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

Didier Dambrin didid at skynet.be
Wed Jun 17 09:45:01 EDT 2009


Even there you certainly can't rely on names because what's offered as a 
sawtooth in synths is quite often not a pure sawtooth, just something that 
sounds alike.



> It's worth remembering that sometimes in sound synthesis
> (and other engineering applications) it's the time domain
> properties of a wave that we are really interested in.
>
> For example, as a control waveform (say the sawtooth/phasor
> used as a display scanline) or if a sound synthesis design
> despends upon subsequent non-linear stages (waveshaping).
> In these cases we are interested in the shape, so classical
> waveform names are really about naming the shape.
>
> a.
>
>
> I don't see why waveforms would necessarily need a name.
>
> IMHO to generate any bandlimited (short) waveform efficiently, an inverse
> FFT is really the best choice. These days it's very little CPU.
>
> Then once you have direct access to harmonics & phases, you forget
> traditional (named) waveforms and you play with sound in a better way.
>
>
>
>
>
>> Hello,
>>
>> What is the name of the waveform which has even harmonics which fall
>> off at 6dB/octave?
>>
>> By comparison:
>>
>> 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
>>
>> You can see what it looks like using this matlab/octave code:
>>
>> # even wave
>> N = 2000;
>> t = ([0:1000] / 1000) * 4 * pi;
>> f = zeros (1,1001);
>> for k = [1,(1:2:N)+1]
>>  f = f + sin (k * t) / k;
>> end
>> f = f * 0.88678;
>> plot(t,f)
>> set(gca,'XTick',0:pi/2:4*pi)
>>
> set(gca,'XTickLabel',{'0','pi/2','pi','3pi/2','2pi','5pi/2','3pi','7pi/2','4pi'}
> )
>> grid on
>> axis normal
>>
>> Are there any nifty ways to generate this waveform efficiently?
>>
>> thanks!
>> - jeremy
>> --
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>
>
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