F_TONNTZ

F_TONNTZ (Tonnetz Triad Navigator) — Manual

Overview
F_TONNTZ is a harmonic sequencer that moves through a Tonnetz-style hex grid and outputs a playable triad on every clock step. Instead of stepping through a fixed note list, it navigates a harmonic field: the module selects a small triangle (3 connected nodes) around the current position, interprets it as a chord (Major, Minor, or extended color), and outputs the triad as three separate 1V/Oct CV signals. Movement across the field is influenced by ENGINE, BIAS, TENSION, probability, directional inertia, and temporary burst behavior.

How the Tonnetz works (musical logic)
The Tonnetz is a harmonic grid where each node represents a pitch class. The grid is arranged so that neighboring nodes are related by simple musical intervals (perfect fifths and major/minor thirds). Because of this structure, small movements across the grid tend to preserve one or two common tones between chords.

F_TONNTZ always selects a triangle of three connected nodes. In this grid, any such triangle naturally forms a triad (three-note chord). Moving to a neighboring triangle usually changes only one note while the other two remain the same. This is known as parsimonious voice leading: harmonic changes occur with minimal note movement, which creates smooth and musical chord progressions.

The q and r values shown on the display are axial hex coordinates that define the current position in the Tonnetz field. They are not musical notes themselves, but determine which pitch classes form the current triangle and therefore the resulting chord.

What it outputs
On every clock step, the module outputs:
• CV1 = chord root (1V/Oct)
• CV2 = chord third (1V/Oct)
• CV3 = chord fifth (1V/Oct)
• GATE = 5V gate pulse (length set by the Gate control)
• ACC = short 5V accent pulse when the harmony makes a meaningful change (quality flip, root change, or extended color)
• DEG = chord-root pitch class as a meta-CV (0..10V mapped from 0..11 semitones)

Important note
F_TONNTZ does not generate audio. It generates control voltages (pitch and gates). To hear it, patch the CV outputs to oscillators and use the Gate output to trigger an envelope that opens a VCA.

Quick Start Patch (triads)

1) Patch a clock or trigger stream into CLK.
2) Patch CV1 to VCO1 1V/Oct, CV2 to VCO2 1V/Oct, CV3 to VCO3 1V/Oct.
3) Mix the three oscillators into a VCA (or a mixer then VCA).
4) Patch GATE to an envelope generator’s gate input.
5) Patch the envelope output to the VCA level/CV input.
6) Adjust oscillator waveforms and detuning to taste. You now have a clocked triad progression.

Quick Start Patch (single voice)

1) Patch a clock into CLK.
2) Patch CV1 to a single VCO 1V/Oct.
3) Patch GATE to an envelope, envelope to a VCA.
4) Optionally patch ACC to a filter envelope amount or VCA accent input for dynamic phrasing.

Inputs

CLK
Rising edge advances one step. On each step the module may move in the Tonnetz field (depending on PROB and FREEZE), chooses a triangle around the current position, and outputs the resulting chord plus Gate/Accent pulses.

RST
Rising edge resets the position to the center (q=0, r=0). Use this to restart harmonic exploration from a known anchor point.

ROOT IN
1V/Oct transposition added to all three CV outputs. This is the global transpose input: it shifts the entire chord up or down without changing the internal Tonnetz structure. Use for keyboard tracking, sequencer transposition, modulated key changes, or slow harmonic drift.

ENG (ENGINE CV)
Adds to the ENGINE control (scaled so roughly 10V ≈ +1.0). ENGINE shapes how the module chooses its next move. Lower values allow wandering and randomness. Higher values create directed harmonic motion. When ENGINE crosses a high threshold, the module enters a short “Burst” phase for several steps, increasing exploration, tension bias, and directional shifts.

BIA (BIAS CV)
Direction preference input. This voltage is mapped from -10V..+10V into a 0..1 range and selects a preferred direction among the 6 hex directions. With higher ENGINE, BIAS strongly influences movement. With lower ENGINE, movement is more random and BIAS has weaker influence. Slow modulation here produces rotating harmonic motion; stepped CV can enforce recurring directional patterns.

