# Modulation

Modulation effects vary parameters over time using LFOs or envelopes.

## Vibrato

Vibrato modulates pitch with an LFO.

```forth
saw 5 vib 0.5 vibmod .       ( 5 Hz, 0.5 semitone depth )
```

| Parameter | Range | Description |
|-----------|-------|-------------|
| `vib` | Hz | LFO rate |
| `vibmod` | semitones | Modulation depth |
| `vibshape` | shape | LFO waveform (sine, tri, saw, square) |

## FM Synthesis

FM modulates the carrier frequency with a modulator oscillator.

```forth
sine 440 freq 2 fm 2 fmh .   ( modulator at 2× carrier frequency )
```

| Parameter | Range | Description |
|-----------|-------|-------------|
| `fm` | 0+ | Modulation index |
| `fmh` | ratio | Harmonic ratio (modulator / carrier) |
| `fmshape` | shape | Modulator waveform |

Use `env` to apply a DAHDSR envelope to FM depth: `0 5 0.01 0.1 0.3 0.5 env fm`.

## Amplitude Modulation

AM multiplies the signal by an LFO.

```forth
pad 4 am 0.5 amdepth .       ( 4 Hz tremolo )
```

| Parameter | Range | Description |
|-----------|-------|-------------|
| `am` | Hz | LFO rate |
| `amdepth` | 0-1 | Modulation depth |
| `amshape` | shape | LFO waveform |

## Ring Modulation

Ring modulation multiplies two signals, producing sum and difference frequencies.

```forth
saw 150 rm 0.8 rmdepth .     ( ring mod at 150 Hz )
```

| Parameter | Range | Description |
|-----------|-------|-------------|
| `rm` | Hz | Modulator frequency |
| `rmdepth` | 0-1 | Modulation depth |
| `rmshape` | shape | Modulator waveform |

## Phaser

Phaser sweeps notches through the frequency spectrum using allpass filters.

```forth
pad 0.5 phaser 0.6 phaserdepth .
```

| Parameter | Range | Description |
|-----------|-------|-------------|
| `phaser` | Hz | Sweep rate |
| `phaserdepth` | 0-1 | Sweep depth |
| `phasersweep` | cents | Sweep range |
| `phasercenter` | Hz | Center frequency |

## Flanger

Flanger mixes the signal with a short modulated delay (0.5-10ms).

```forth
pad 0.3 flanger 0.7 flangerdepth 0.5 flangerfeedback .
```

| Parameter | Range | Description |
|-----------|-------|-------------|
| `flanger` | Hz | Modulation rate |
| `flangerdepth` | 0-1 | Modulation depth |
| `flangerfeedback` | 0-0.95 | Feedback amount |

## Chorus

Chorus uses multiple modulated delay lines with 120° phase offset for stereo width.

```forth
pad 1 chorus 0.4 chorusdepth 20 chorusdelay .
```

| Parameter | Range | Description |
|-----------|-------|-------------|
| `chorus` | Hz | Modulation rate |
| `chorusdepth` | 0-1 | Modulation depth |
| `chorusdelay` | ms | Base delay time |