[sdiy] Additive Synthesis questions

[David G. Dixon]

> Arrgghhh!

Well, Ian, that'll learn ya!  :)

But seriously, folks, why do we have to use the (certainly possible, yet
undeniably inconvenient) sine wave for additive synthesis?  The triangle
wave has only odd harmonics in proportion to 1/n^2 (i.e., the fundamental at
1, the 3rd harmonic at 1/9, the 5th harmonic at 1/25, the 7th harmonic at
1/49, etc...).  Indeed, 80% of its amplitude is just the fundamental.
Hence, it would seem as if one could just about use unfiltered triangles to
build up more complex waveforms with only minor error.  Plus, triangles are
fairly easy to divide (simply rectify, double and shift), which means that
one would only have to generate the odd multiples of any given frequency.

Of course, once you've got a bunch of tuned triangle waves, it's pretty
trivial to shape them into sines...