggiation
The arpeggio cycles through N voices according to the selected pattern. On each step, CV Out 1 jumps to the next voice's pitch, CV Out 2 holds the root. Audio Out 1 mirrors CV Out 1, Audio Out 2 holds the previous note. The cycle resets to step 0 when:
- A reset trigger is received (Pulse In 2 rising edge)
Audio Inputs (Transpose)
Audio In 1 and Audio In 2 work as additional CV inputs for pitch transposition. When nothing is connected, they have no effect (readings are zeroed by hardware).
- Audio In 1 (pitch transpose): Adds a semitone offset to the arpeggiated voice outputs (CV Out 1, Audio Out 1, Audio Out 2). Uses 1V/oct scaling (≈341 counts per octave, ≈28 counts per semitone). Does not affect the root note (CV Out 2). Ideal for vibrato, envelope-driven transposition, or sequenced pitch shifts from an external LFO or EG.
- Audio In 2 (root transpose): Adds a semitone offset to the root note, which shifts the entire harmonic framework — both the root (CV Out 2) and all derived chord notes. Same 1V/oct scaling. Use for key changes or root modulation from external CV.
Timing
- Internal clock: default 120 BPM, adjustable via tap tempo (Z Down). Phase accumulator at 48 kHz.
- External clock: when Pulse In 1 is connected, each rising edge advances one step.
- Gate length: ~50ms (2400 samples at 48 kHz)
- Trigger length: ~10ms (480 samples at 48 kHz)
Example Patch
Building
# Configure (first time)
cmake -S . -B build
# Compile
cmake --build build -j$(sysctl -n hw.logicalcpu)
# Output: build/tesserae.uf2
Flash by holding BOOTSEL and copying tesserae.uf2 to the mounted drive.
Files
Tesserae/
├── main.cpp — card implementation
├── CMakeLists.txt — build configuration
├── ComputerCard.h — hardware abstraction (from Workshop Computer repo)
├── pico_sdk_import.cmake — Pico SDK import
├── info.yaml — card metadata
├── README.md — this file
└── .gitignore
Credits
Inspired by Laurie Spiegel's Music Mouse (1986) and Patchwork (1977). The concept of navigating harmonic space through a 2D grid comes from Music Mouse; the name Tesserae honours both — each voice is a tessera in the sounding mosaic, just as Spiegel's Patchwork wove musical threads into a larger pattern.
Algorithm adapted from Music Mouse emulations by Tero Parviainen and ulmert/laurie (Korg NTS-1 port).
License
This project is released under the MIT License. Use it, modify it, fork it, break it, improve it. No warranties, no liabilities. If you build something from this, you don't owe me anything — but I'd love to hear about it. Build using opencode and glm5.1. Many thanks to Tom Whitwell for making this highly addictive and inspiring musical platform.