Hello there!
Recently at work I had to do with the hyperbolic secant function
(sech(x) = 1/cosh(x)), which when plotted looks similar to a gaussian
function, (especially its square
https://www.rp-photonics.com/sech2_shaped_pulses.html) but with subtle
differences, namely stronger wings.
I had yoshimi's AddSynth in the back of my head and I wondered what
functions of this type sound like, especially when compared to the
Gaussian function. So I quickly hacked this function into the code (I
just replaced the basefunc_abssine so I wouldn't have to change the GUI
code, but below I renamed the function).
Generally speaking, the HypSec function sounds somewhat brighter than
the Gaussian function. The harmonic structure of its fundamental looks
interesting (to me): for parameters beween ~-16–63, it seems to be
linearly decreasing, while for parameters between -64–-15, it looks like
it's parabolically decreasing (if the attachment goes through: see
attachment).
I thought I'd share this little experiment with the mailing list.
float OscilGen::basefunc_hypsec(float x, float a)
{
x = (fmodf(x, 1.0f) - 0.5f) * expf(1.2f * (a - 0.2f) * logf(128.0f));
return 1.0f/coshf(x * PI);
}
Greetings,
Thomas
Attachment:
hypsecant.png
Description: PNG image
