I'll never forget a friend showing me a Japanese made DS-1 from 1983, which had all those pleasant artifacts stemming from the circuits non-ideal performance. Newer ones sound really harsh in comparison.
The DS-1 is itself surprisingly complex. I'm particularly a fan of the little hidden RC circuit in the clipping stage(here spanning from R14 to C10):
https://www.electrosmash.com/boss-ds1-analysis#layout
As said in section 6.3, its effect is only significant below the diodes' forward voltage. I exchanged one diode in my unit with a yellow LED (a diode is a diode, all in all) and it was particularly audible. Initially I thought it's the LEDs junction capacitance, but that measures in tens of picofarads - not nearly enough to register.