TEN (TENSION CV)
Adds to the TENSION control (scaled so roughly 10V ≈ +1.0). Higher tension increases minor coloring, extended chord probability, and harmonic instability. Lower tension favors brighter and more stable triads. The result is clamped to 0..1.

Outputs

CV1 (Root)
Chord root in 1V/Oct.

CV2 (Third)
Chord third in 1V/Oct. Outputs major or minor third depending on detected chord quality.

CV3 (Fifth)
Chord fifth in 1V/Oct.

GATE
5V gate pulse on every clock step. Length is controlled by the GATE control (milliseconds).

ACC
Short 5V accent pulse on harmonic events: Major/Minor flip, root pitch-class change, or extended color appearance. Use to trigger filter accents, secondary envelopes, percussion, or effects modulation.

DEG (Degree)
Meta-CV representing the current chord-root pitch class (0..11) mapped to 0..10V. Use this to drive conditional modulation, scale-dependent changes, or let other modules react to harmonic context.

Controls

ROOT
Sets the pitch-class anchor (C..B). Discrete semitone transposition of the Tonnetz field. ROOT IN provides continuous 1V/Oct transposition on top.

ENGINE
Coherence and motion control. Low ENGINE = wandering and softer direction memory. Mid ENGINE = directed harmonic navigation with inertia (movement tends to continue in its previous direction). High ENGINE = stronger direction control and potential Burst behavior, creating brief exploratory surges.

TENSION
Color and instability control. Higher values increase minor shading and extended chord probability (Sus2, Sus4, Add6 depending on context). Lower values maintain stable major/minor structures.

PROB
Probability of movement on each clock step. At 1.0 the module attempts to move every step (unless FREEZE is enabled). Lower values repeat the current harmony more often, creating rhythmic stasis.

RANGE
Limits how far the position can drift from the center. Lower range creates tight, loop-like harmonic areas. Higher range allows broader exploration.

GATE
Gate length in milliseconds.

FREEZE
Stops harmonic movement while gates continue. The current chord remains active until unfrozen or reset.

Behavior: Inertia & Burst

F_TONNTZ includes directional inertia: movement tends to continue in the same direction, especially at moderate ENGINE settings. This produces smoother harmonic paths instead of jittering motion. When ENGINE rises above a threshold (via knob or CV), the module temporarily enters Burst mode for a few steps. During Burst, randomness and tension weighting increase, center attraction decreases, and the harmonic path becomes more exploratory and dramatic.

The Canvas Display

The canvas shows a hex grid representing the Tonnetz field around the current position. The current position is marked with a ring. The selected chord is shown as three highlighted nodes with color indicating chord type (Major, Minor, or extended color). The top-left readout shows q and r coordinates (axial hex coordinates). The top-right label shows the current chord type. The display reflects exactly what the CV outputs generate.

Tips & Creative Uses

• Harmonic bursts: Modulate ENGINE with a slow envelope or manual control to trigger temporary exploratory surges.
• Directed progressions: Raise ENGINE moderately and steer with BIAS for controlled harmonic arcs.
• Rotating fields: Patch a slow LFO into BIAS for cyclical harmonic movement.
• Context-aware modulation: Use DEG to modulate filters, effects, or rhythm density based on harmonic position.
• Dynamic phrasing: Use ACC to emphasize structural changes in harmony.

Troubleshooting

• No sound: Patch CV outputs to oscillators and use GATE to trigger an envelope/VCA.
• Too random: Increase ENGINE, reduce RANGE, or lower TENSION.
• Too static: Increase RANGE, lower ENGINE, or modulate BIAS and TENSION.
• Not dramatic enough: Increase ENGINE or modulate it to activate Burst behavior.

Specifications

• Clocked Tonnetz navigation with triangle-based chord selection
• Directional inertia for smoother harmonic motion
• Engine-triggered Burst mode for temporary exploration
• 3× pitch CV outputs (1V/Oct, clamped to ±10V)
• Gate output (5V) with adjustable pulse length
• Accent output (5V) on harmonic events
• Degree meta-output (0..10V) derived from chord-root pitch class
• Inputs for ENGINE, BIAS, TENSION modulation plus ROOT IN transposition