Markov

Dual generative Markov chain module for the Music Thing Modular Workshop Computer.

Two independent Markov chain engines run in parallel — a melodic generator on the left side and a rhythmic percussion generator on the right — driven by a shared clock. An internal synth voice combines both into a self-contained generative instrument.

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Overview

A Markov chain is a probabilistic state machine: the next state depends only on the current state, weighted by a transition probability table. Each engine has several pre-programmed profiles — curated probability matrices that give each one a distinct musical character. Over time, the chains wander through their state spaces in ways that feel intentional but never exactly repeat.

MarkoV (melody) has 10 states representing scale degrees. The current state maps to a pitch, quantised to a selected scale and transposed by CV and knob.

MarkovPerc (percussion) has 8 states representing hit types: rests, plain hits, accented hits, flams (grace note + main hit), and ratchets (2, 3, or 4 evenly spaced triggers per clock pulse). The percussion engine drives Pulse Out 2 with the appropriate sub-trigger pattern each clock cycle, and also gates the internal synth voice.

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I/O

Jack	Direction	Function
Pulse In 1	Input	Master clock. Rising edge advances both chains. Falls back to CV In 2 internal clock after 3 seconds with no pulse.
CV In 1	Input	Post-scale transpose ±12 semitones. Shifts the already-quantised pitch by whole semitones. Bipolar; 0 V = no shift. Inactive while Switch DOWN is held.
CV In 2	Input	Internal tempo. Active only when Pulse In 1 is absent. 0 V = 120 BPM; range ≈ 20–220 BPM.
Pulse Out 1	Output	Gate pulse (10 ms) on every melody step where the quantised pitch changes.
CV Out 1	Output	Pitch CV for the MarkoV melody. V/Oct, hardware-calibrated.
Pulse Out 2	Output	Trigger for MarkovPerc hits. Fires multiple times per clock for ratchets and flams.
CV Out 2	Output	Accent CV for MarkovPerc. 0 V = rest/silent; +5 V = full accent. 5 levels.
Audio Out 1	Output	Internal synth voice — square-wave oscillator pitched by MarkoV, shaped by a long decaying envelope and gated by MarkovPerc hits. In Dual Melody mode: voice A synth only.
Audio Out 2	Output	Unused in primary mode. In Dual Melody mode: voice B synth (independent).

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Controls

Knob X — Melody Profile

Selects one of five MarkoV transition profiles. Fully CCW = profile 0, fully CW = profile 4.

Zone	LEDs	Profile	Character
0	OO OO OO	Pentatonic Stability	Root and fifth are strong attractors. Grounded and tonal.
1	XO OO OO	Chromatic Tension	Stepwise motion dominates (±1 state). Snake-like lines.
2	OO XO OO	Jazz Tendencies	Strong pull toward the 7th degree from almost anywhere; resolves back to root.
3	XO XO OO	Glacial	Stays on the current note most of the time. Very slow evolution.
4	OO OO XO	Drone	Overwhelming self-loop weight (~83%). Barely moves unless disturbed.

While Knob X is being turned, LEDs 0, 2, 4 (left column) show the current profile index at half brightness. After ~1 second of no movement the LEDs revert to their idle state.

Knob Y — Percussion Profile

Selects one of four MarkovPerc transition profiles. Fully CCW = profile 0, fully CW = profile 3.

Zone	LEDs	Profile	Character
0	OO OO OO	Steady	Rock/pop feel. Frequent hits and accented hits; rests are brief.
1	OX OO OO	Syncopated	Funk/Latin feel. Structural rests, frequent flams, Ratchet 2 as a syncopation device.
2	OO OX OO	Jazz/Free	Complex patterns. Ratchets are common fills; accented flams are the signature gesture.
3	OX OX OO	Sparse	Long silences punctuated by single hits. Ratchets and flams nearly absent.

While Knob Y is being turned, LEDs 1, 3, 5 (right column) show the current profile index at half brightness. After ~1 second the LEDs revert.

