Boltzmann

What is Boltzmann?

Boltzmann is a MIDI sequencer and arpeggiator that draws each note from an energy landscape. Instead of stepping through a fixed pattern, it assigns every pitch a probability based on its musical "energy": low-energy notes near the root are more likely, high-energy notes are rarer, and one Temperature control determines how sharply the system favors the ground state.

Cold settings make the sequence stable, tonal, and root-biased. Hot settings flatten the probability field, letting higher-energy tones appear more often. The result is a sequencer that can move from locked, minimal patterns to unstable melodic motion without abandoning the scale.

What's the mechanism?

Boltzmann is built around the Boltzmann distribution from statistical mechanics. In physical systems, the distribution describes how particles occupy energy states at a given temperature. Low-energy states are favored when temperature is low; higher-energy states become more accessible as temperature rises.

Boltzmann maps that idea onto pitch selection. Each possible note is treated as an energy state. The plugin weights those states according to their distance and dissonance from the root, then uses Temperature to control the probability curve. A partition function normalizes the field so the probabilities always sum correctly.

The histogram shows the distribution directly: turn Temperature down and the probability mass collapses toward the root; turn it up and the field spreads.

How do you use it?

Boltzmann can run as a sequencer, arpeggiator, or probabilistic MIDI generator. Set the scale, root, rhythm, and range, then use Temperature to control how adventurous the note selection becomes.

Cold temperatures produce grounded, repetitive patterns. Moderate temperatures create musical variation while preserving tonal center. Hot temperatures push the system toward wider melodic jumps and less predictable motion.

Additional controls shape the rhythm, octave behavior, density, and output feel, so the generator can act as a tight melodic engine, a sketching tool, or a controlled source of variation for synths and samplers.

Where does it fit?

Boltzmann works as a generative sequencer for melodic hooks, basslines, arpeggios, evolving ostinatos, and controlled randomness. It is useful when you want variation without fully random note choice, or when you want a sequence to feel like it is heating up, cooling down, freezing, or melting.

The mechanism is probability, not dice-roll randomness. Every note is chosen from a structured field, and Temperature gives you one musical control over how ordered or unstable that field becomes.

Boltzmann can be programmed into a project or played live as a performance sequencer.

Learn more at https://chiral.audio/boltzmann.