The first video is a test of the Arduino Nano based Synthesizer I built. It takes MIDI input and generates an audio signal that can go to an amp.
I used the schematic referenced here to build the Midi input circuit.
The audio out uses just a couple capacitors and a resistor and is detailed in this Instructable link, and also in the comments of the library.
The Arduino Nano is running the example Midi sketch that is part of the_synth library on github.
The second video is a test of my synthesizer using a better midi example. This time I picked a midi file of some scales, and included the PC's output at the end using the TuxGuitar synthesizer Gervill.
I know there are some more parameters that can be set on the Arduino Synth, but I haven't messed with any yet. They might help clean up the sound some, but it sounds pretty neat as is.