Pratt

Based on pratt-synth — the original Pratt-polynomial MIDI synthesizer and sonification code (Python, offline renderer, with the source paper and example recordings). Pratt is a real-time port of that work; the voice spectra match the original renderer to within 0.12 dB.

Opinion

An odd and likeable instrument: neighbouring keys have unrelated spectra because their indices factor differently, so a scale sounds slightly “alive” in a way ordinary filtered oscillators do not. The filter is gentler than it looks on paper — low indices are smooth low-passes, and the interesting territory is in the composites, where cascading Index A and Index B stacks poles in pairs that only the number theory predicts. Treat the drums as a bonus, not a kit.

Functionality

Pratt is a real-time port of the offline pratt-synth renderer. Everything comes from the Pratt polynomials: f_1 = 1, f_2 = x, f_p = 1 + f_{p-1} for odd primes, multiplicative otherwise, with f_n(2) = n. The filter

H_n(s) = n / f_n(2 + s/w0)

is all-pole, has unity gain at DC and is strictly stable (poles at least 0.99 w0 into the left half plane for every n up to 8192). Because H_m H_n = H_mn, two index controls cascade into one filter of index A x B.

Synth mode. Each note gets index n = (note + 1) x base; partial k of the note is weighted by k^-roll * H_n(i xi k) using both magnitude and phase, then summed into a band-limited table. Eleven families follow the General MIDI program (or can be fixed): piano, electric piano, organ, pluck, bass, strings, brass, reed, flute, pad and timpani. Sustain pedal, channel volume, expression, pan and pitch bend are handled; channel 10 plays procedural drums (a swept-sine kick, the rest noise through H_(note+1)). A fixed 14-tap diffuse room and a soft clip finish the voice path.

Timbre Index. A large Pratt base darkens a voice but also washes out the key-to-key variation, because the same factors are multiplied into every note. Timbre Index instead cascades one fixed filter H_timbre onto every note (H_mn = H_m H_n), so the character from (note + 1) x base stays and the chain only adds roll-off. It defaults to 1, which adds nothing; it is applied when a wavetable is built, so it costs no extra time per sample at any setting.

Filter mode. Audio in goes through the Pratt filter at the chosen cutoff with a dry/wet mix. The panel plots the magnitude response and the poles. Synth + Filter sums the voices and the audio input before the filter.

The voice wavetables are built on a background thread after the plugin is activated, so the first chord does not pay for them.

Parameters

Status

Core DSP, voice parity with the Python renderer (within 0.12 dB), deterministic core, engine, state and threading tests (the last also clean under ThreadSanitizer), the VST3 target and the catalogue screenshot are complete. Drum levels have not been tuned by ear, and host validation in REAPER remains.