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, optional manual node selection, and optional strummed note output.

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)
• NOTE = monophonic note output (Placed BELOW SPREAD knob is used for strum playback)
• 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.

Strum Behavior (SPREAD)
When SPREAD is set above zero, F_TONNTZ switches from simultaneous chord output to a strummed note mode. Instead of all three notes sounding at once, the chord is played sequentially using the NOTE output.

The first note always occurs exactly at the start of the gate, ensuring tight timing. The remaining notes are delayed according to the SPREAD setting, creating a natural strumming or arpeggio effect.

In this mode:
• CV1–CV3 still represent the full chord structure
• NOTE outputs individual notes in sequence
• GATE outputs short pulses per note instead of a single long gate

With SPREAD set to zero, the module behaves as a traditional chord generator with all notes played simultaneously.

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 (strum / single voice)
1) Patch a clock into CLK.
2) Patch NOTE to a single VCO 1V/Oct.
3) Patch GATE to an envelope, envelope to a VCA.
4) Increase SPREAD to introduce timing between notes.
5) Optionally use ACC for dynamic accents.

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).

ROOT IN
1V/Oct transposition added to all outputs.

ENG (ENGINE CV)
Controls movement behavior and Burst activation.

BIA (BIAS CV)
Controls preferred movement direction.

TEN (TENSION CV)
Controls harmonic color and instability.

Outputs

CV1 / CV2 / CV3
Chord tones in 1V/Oct.

NOTE
Sequential note output for strum mode.

GATE
Gate output. Acts as a chord gate in normal mode and as per-note trigger in strum mode.

ACC
Accent trigger on harmonic changes.

DEG
Pitch-class output (0..10V).

Controls

TRANSPOSE
Global semitone transposition applied to all outputs.

ROOT
Sets pitch-class anchor.

ENGINE
Controls movement coherence and Burst behavior.

TENSION
Controls chord color and instability.

PROB
Controls movement probability.

RANGE
Limits movement distance.

GATE
Sets gate length.

SPREAD
Controls timing between notes in strum mode.

FREEZE
Stops movement while maintaining output.

Behavior: Inertia, Burst & Memory
Directional inertia smooths movement. Burst mode increases exploration. A memory field stores visited nodes and subtly influences future movement, creating evolving harmonic paths.

The Canvas Display
Shows the Tonnetz grid, current position, selected chord, and fading memory paths.

Tips & Creative Uses
• Modulate ENGINE for dynamic harmonic motion
• Use SPREAD for strummed or arpeggiated chords
• Use DEG for harmonic modulation elsewhere
• Combine manual clicking with clocked movement

Troubleshooting
• No sound: patch CV + GATE correctly
• Too random: increase ENGINE
• Too static: increase RANGE or modulate BIAS
• No timing variation: increase SPREAD

Specifications
• Tonnetz-based harmonic navigation
• Manual node interaction
• Strum engine with NOTE output
• Memory-based harmonic behavior
• 3× CV outputs + NOTE output
• Gate and Accent outputs
• Full CV control over movement parameters

About the Tonnetz
The Tonnetz (German for “tone network”) is a theoretical harmonic map that represents pitch classes in a geometric grid. Neighboring nodes correspond to simple musical intervals such as perfect fifths and thirds. Triangles within the grid naturally form triads, and movement across the grid preserves common tones, resulting in smooth harmonic transitions.

F_TONNTZ transforms this concept into a playable system, allowing real-time navigation of harmonic space with consistent voice leading and musical coherence.