CUBICUM SYNTH

CUBICUM SYNTH — A microtonal browser instrument built on the Z₇³ toroidal harmonic lattice.

WHAT IS IT?

Cubicum Synth is a synthesizer with no equal-temperament compromise. Every key maps to a precise node in a 343-point toroidal frequency lattice, where pitch is computed as:

f(x,y,z) = 256 × (3/2)ˣ × 2ʸ × (7/4)ᶻ

The three axes represent the perfect fifth, the octave, and the harmonic seventh. The space wraps toroidally — mod 7 in each dimension. This is not a plugin. This is not a DAW. This is geometry you can play.

HOW TO USE

Open in any modern browser. Press keys. Listen. No install, no account, no server. Runs offline.

BACKGROUND

The Z₇³ system was developed over approximately 20 years by Ion Piono, independent researcher from Iași, Romania, working under the Jahbalon Research brand. Published on Zenodo (DOI: 10.5281/zenodo.19853059), co-authored with Claude Sonnet 4.6 AI.

FOR WHOM?

— Composers interested in microtonality and alternative tuning

— Researchers in music theory or computational harmony

— Anyone curious what it sounds like when music is built from a torus, not a line

"E pur si torque." — And yet it rotates.

# CUBICUM SYNTH — User Manual

### Z₇³ Toroidal Harmonic Lattice · Jahbalon Research

---

## What is Cubicum Synth?

Cubicum Synth is a microtonal browser synthesizer built on the **Z₇³ harmonic lattice** — a 343-node toroidal frequency system where every note is a precise mathematical coordinate, not a compromise.

Every pitch is computed as:

```

f(x, y, z) = 256 × (3/2)ˣ × 2ʸ × (7/4)ᶻ

```

The three axes represent: **X** = perfect fifth (3/2), **Y** = octave (2), **Z** = harmonic seventh (7/4). The space wraps toroidally — mod 7 in each dimension. This is not equal temperament. This is geometry.

No install. No plugin. One HTML file. Runs in any modern browser, online or offline.

---

## Sections Overview

The interface is divided into six main sections, from top to bottom:

1. **MOTOR SONIC** — Synthesizer engine

2. **Active Note Display** — Current note info

3. **Oscilloscope** — Waveform visualizer

4. **GRID Z₇³** — Microtonal grid keyboard

5. **ORGĂ CROMATICĂ** — Chromatic piano keyboard

6. **RECORDER** — Recording and playback

7. **SEQUENCER** — Step sequencer

8. **PRESETS** — Save and load patches

---

## 1. MOTOR SONIC — Synthesizer Engine

The synth engine has two oscillators, a filter, envelope, LFO, and delay.

### Oscillator 1 (OSC)

| Control | Description |

|---|---|

| **WAVE** | Waveform shape: SIN (sine), SAW (sawtooth), SQ (square), TRI (triangle) |

| **FILT** | Filter type: LP (low-pass), HP (high-pass), BP (band-pass) |

| **CUT** | Filter cutoff frequency — controls brightness |

| **RES** | Filter resonance — adds emphasis at cutoff frequency |

| **FBK** | Delay feedback — how much the echo repeats |

### Envelope & Modulation (right column)

| Control | Description |

|---|---|

| **ATK** | Attack time — how fast the note fades in (Fibonacci steps) |

| **REL** | Release time — how fast the note fades out (Fibonacci steps) |

| **LFO** | Low Frequency Oscillator rate — modulates the filter for tremolo/wobble effects |

| **DLY** | Delay time — based on Pisano period mod 7 (mathematically derived from Z₇³) |

| **MIX** | Delay wet/dry mix |

> **Note on timing:** Attack, release, and delay times are not arbitrary — they follow **Fibonacci** and **Pisano(7)** sequences, keeping the temporal dimension consistent with the Z₇³ harmonic framework.

### Oscillator 2 (OSC 2)

Press **OFF** to toggle OSC 2 on. When active:

| Control | Description |

|---|---|

| **WAVE** | Independent waveform for OSC 2 |

| **DET** | Detune in cents — offsets OSC 2 from OSC 1 for chorus/thickening effect |

| **VOL** | OSC 2 volume mix |

---

## 2. Active Note Display

Shows the currently playing note in real time:

- **Note name** (e.g. A#0, C1)

- **Frequency** in Hz

- **Z₇³ coordinates** (x, y, z) — the exact lattice position

- **Color swatch** — each node has a unique color derived from its coordinates

---

## 3. Oscilloscope

Live waveform display. Shows the actual output signal shape as you play.

