Waldorf Quantum/Iridium: convert the vibrato and the tremolo of a source

[douglas-carmichael]

The Waldorf Quantum/Iridium was the last of the larger formats without any LFO support: a source which carries a vibrato or a tremolo lost it, and a preset of the device which has one was read without it. This adds both, in the creator and in the detector.

Where the modulation goes

The device has 6 low frequency oscillators and 40 modulation matrix slots. The slots 1-3 are already spent on the pitch envelopes of the three oscillators (createPitchEnvelopeModulator, keyed to the oscillator index), so the two new modulations take the next free ones:

Slot	Source	Destination	What
1-3	Free Env1-3	Osc1-3 Pitch	pitch envelopes, unchanged
4	LFO 1	Pitch (index 1)	vibrato
5	LFO 2	VCA (index 117)	tremolo

Nothing has to give way: 5 of 40 slots and 2 of 6 LFOs is the most this creator ever writes, so the slots 6-40 and the LFOs 3-6 stay free for the user.

The vibrato uses the destination Pitch, which moves all three oscillators at once, rather than one slot per oscillator. That is one slot instead of three, and it matches what a vibrato of a multi-sample is - a property of the whole instrument, not of one of its layers. Reading also accepts the per-oscillator destinations Osc1/2/3 Pitch, since a preset written on the device may well use them.

The tremolo uses the destination VCA, the amplifier of the voice. Its oscillator is written unipolar with a negative amount, so the modulation attenuates from the full level downwards. A bipolar oscillator would press the first half of every cycle against the upper end of the amplifier and leave only the rectified half of the waveform audible - which is why the two modulations cannot share one LFO, the vibrato needs the bipolar swing around the played note.

The laws

The waveform, rate, delay and fade-in are converted with the laws of the sound engine, read out of the Iridium MK2 firmware (4.0.5). The parameter registrar at 0x100BE938 names every QPAT parameter and hands it the function which formats its value; those formatters are the laws:

• rate: 1/240 Hz + (100 Hz - 1/240 Hz) * x^4 - the quartic gives 6.2539 Hz at the middle of the range, which is the default the manual documents, and 240 seconds at zero, which is the slowest speed it documents
• delay: 20 * x^2 seconds
• fade-in (the device calls it Attack): 10 * x^2 seconds
• shapes: [0] Sine [1] Triangle [2] Square [3] Saw (down) [4] Saw (up) [5] S&H - a one-to-one map onto LfoWaveform

The vibrato depth converts the model's cent scale (IEnvelope.MAX_ENVELOPE_DEPTH) to the ±24 semi-tones one matrix slot reaches. The tremolo depth is scaled with the loudness law of the device (dB = 40*log10(x), the one Osc{n}Vol already uses), so a depth of 6 dB is an amount of -29.21 % and the maximum depth of the model, 96 dB, is -99.60 % - the swing from the full level down to silence, i.e. the end of the range of a slot. That the two ends coincide is the reason for using that law.

Every parameter the modulation depends on is written explicitly (Speed, Sync, Global, Shape, Polarity, Phase, Delay, Attack, Decay), so the result does not depend on what the previously loaded preset left in that oscillator.

Two things are deliberately not carried:

• An oscillator of a read preset which is synchronized to the tempo of the song is skipped - its speed is a note length, and a multi-sample carries no tempo with which that could be converted into Hertz.
• The key sync flag of the model is not written; both oscillators are always written in the Poly mode. No source format fills that flag today, so honouring its false default would put every converted preset on a free-running, voice-shared LFO, which is not what a vibrato or a tremolo of a sampled instrument does.

What was verified

In software, with a build of this branch:

• SFZ -> QPAT: every written value matches the firmware laws by hand-calculation (rate 5.5 Hz -> 0.48418677, delay 0.25 s -> 0.1118034, fade-in 1.5 s -> 0.38729835, 50 cents -> +2.08 %, 6 dB -> -29.21 %).
• SFZ -> QPAT -> SFZ: Tremolo: 4.00 Hz, depth 6.0 dB, delay 0.100 s, fade-in 0.800 s and Vibrato: 5.50 Hz, depth +50 cents, delay 0.250 s, fade-in 1.500 s come back identically (the analysis details of -ad).
• QPAT -> QPAT is a fixpoint: 44 parameters in, 44 out, zero differences.
• All six waveforms round-trip through QPAT -> QPAT.
• Edge cases, on hand-patched presets: a disabled slot reads nothing; a tempo-synchronized oscillator reads nothing; a free phase is not read; a vibrato on Osc2 Pitch is correctly not applied to oscillator 1; a full-range tremolo reads back as exactly 96 dB; an over-range source is clamped (-9600 cents -> the -2400 the device can reach, 120 Hz -> 100 Hz, a 40 s delay -> 20 s).
• No regression: a source without LFOs writes no Lfo* and no Matrix* parameter at all, and the 141 presets of an Iridium library read with zero errors and zero spurious vibrato or tremolo - none of them routes an LFO to Pitch or VCA.

Not verified on hardware: the scale of the VCA destination. The modulation matrix is additive in the destination's own normalized units (ModMatrix::calc at 0x100A1884: dest += source * (2*amount - 1), clamped), but the consumer which turns the VCA slot into a gain is not in the part of the firmware I decoded, so how many dB an amount of 100 % actually attenuates is inferred from the device's level law rather than read out of it. Everything else above is either firmware-exact or a round-trip result. I have an Iridium MK2 and can check the tremolo depth against the device.

Base

Branched on top of #367 (Waldorf Quantum/Iridium: keep the instant attack of a percussive sound), which touches the same creator - that PR's commit is the first of the two here. Merging #367 first leaves this one as a single commit.