How to procedurally generate basic percussive sounds (e.g. metronome like clicks)?

Question

I'm wondering if there are some standard techniques to procedurally generate basic percussive sounds like metronome like clicking sounds?

Regarding periodic sounds, I'm aware of many procedural techniques like mixing basic oscillating waveforms (sine, square, triangle, sawtooth) or frequency modulation synthesis.

Are there any similar basic techniques when it comes to percussive sounds?

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A naive approach would be to generate samples based on some kind of noise (white?) for a short, limited time window like 1 ms. This of course somehow produces a percussive sound, but it doesn't seem to be a commonly used sound that e.g. old electronic metronomes are using. I'm wondering if it is possible to formalize the waveforms that are typically used on metronome circuits.

Answer 1

I'm not familiar with electronic metronomes, but from the world of modular synthesizers, here are a couple of popular basic ingredients for synthesizing percussive sounds:

1. Use an attack-decay envelope generator which has a very short to nonexistent attack, and a decay suitable for the instrument. Shorter attacks create “click” sounds. This might be used to control the amplitude of white noise as you mention, or other parts of the sound.

2. “Ping” or “excite” a resonant filter. That is, send a very short, high amplitude signal (possibly the exact output of the above envelope generator!) into the audio input of a filter with high resonance. The filter will produce a decaying sine tone (decay time dependent on the resonance).

   This is in fact an electronic (or software) model of the very basic physics of an instrument which produces a specific pitch when struck. (Except that it has only the one “vibration mode” and almost no harmonics.)

Both of these produce very particular and artificial sounds, but you can combine multiple copies and/or both techniques, add modulation, other sound sources, etc.

The one general rule I would suggest is to make sure you are using simple decay or attack-decay envelopes. “Sustain” doesn't fit the physics — as the energy of the initial hit leaves the instrument as sound, the volume must continuously decrease.

Answer 2

Percussive sounds usually don't have harmonics, their texture is produced by frequencies which aren't multiples of each other. Let me explain. Say you have a sine wave at 440 hz which is decaying quickly because of an envelope. If you want to experiment with making percussive sounds, add more nodes with random frequencies (1234 hz, 5678 hz, or whatever as long as it isn't a harmonic and is decaying). This is one technique called "modal synthesis" which you can read about in some technical papers but there are others. You can generate kick, snare and other percussive sounds with FM synthesis. There is a good tutorial on YouTube about it. Cymbals are just different kinds of noise with envelopes. Ultimately, you can use any of these techniques to generate synth patches and different sounds. Realistically, if you want a metronome, just use a sample of a metronome.