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, temporary Burst behavior, memory field attraction, and optional manual node selection.

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 or manual instantiation, 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.

Manual Interaction (Canvas Clicking)
F_TONNTZ can operate purely from clock input, but it also allows direct harmonic instantiation from the canvas.

Left Click: Instantiates a triad centered on the clicked node. Clicking the same node repeatedly produces the same chord, ensuring deterministic behavior.
Shift + Click: Instantiates the same triad but forces an extended chord color (Sus2, Sus4, or Add6 depending on context).
No Clock Required: Manual clicks immediately generate chord CV and a gate pulse even when no clock is connected.

This allows F_TONNTZ to function both as a generative harmonic engine and as a playable harmonic surface.

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 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.

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 shifts the entire chord up or down without changing internal Tonnetz relationships.

ENG (ENGINE CV)
Adds to the ENGINE control. 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 temporarily enters Burst mode for several steps, increasing exploration, tension bias, and directional shifts.

BIA (BIAS CV)
Direction preference input. Mapped from -10V..+10V into a 0..1 range selecting a preferred direction among the 6 hex directions. With higher ENGINE, BIAS strongly influences movement.

TEN (TENSION CV)
Adds to the TENSION control. Higher tension increases minor coloring, extended chord probability, and harmonic instability. Lower tension favors brighter and more stable triads.

Outputs

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

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

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

GATE
5V gate pulse on every clock step or manual instantiation. Length is controlled by the GATE control.

ACC
Short 5V accent pulse on harmonic events: Major/Minor flip, root pitch-class change, or extended color appearance.

DEG (Degree)
Meta-CV representing the current chord-root pitch class (0..11) mapped to 0..10V.

Controls

ROOT
Sets the pitch-class anchor (C..B). Discrete semitone transposition of the Tonnetz field.

ENGINE
Coherence and motion control. Low ENGINE = wandering. Mid ENGINE = directed harmonic navigation with inertia. High ENGINE = stronger direction control and Burst behavior.

TENSION
Color and instability control. Higher values increase minor shading and extended chord probability (Sus2, Sus4, Add6).

PROB
Probability of movement on each clock step. Lower values repeat the current harmony more often.

RANGE
Limits how far the position can drift from the center.

GATE
Gate length in milliseconds.

FREEZE
Stops harmonic movement while gates continue. The current chord remains active.

Behavior: Inertia, Burst & Memory
Directional inertia causes motion to continue in similar directions at moderate ENGINE settings. Burst mode temporarily increases exploration and tension when ENGINE exceeds a threshold. The module also maintains a harmonic memory field: previously visited nodes glow on the canvas and subtly influence future movement. This creates evolving harmonic paths instead of purely random walks.

The Canvas Display
The canvas shows a hex grid representing the Tonnetz field. 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). Previously visited paths fade gradually over time, visualizing harmonic memory. The top-left readout shows q and r coordinates. The top-right label shows the current chord name and type. The display reflects exactly what the CV outputs generate.

Tips & Creative Uses
• Modulate ENGINE to trigger harmonic bursts.
• Use BIAS with slow LFOs for rotating harmonic motion.
• Reduce RANGE for tight harmonic loops.
• Use DEG to drive harmonic-dependent modulation elsewhere.
• Use manual clicking for performance-based chord instantiation.

Troubleshooting
• No sound: Patch CV outputs to oscillators and use GATE to trigger an envelope/VCA.
• Too random: Increase ENGINE or reduce RANGE.
• Too static: Increase RANGE or modulate BIAS/TENSION.
• Want playable behavior without clock: Use manual clicking on the canvas.

Specifications
• Clocked Tonnetz navigation with triangle-based chord selection
• Manual node instantiation (left-click / shift-click)
• Directional inertia and Burst mode
• Harmonic memory field visualization
• 3× pitch CV outputs (1V/Oct, ±10V clamp)
• Gate and Accent outputs (5V)
• Degree meta-output (0..10V)
• ENGINE, BIAS, TENSION CV inputs plus ROOT IN transposition

About the Tonnetz
The Tonnetz (German for “tone network”) is a theoretical harmonic map that represents pitch classes in a geometric grid. In this structure, neighboring nodes are related by simple musical intervals such as perfect fifths and major or minor thirds. Because of this arrangement, any triangle formed by three connected nodes naturally produces a triad. Moving across adjacent triangles often preserves one or two common tones, resulting in smooth and musically coherent harmonic transitions.

F_TONNTZ is directly based on this concept. It transforms the Tonnetz from a theoretical visualization tool into a playable harmonic engine, navigating the grid to generate triads with minimal voice movement and structurally consistent chord relationships.