At some point I was missing a sound where all harmonics have the same amplitude as generated by the opcode buzz buzz in Csound. That made me look into wavetable generation by code and I came up with a couple of wavetables included here: RZ.vitalbank (5.6 MB).
The wavetables differ by the selection of harmonics:
- Ultrasaw: all integers
- Ultrasquare: odd integers
- Squares: only square numbers
- Primes: fundamental + prime numbers
- Fibonacci: the Fibonacci series
- Weierstrass: only powers of two (The waveform is related to the Weierstrass function.) Combined with a bandpass filter this generates a Shepard tone Shepard tone - Wikipedia.
The wavetables consist of 256 frames * 2048 samples. The first frame has the constant amplitude harmonics I was originally looking for. The last one is always a pure sine. In between the amplitudes decrease by 1/f^x where frame #128 has x=1. So Ultrasaw[128] sounds exactly like a saw wave (although it looks different due to the phase randomisation), Ultrasquare[128] like a square wave, and Ultrasquare[171] roughly like a triangle wave.
If you are interested in the python code you can find it here: gen_wavet.zip (853 Bytes).
). Also the selection of harmonics could probably be done by using a conditional expression in line 4 but I guess to identify prime numbers would not work out of the box.