Question

I’ve searched the net but didn’t found anything interesting. Maybe I’m doing something wrong.

I’m looking for sound synthesis API written on C, C++ or even Objective-C, which can synthesize different types of waves, effects are optional.

Answer 1

Here’s a complete library/toolkit for FM (Frequency Modulation) synthesis:

link1
link2

If you have time to spare… creating simple sound synthesis from scratch is actually a fun endeavor. If you create a small buffer of 256 16 bit samples which represent either a sine. a sawtooth, block or pulse, you can copy these to a live audiobuffer (e.g. a small buffer (say 16kb)) which constantly loops. By staying ahead of the playposition, and constantly filling up the buffer with new values, you can create the soundoutput.
You can use the small buffers to combine these in interesting ways (simplest is just to add them together (additive synthesis)).

The frequency of the tone can be manipulated by using a bigger or smaller sampling step through the small buffers. Amplitude can be manipulated by scaling the samples before putting them into the output buffer.

Great fun experimenting with this!

If you have this step nailed, you can add more sophisticated effects like filters (low pass, high pass, etc) and effects (reverbs, echoes, etc)

R