Pythagoras Loop V1.0.1.

                                                                                         Pythagoras Loop

                                                                                           Hear the Mathematics

Pythagoras Loop is a generative mathematical synthesizer in which melodies and rhythms are created by functions, geometric shapes, number sequences, chaotic systems, and bitwise operations.

Choose a mathematical formula, adjust its variables, and watch an abstract equation transform into a scale-quantized musical sequence.

Pythagoras Loop is not a conventional random generator. Every system is deterministic: the same settings always produce the same recognizable structure. This makes it more than an experimental instrument—it is a repeatable source of melodies, evolving patterns, and complete compositional ideas.

94 Mathematical Systems

Pythagoras Loop includes five distinct formula families:

Waves – wave functions, harmonic systems, and quasiperiodic motion

Geometry – circles, spirals, Lissajous curves, cycloids, and parametric shapes
Sequences – Fibonacci, Lucas, Tribonacci, Collatz, prime numbers, and many more
Chaos – Logistic, Hénon, Lorenz, Rössler, and other chaotic systems

Bitwise – XOR, AND, OR, cellular automata, and bytebeat-inspired structures

Each family has its own meaningful variables and controls. The interface shows the active formula, its equation, its current values, and a detailed explanation of how each variable influences both the mathematical shape and the generated music.

From Formula to Melody

Every mathematical output passes through a flexible musical mapping system:

Formula → Traversal → Mapping → Scale Quantizer → Gate → Synthesizer

You can control:

- root note and musical scale;
- note and octave range;
- sequence length and playback rate;
- formula traversal;
- pitch, gate, and velocity sources;
- value shaping, folding, wrapping, and mapping.

Alongside Forward, Reverse, and Ping Pong playback, Pythagoras Loop includes unusual traversal methods such as Golden Jump, Prime Jump, and Bit Reverse.

The mathematics provides the structure. You decide how that structure becomes music.

See What You Hear

The Live Mathematical Output displays the active formula, generated sequence, and currently playing step in real time.

A dedicated vintage-style X–Y Oscilloscope follows the actual mathematical coordinates. A Circle traces a circular path, a Lissajous formula draws its characteristic curve, and chaotic systems reveal the movement of their attractors.

A glowing phosphor point moves through the coordinate system, leaving a softly fading trail behind it. You are not simply watching an audio waveform—you are seeing the mathematics that creates the music.

Drag the Sequence into Your DAW

When a formula produces the right musical idea, there is no need to recreate it manually.

Use the Drag MIDI control in the display and drop the complete sequence directly onto your DAW timeline.

Notes, rests, timing, note lengths, and velocity values are exported as a fully editable MIDI clip. Continue arranging it, assign it to another instrument, or use it as the foundation of an entirely new track.

Pythagoras Loop is a synthesizer, an idea generator, and a composition tool in one instrument.

A Focused, Pure Sound Engine

The sound engine was designed to reproduce mathematical structures with clarity, precision, and a smooth musical character.

- two precision sine oscillators;
- individually switchable second oscillator;
- musical interval and fine-tuning controls;
- multimode 12/24 dB filter;
- dedicated amplitude and filter envelopes;
- delay and reverb;
- clean, carefully controlled signal path;
- 24-voice polyphony.

There are no unnecessary layers or oversized modulation systems. The focus remains on the formula, the sequence, and the purity of the resulting sound.

Made for Exploration

Pythagoras Loop is designed for:

- electronic music producers;
- ambient and cinematic composers;
- trance, techno, and experimental artists;
- sound designers;
- anyone curious about generative systems and mathematical music.

You do not need to be a mathematician.

Choose a formula. Change its variables. Hear what the equation has been hiding.