---

## 4. GRID Z₇³ — Microtonal Grid Keyboard

The main keyboard of the Z₇³ system. A 3×7 grid where:

- **Columns (X=0 to X=6)** = movement along the perfect fifth axis

- **Rows (Y=0, Y=1, Y=2)** = octave layers

- **Z axis** = selected at the bottom with buttons Z0–Z6

Each cell shows the note name and its exact frequency in Hz. Colors correspond to Z₇³ coordinates.

### Z Axis Selector

At the bottom of the grid: **Z0, Z1, Z2, Z3, Z4, Z5, Z6**

Switching Z values transposes the entire grid through the harmonic seventh dimension — accessing 7 complete layers of the toroidal space.

**Touch/click:** Tap any key to play it. On desktop, keys also respond to mouse hold.

---

## 5. ORGĂ CROMATICĂ — Chromatic Piano Keyboard

A standard-layout chromatic keyboard mapped to Z₇³ frequencies. Each key is colored according to its lattice position.

Useful for players familiar with traditional keyboard layout who want to explore Z₇³ tuning through a familiar interface.

**Swipe:** On mobile, you can swipe across keys for glissando-style playing.

---

## 6. RECORDER

Record, play back, and loop your performances.

| Button | Function |

|---|---|

| **REC** | Start recording — blinks pink while active |

| **PLAY** | Play back the last recording |

| **LOOP** | Toggle loop mode — recording plays continuously |

| **CLEAR** | Delete the current recording |

The **timeline** bar visualizes the recorded notes as colored blocks. The **playhead** (green line) shows current position during playback.

Below the timeline:

- **Duration** of the current recording

- **Number of notes** recorded

### Volume

The **VOL** slider at the bottom controls master output volume.

---

## 7. SEQUENCER

A step sequencer with up to 16 steps. Each step is a Z₇³ coordinate (x, y, z).

| Control | Function |

|---|---|

| **PLAY / STOP** | Start or stop the sequencer |

| **LOOP** | Toggle loop |

| **BPM** | Tempo in beats per minute |

| **CLEAR** | Reset all steps |

### Editing Steps

Each step shows its note name and color. Tap a step to select it, then use the **x / y / z** controls to change its pitch. Toggle **MUTE** on individual steps to create rhythmic patterns.

---

## 8. PRESETS

Save and reload complete synth states (oscillator settings + sequencer pattern).

- **SAVE** on any slot to store the current state

- **LOAD** to restore it

- Each preset shows a color swatch derived from the first sequencer step

- **EXPORT** — saves all presets as a `.json` file for backup or sharing

---

## Quick Start

1. Open the file in any modern browser (Chrome, Firefox, Safari, Edge)

2. Tap any key on the **GRID Z₇³** or the **piano** to hear a note

3. Adjust **CUT** and **RES** to shape the sound

4. Try different **Z values** (Z0–Z6) for different harmonic layers

5. Press **REC**, play a melody, press **LOOP** to loop it

6. Explore **OSC 2** for richer textures

7. Build a sequence in the **SEQUENCER** panel

8. Save your patch with **PRESETS**

---

## Technical Notes

- **No external dependencies** — everything runs from the single HTML file

- **Web Audio API** — all sound synthesis happens in the browser

- **Offline capable** — works without internet after first load

- **Mobile friendly** — touch support on all keyboards

- **Preset storage** — uses browser localStorage; presets persist between sessions on the same device

---

## About the Z₇³ System

The Z₇³ toroidal harmonic lattice was developed over approximately 20 years by **Ion Piono** (Jahbalon Research, Iași, Romania). The theoretical framework is published on Zenodo:

> **DOI: 10.5281/zenodo.19853059**

Co-authored with Claude Sonnet 4.6 (Anthropic) as computational research assistant.

*"E pur si torque."* — And yet it rotates.

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*Cubicum Synth is released as open research. Use freely. Build on it.*