https://www.youtube.com/watch?v=gTOKDwQ97wI

It evolved from simple observations such as:

arcsin(sin(x))*(2/pi) = triangle wave which swings in range (-1,1)

arctan(cot(x))*(2/pi) = sawtooth wave which swings in range (-1,1)

which I then conceptually extended to compound (nested) expressions like these:

sin(atan(2*sin(a*tanh(b*tan(x)))))

sin(8*atan(1/sinh(a*tan(x))))

asin(cos(a*tanh(b*tan((x)))))*(2/pi)

tanh((a*cos(a*atan(b*sin(x)))))

which produce a wide range of interesting, evolving sounds both IMO 'FMish' in character, and otherwise. You can see one of the comments to the video re this technique:

Effectively this IS FM synthesis with operators sequentially modulating the phase of each other. Just you have access to other functions than sin

hmm...am interested in anything you can offer to reasonably explain from a mathematical standpoint the similarity AND the differences between 'traditional FM', phase distortion/modulation, and the above technique