[music-dsp] What is the waveform with even harmonics called

Didier Dambrin didid at skynet.be
Wed Jun 17 20:38:46 EDT 2009

> So, in summary,
> At first it seems unusual that we have names for simply defined wave forms 
> such as:
> sawtooth wave = even + odd harmonics falling off at 6dB/octave
> square        = odd harmonics falling off at 6dB/octave
> triangle wave = odd harmonics falling off at 12dB/octave
> But that we don't have a counterpart to square and triangle for even
> harmonics. But, upon further examination it makes more sense. The
> above waveforms (as well as sine)
> 1. sound fairly distinct

triangle isn't much interesting, sounds like a slighty saturated sine

> 2. are close to other fairly primative shapes (squares, triangles, 
> circles)

that's pretty much the only reason IMHO

> 2. are not trivially generated by simple additions of two existing 
> waveforms (ie, not easy to create on a two oscillator synth)

square can be computed out of saws

> The waveform with even harmonics falling off at 6dB/octave has none of
> these properties:
> 1. it sounds like a sawtooth with a sine-wave sub-osc an octave down
> 2. it looks really funny
> 3. it is trivial to recreate using a normal two oscilator synth
> And, in fact, when creating the matlab code, my code initially had a
> bug where it did not include the 'fundamental' frequency, and so I
> just got out a sawtooth wave. :p
> As for wanting a name -- it makes it easier to search on google for a
> waveform that has a name versus one that does not. But, in this case,
> it seems like a very uninteresting waveform anyway.
> I was curious about it, because I have seen many people claim that
> people prefer distortion that provides even order harmonics instead of
> odd order harmonics. So, it seemed amiss that there was not a common
> waveform with only even order harmonics...
> (Actually, I did create a different wave with even order harmonics --
> namely the fully-rectified sine wave).
> Thanks!
> - jeremy
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