That means we don't have f(x), we have f(g(x)).
f(x) is always a sine in case to Regency. And g is given by one "distortion shape". with three distortion shapes we actually have f(g(h(i(x))) ... ahhhhhh ... headaches!
If you want you can try out function composition, then let's go here:
Jump to symbolab.com
The link directly jumps to an interessting example, which is sin(tan(x)) ... Look at the graph. Parts of it resemble a sawtooth like form. In this example the g(x) is tan(x) ...
How can you transform this into Regency? How do you get a tangens shape into a distortion shap to start with? For now I have come up with a example to dial into the formula window: tan(-pi/2+0.2 + x*(pi-0.4))
For the math inclined. tan has an asymptotic value at -pi/2 and a periodicity of pi, therefore we must map the definition area of the distortion window which runs between [0, 1] to [-pi/2, pi/2] ... and we should better not use -pi/2 directly because asymptotic value means the y value goes to infinity... this is why I added the +0.2 part to result in -pi/2 + 0.2... and the -0.4.
If you choose smaler values, say for instance +0.05 and -0.1 then the shape get's different ... try it out.
Already there? No, not yet ... we have to shift phase of the oscillator about pi/2 which means we have to set the phase knob to 50%...
The result looks like a sawtooth ... but it's more of a softened version of it. Anyway hope this gives you some inspiration about how to deal with function composition
