@audio/synth-tonewheel-fit

Tonewheel registration from audio: a sustained organ note or chord → nine drawbars 0..8, percussion, scanner setting and a score

import fit from '@audio/synth-tonewheel-fit'

The inverse of synth-tonewheel. The keys fix which tonewheels can sound; each wheel's amplitude is tracked in its own band of a Hann STFT, reaching halfway to the neighbouring wheel and at most ±1.5 semitones, wide enough to hold the scanner's and a Leslie's frequency modulation. Nonnegative least squares against the organ model (a wheel carries the drawbars of every key that taps it) gives the nine levels, reweighted toward relative error because rooms and cabinets scale each partial; the levels then snap to the drawbar law in dB. Percussion hypotheses, 4' or 2⅔' at fast or slow decay, add a decaying column and drop the 1'. The scanner setting is read from how much of each wheel's energy stays in its carrier line: vibrato keeps sinc²(πfD) of it, chorus adds the undelayed half back.

let r = fit(audio, { freq: 261.63 })   // freq: [..] for a chord; omit it for one key
r.drawbars     // '888000000'
r.percussion   // null | { harmonic: 'third', decay: 'fast', volume: 'normal' }
r.vibrato      // null | 'v1' … 'c3'
r.score        // 0..1
r.levels       // fitted levels before rounding, 1 = drawbar at 8
r.keys         // MIDI keys analyzed

Levels are relative. A registration and the same one a few steps quieter differ only in gain, so without amp the fit returns the canonical form, loudest drawbar at 8, at the gain that puts every level closest to a tap.
The key. Without freq, the key is the pitch heard: of the keys whose wheels hold the spectrum, the lowest whose 8' sounds. 888000000 on C4 reads as 008880000 on C3, the same three wheels; pass freq to keep the organist's key. Chords need freq.
Foldback. Where two drawbars of a key reach one wheel, only their sum is audible; the level goes to the unfolded drawbar first.
Scanner. A Leslie on tremolo reads as vibrato: its rotor turns at 6.7 Hz, the scanner at 6.87 Hz. Vibrato changes no level, so the drawbars are unaffected.
Score. The share of the note's spectrum inside the wheel bands, times the share of the wheel tracks the rounded registration explains: 1.000 for the organ, 0.997 through reverb, 0.92 for a sawtooth (its 7th and 9th harmonics fall outside), 0.72 for the DX7's E.PIANO 1, 0.04 for white noise. It measures fit, not identity: any harmonic sound scores high.

Measured: random registrations on keys C3–C5, 1.5 s notes, 100 per row, node packages/synth-tonewheel-fit/bench.js from the family root:

The misses come from the effects, which color each partial by more than the ±1.5 dB between drawbar steps: the Leslie's crossover costs one mic up to 2 dB near 800 Hz, summing its two mics combs the horn band by up to 4.5 dB, and a room gives every steady partial its own ±1.7 dB. More keys average the room out; two mics beat one. A fit takes about 45 ms of CPU for a 1.5 s note.

Use when: naming the registration of a Hammond in a recording (the first rung of synth recognition), or checking a rendered registration.
Not for: the pedals or the lower manual, keys held with different registrations at once, or proving that a sound is a Hammond (see Score).

References

• C. L. Lawson, R. J. Hanson, Solving Least Squares Problems, Prentice-Hall, 1974, ch. 23: the NNLS active-set algorithm.
• Hammond Organ Company, Hammond Organ Service Manual, early models: Table III (keys to wheels) and "The Hammond Vibrato" (412 rpm scanner, about 1.5% shift at V3), via synth-tonewheel.
• L. Hammond, US Patent 1,956,350 (1934), p. 12: the matching-transformer taps behind the drawbar law.

Part of @audio/synth, the synth family umbrella.

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