experimental tinnitus sound treatment

I actually was making a microcontroller program that would make sounds like this: the REAL way to do it would be to take a couple of seconds of gaussian white noise, and then to filter out the frequencies that aren't desired. But the microcontroller only has 192 bytes of RAM so that's impossible. To distinguish between 11 Hz and 1/23 of an octave above that, one needs at least 3 seconds of time in the sample. And then sufficient analog to digital bits to be reasonable, and then to take the fourier transform. So I tried to generate the same sound with some sort of cheat. What I tried to do was generate Morlet wavelets. Specifically, the 1 Hz fundamental kernal would be: sigma=.019303707455951 gaussian windowed sine=sin(2*pi*t)*e^(-2*pi^2*sigma^2*t^2) where t goes from about -25 to +25, and then that kernel (or "atom" as morlet called it) would be compressed by a factor of 11 to 24000 to be whatever randomly chosen frequency was chosen next, chosen randomly between 11 Hz and 24 kHz, by a random variable which is uniform on a logarithmic frequency scale. And then finally, 4 of them would be played simultaneously at any moment. And the idea was, that there would be 256 user-settable values - 23 per octave - where the user could have each of those frequency components present or absent, or present in 1/4 power intensity or present in 1/16 power intensity. The windowing of the "atom" is chosen so that the power is approximately uniformly represented: that is, it isn't just 23 well defined and isolated tones per octave, but that the bandwidth of each one would be about 1/23 octave so that the in-between frequencies would be about equally strong as the center frequencies. I thought I finally had found the perfect application for my many PIC16C63 chips, that used all its RAM and various features without being wasteful. Unfortunately when I simulated the output using matlab, this sounded very silly and I was actually hoping it would much more closely approximate gaussian white noise, so no dice. But hey. Maybe it is actually weird in a good way. So tell me what you think in comments. Also, if you have the means to modify the sound to your particular case of tinnitus, that is, filtering out certain frequencies at will, by all means try it. Although it obviously isn't gaussian white noise, it has the same frequency magnitude spectrum one would expect out of gaussian white noise that is bandlimited between 11 and 24000 Hz and then amplified inversely in proportion to the square root of the frequency (so that it is the same power per octave across all frequencies.