headphone-jack
------------------------
An easy hack: adding a switch to switch between speaker and headphone jack (I did not have a switching headphone jack) and leading the output from the LM386 through a 500Ohm-pot as master-volume control.

Pitch-bend
----------------
Toy-pianos usually have a resistor somewhere that defines the pitch (tone height). It can be found by shorting out random resistors with a 10-20KOhm resistor and checking whether the tone changes. I replaced the 100KOhm pitch resistor with a 500KOhm pot. A 50K resistor in row and a 500KOhm resistor parallel make sure that the resistance varies between 50K and 250K when I spin the knob.

Overdrive
--------------

A stereo headphone amp circuit taken from an under-a-DELL-monitor speaker is wired in a way that the output of one channel goes into the input of the other one. The gain-pot is between the two amps, the vol-pot after the second amp. I also changed the input-capacitors of the amps to larger ones to get more bass.  A capacitor to ground after a resistor acts as low-pass filter to get rid of too-aggressive noise.

reverb
----------

Two speakers taken from the aforementioned DELL-speaker are attached to a wooden rular. The membranes are attached to the side of a metal spring, which is put under tension. The spring is wound from old guitar strings. One speaker vibrates the spring and the other speaker acts as microphone to take up the vibrations.

A TDA2022-based amp from cheap multimedia speakers is used to power the reverb. One channel drives the speaker, the other channel amplifies the input from the speaker that acts as microphone. The gain-pot is a 500Ohm pot that adjusts the level from the mic-speaker, the volume-pot adjusts the output-level after the amp.
Video with a musical demonstration embedded above.