This plugin is for generating a tone consisting of a fundamental frequency and its harmonics, with the harmonics’ amplitudes specified by the user and allowed to vary over time.

The “Decay Coefficients” parameter is used to determine the timbre, and expects a (possibly deep) list of positive numbers.

The numbers specify a power law which describes how fast the harmonics attenuate according to frequency.

For example, entering “(2)” will produce a tone where amplitude decays with the square of frequency: the second harmonic is four times as quiet as the fundamental, the third is nine times as quiet, and the fourth sixteen.

If several terms are entered, the tone will interpolate smoothly between the specified timbres. For example, entering “(2) (5.72) (2)” will produce a tone that starts relatively bright, is dimmest after one third of the duration, returns to its normal brightness by two thirds of the duration, and remains bright until the end.

If a given list has k sublists, this is interpreted as specifying what happens to every kth harmonic. For example, entering “(2 4.2)” will produce a tone where the even harmonics are louder than the odd harmonics. Entering “(2 4 3)” has the 0 mod 3 harmonics loudest, the 2 mod 3 harmonics quieter, and the 1 mod 3 harmonics quietest.

This list may be arbitrarily deep. For example, “((5 (4 2)) 3)” gives the following relative amplitudes for each harmonic:

```
Harmonic Frequency Amplitude Amplitude
1 440 1^-5 1.000000
2 880 2^-3 0.125000
3 1320 3^-4 0.012345
4 1760 4^-3 0.015625
5 2200 5^-5 0.000320
6 2640 6^-3 0.004630
7 3080 7^-2 0.020408
8 3520 8^-3 0.001953
```

The remaining parameters are more self explanatory.

“Pitch (Steps)” specifies the MIDI pitch of the tone, where 69 is 440Hz, and an increase of 1 increases the pitch by one semitone.

“Length (Seconds)” specifies the length of the tone in seconds.

“Vibrato Speed (Hz)” specifies the frequency of the sine LFO which modifies the pitch. The vibrato applied to the entire tone, i.e. the harmonics are still harmonics of the fundamental frequency. If this is set to 0, no vibrato is applied. If this is set higher than the *control-srate* (one twentieth of the sample rate by default), aliasing artifacts may occur.

“Vibrato Depth (Hz)” specifies the depth of the vibrato.

ADDITIVE3.ny (5.24 KB)