Main Knob (Z) — Switch-Dependent

The Main Knob's function changes with the 3-way switch position.

Switch UP — Transpose

Sets the melody base note. Range: −12 to +12 semitones (centre = 0). Applied before scale quantisation — turning the knob shifts which scale degrees get played, changing the melodic character rather than just the octave. CV In 1 is applied separately, after quantisation.

Switch MIDDLE — Loop & Lock

Controls looping. The knob is symmetric around its centre position:

Knob position	Behaviour
Centre	Free running. No loop, no LEDs.
CW → 16 / 8 / 4 / 3 / 2 beats	Locked replay. The last N beats of play are captured and repeat exactly. Clean, unchanging loop.
CCW → 16 / 8 / 4 / 3 / 2 beats	Locked replay with mutation. Same capture mechanism, but each step has a 1-in-8 chance of being recalculated from the previous step via a Markov transition. The loop drifts gradually over many passes.

When the knob moves away from centre, the last N beats already played are captured into the loop buffer immediately. Returning to centre releases the loop and resumes free running from where the chains left off.

A single LED (at half brightness) indicates the active loop length:

Loop length	LEDs
16 beats	XO OO OO
8 beats	OO XO OO
4 beats	OO OO XO
3 beats	OO OO OX
2 beats	OO OX OO
Free (centre)	OO OO OO

Switch DOWN — Scale Select (momentary)

While held, the Main Knob selects the quantisation scale applied to CV Out 1. All six LEDs show the current scale index in 6-bit binary at half brightness.

Release the switch to return to normal LED state. The new scale takes effect on the next clock pulse.

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LED Display

LEDs are off by default and illuminate only when relevant:

State	LEDs 0, 2, 4 (left)	LEDs 1, 3, 5 (right)
Idle / free	Off	Off
Loop locked	Single LED at half brightness indicates loop length (see table above)	—
Knob X just turned	mel_profile (0–4) in 3-bit binary, half brightness, ~1 s	unchanged
Knob Y just turned	unchanged	perc_profile (0–3) in 3-bit binary, half brightness, ~1 s
Switch DOWN held	Scale index (0–11) in 6-bit binary across all LEDs, half brightness	—

Knob X/Y feedback takes priority over loop lock display while the timer is active. Scale display takes priority over both.

In Dual Melody mode, the right column (1, 3, 5) shows voice B profile instead of percussion profile when Knob Y is turned.

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Scales

Twelve scales arranged CCW (dark/minor) to CW (bright/ambiguous):

LED display shows the scale index in 6-bit binary across all six LEDs (X = lit, O = off). Left column = LEDs 0/2/4 (bits 0/1/2), right column = LEDs 1/3/5 (bits 3/4/5), read top to bottom.

Index	LEDs	Scale	Notes	Character
0	OO OO OO	Phrygian	7	Dark, unresolved minor. The flat 2nd gives an ancient or Spanish flavour.
1	XO OO OO	Hirajōshi	5	Tense, cinematic minor. A Japanese koto scale with wide leaps.
2	OO XO OO	Harmonic Minor	7	Dramatic; the augmented 2nd between ♭6 and 7 is the defining interval.
3	XO XO OO	Natural Minor	7	The standard minor centre. Neutral and versatile. (Default)
4	OO OO XO	Minor Pentatonic	5	Open, classic minor. No semitone steps; very forgiving.
5	XO OO XO	m7 Arpeggio	4	Root, ♭3, 5, ♭7 only. Pure minor 7th chord tones.
6	OO XO XO	Dorian	7	Minor with a raised 6th. Sophisticated — melancholic but lifted.
7	XO XO XO	Major Pentatonic	5	Open, consonant major. Pastoral and unambiguous.
8	OX OO OO	Ionian (Major)	7	The standard major scale. Bright and resolved.
9	XX OO OO	Maj7 Arpeggio	4	Root, 3, 5, 7. Pure major 7th chord tones. Lush and stable.
10	OX XO OO	Whole Tone	6	Dreamy, floating, rootless. Every interval is a tone; no leading-note pull.
11	XX XO OO	Chromatic	12	All 12 semitones. The raw Markov output — total ambiguity.

