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Subharmonic or Undertone Series

The harmonic series, or the overtone series is pretty simple. You have a fundamental frequency. The harmonics go upward in whole number multiples of that frequency. All of the overtones fit neatly "inside" the fundamental.

If you think of it as a rhythm, the fundamental is a beat, and each overtone is 2 per beat, 3 per beat, 4 per beat going up and up. As you continue to add overtones eventually you end up with a sawtooth wave.

The subharmonic series, or the undertone series is way more problematic. You have a fundamental frequency. The subharmonics go down from there, first is 1/2 the fundamental, then 1/3, 1/4, 1/5 and so on.

If you think if this as a rhythm, the fundamental is a beat. Then you have 2 beats (1/2 rate) then 3 beats (1/3 rate) then 4 beats (1/4 rate), etc. As you continue to add undertones, you don't end up with a pure wave at all. You end up with a strong attack, where all the waves are initially aligned (starting together), but they they spread out and disperse, never looping, ever.

I built a 48 wave subharmonic tone, and did some experiments with it. At a high frequency, it sounds like an 808 cymbal.

I really love the sound of subharmonic tones. I was messing with Reaktor's Subharmonic. The dumb thing is that it only gives you 4 sines. Would love to see an additive synth with a subharmonic mode. I'll add it to the list.
Just had an interesting thought to take the undertone series, and "invert" it. In essence, this would involve taking each subharmonic and moving it up in octaves until it is roughly the same distance above the fundamental as it was below.

Did a little test. Sounds cool, and actually does sound pretty similar-- especially in that it has a kind of minor-triad kind of sound.
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