I'll add SynthEdit, because the demo version is fully-featured, intuitive, standalone and free.
If you just want to do it by numbers without interface, and get as mathematically crazy as you like, R has some simple "turn a timeseries to a wav file" libraries.
Also to add: quite a few ipad apps that let you sketch in either a wave form or a spectrum, then turn knobs on it like a synth. Addictive Synth is one that lets you draw spectra freehand; WaveGenerator lets you put in various surfaces or even pictures and "listen" to them. This specific method is called "Wavetable Synthesis".
Oh good catch, I had forgotten about that. Good product, but their website really, really needs an overhaul.
I should also have mentioned that Mathematica makes this sort of thing quite accessible as well, and if you can't afford it or are just a hobbyist they are pretty liberal with their student licensing. http://reference.wolfram.com/mathematica/guide/SoundAndSonif...
Just FYI editing the spectra is usually referred to spectral or additive sysnthesis.
Wavetable synthesis involves a table of single-cycle waveforms that you then sweep through, either manually or preferably with some sort of modulation source. The PPG Wave is the most famous case, and Ensoniq's Transwave technology was basically the same thing. Typically you'll start with 2 waves of completely different harmonic spectra and interpolate between them. IIRC there's a quite affordable PPG wave for iPad now from Wolfgang Palm (who is the authority on this method of synthesis).
I was forgetting for a moment the key part of wavetable was the sweep/interpolation. Silly me! The name of the Wolfgang Palm App is the Wavegenerator I mentioned above -- been playing with it a while, v. v. cool, but (as per your original comment) I can't stray to far from presets without sounding horribly metallic.
If you just want to do it by numbers without interface, and get as mathematically crazy as you like, R has some simple "turn a timeseries to a wav file" libraries.
Also to add: quite a few ipad apps that let you sketch in either a wave form or a spectrum, then turn knobs on it like a synth. Addictive Synth is one that lets you draw spectra freehand; WaveGenerator lets you put in various surfaces or even pictures and "listen" to them. This specific method is called "Wavetable Synthesis".