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Percussion Hit Types

The current MarkovPerc state determines what Pulse Out 2 does during each clock cycle.

State	Pulse Out 2	Accent CV
REST	Nothing	0 V
HIT	Single trigger at beat start	Low
ACC HIT	Single trigger, full accent	High
FLAM	Soft grace note at tick 0, main hit at 1/8 of clock period	Medium
ACC FLAM	Soft grace note at tick 0, full-accent main hit at 1/8	High
RATCHET 2	2 evenly spaced triggers	Medium
RATCHET 3	3 evenly spaced triggers	Medium
RATCHET 4	4 evenly spaced triggers	Low

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Internal Synth Voice

Audio Out 1 generates a square-wave oscillator pitched to the current MarkoV note, shaped by an AR envelope with a fast attack (0.2 ms) and a long exponential decay (2 seconds to near-silence).

Notes decay naturally across the full clock period and beyond, giving a sustained, ambient quality. Consecutive notes overlap and blend.

Gate behaviour: Pulse Out 1 fires and the envelope retriggers only when the quantised pitch changes from the previous step. Repeated identical pitches do not retrigger — the note sustains smoothly rather than stuttering.

Accent: Full-accent hits reach full envelope peak; plain hits are softer; grace notes (the leadup in flam patterns) start from silence at a reduced peak so the main flam hit punches through clearly.

Ratchets: Each trigger in a ratchet burst restarts the attack from the envelope's current level rather than from zero — the burst sounds like a single energetic note subdivided, not a string of separate staccato hits.

The voice is intentionally minimal: its purpose is to make the module immediately useful standalone. For richer sound, patch CV Out 1 to an external VCO and Pulse Out 2 to an external envelope generator.

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Patch Ideas

Generative melodic voice: CV Out 1 → VCO V/Oct. Pulse Out 1 → envelope trigger. Pulse Out 2 → drum module or second envelope. CV Out 2 → accent input or VCA CV.

Quantised drone: Set Melody Profile to Drone (Knob X fully CW) and Percussion Profile to Sparse (Knob Y fully CW). CV Out 1 → VCO. The melody barely moves; occasional sparse hits gate and accent it.

Clock multiplication: Ratchet states on Pulse Out 2 produce up to 4 evenly spaced triggers per clock pulse. Patch to a clock divider or sequencer reset for polyrhythmic structures.

Loop as a performance tool: Let the chains run freely for a few bars until a good pattern appears, then turn Main Knob CW (Switch MIDDLE) to lock the loop. Turn fully CW for clean repetition; nudge CCW to engage mutation and let the pattern evolve gradually. Return to centre to release.

Scale morphing: Hold Switch DOWN and sweep the Main Knob while a sequence is playing. The scale updates on the next clock pulse. Dramatic shifts (e.g. Phrygian → Whole Tone) create instant reharmonisation without stopping the sequence.

CV transpose as key change: With Switch UP, set the Main Knob to the root you want. Patch a CV keyboard or quantiser output to CV In 1 — it will shift the already-quantised melody up or down in semitones, effectively transposing the whole sequence to follow a chord progression.

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Dual Melody Mode

Hold Switch DOWN while powering on (or pressing reset) to enter Dual Melody mode. The firmware detects the switch position after the ADC settles (~150 ms) and latches the mode for the session.

In this mode both Markov engines are melodic — there is no percussion engine. Two independent MarkoV chains run in parallel, each outputting a pitched CV and driving its own synth voice.

I/O in Dual Melody Mode

Jack	Function
Pulse In 1	Master clock (both chains advance together)
CV In 1	Post-scale transpose for voice A (±12 semitones)
CV In 2	Post-scale transpose for voice B (±12 semitones)
Pulse Out 1	Gate pulse for voice A (10 ms, only on pitch change)
CV Out 1	Pitch CV for voice A (V/Oct, calibrated)
Pulse Out 2	Gate pulse for voice B (10 ms, only on pitch change)
CV Out 2	Pitch CV for voice B (V/Oct, calibrated)
Audio Out 1	Voice A synth (independent)
Audio Out 2	Voice B synth (independent)

CV In 2 is repurposed as a pitch transpose for voice B. The internal BPM clock is not available in this mode; a fixed 120 BPM fallback is used if no external clock is patched.

Controls in Dual Melody Mode

Control	Function
Knob X	Voice A profile (0–4, same profiles as primary mode)
Knob Y	Voice B profile (0–4)
Main Knob + Switch UP	Shared transpose for both voices (pre-scale)
Main Knob + Switch MID	Loop length (same symmetric CW/CCW mechanism; both voices share the same loop)
Main Knob + Switch DOWN	Scale index (shared for both voices)

Patch ideas (Dual Melody)

Two-voice harmony: CV Out 1 + CV Out 2 → two VCOs; Audio Out 1 + Audio Out 2 → two mixer channels. Both voices wander through the same scale on independent Markov paths, creating unexpected intervals. Knob X = voice A character, Knob Y = voice B character.

Interval control: Patch CV In 1 and CV In 2 to different fixed offsets. Voice A and B each transpose independently, so you can anchor them a third or fifth apart while both chains evolve freely.

Canon/round: Set both voices to the same profile but start them from different states. They will occasionally converge on the same pitch before diverging again.

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Technical Notes

• Sample rate: 48 kHz. System clock: 144 MHz (required for CV PWM resolution).
• Integer-only DSP in the audio callback. Float arithmetic is used only at boot time to populate the MIDI-note → phase-increment LUT.
• The two Markov engines are independent; only the clock is shared.
• External clock: rising edge on Pulse In 1. Works with any clock source — Eurorack clock module, LFO square wave, drum trigger, sequencer gate output.
• Internal clock: if no rising edge arrives on Pulse In 1 for 3 seconds, CV In 2 takes over. Tempo is 0 V = 120 BPM, with ±5 V spanning roughly 20–220 BPM. Patching Pulse In 1 again resyncs immediately on the next pulse.
• Transpose signal chain: knob transpose (pre-scale) → scale quantisation → CV In 1 shift (post-scale). The knob changes which scale degrees are used; CV In 1 moves the result chromatically. CV In 1 is frozen at zero while Switch DOWN is held to prevent accidental pitch shifts during scale selection.
• Loop buffer: 16 beats deep. The buffer is filled from a rolling history of recently played states — the loop captures what was already playing, not a newly generated sequence.
• Loop mutation: in CCW loop mode, each step has a 1-in-8 chance of being regenerated via a Markov transition from the previous step. Over many passes the sequence gradually drifts while remaining rhythmically coherent.
• Pitch-change gate: Pulse Out 1 (and voice B gate in Dual Melody mode) fires only when the quantised pitch changes from the previous step. Repeated notes sustain without retriggering.
• Percussion density: the Steady and Syncopated profiles are deliberately active — rests occur but are outnumbered by hits. For more silence, use Sparse (Knob Y fully CW).
• LED knob timeout: after Knob X or Y is turned, the relevant column shows the profile index at half brightness for ~1 second, then reverts. Scale display (Switch DOWN) has no timeout — it persists until the switch is released.
• Dual Melody boot: mode is latched once, ~150 ms after power-on. Hold Switch DOWN before applying power (or during a reset), release after the LEDs first flicker. Power-cycling without holding DOWN returns to primary mode.

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Credits

Markov chain algorithms adapted from the MarkoV and MarkovPerc applets for Ornament & Crime (Phazerville), written by Andy Jenkinson (uglifruit).

Ported to the Music Thing Modular Workshop Computer by Andy Jenkinson (uglifruit).