Thank you for answering! The links provided seem to be useful, but I'm too newbie to find the information I want.
Firstly, I intend to build the switch matrix. Then I will make all the necessary connections, and I will connect the MIDI OUT to a MIDI to USB converter (yeah! I've just found out that there's such a thing!). A USB port on my computer will be used to receive the binary information; that means that I need special software to covert the signals to sound, aren't I? As far as the multiplexing is concerned, I don't think that it is essential. This schematic requires 18 I/O pins on the Arduino, so there is no problem.
So, the problems are the following:
1.Do I need to download the MIDI library for the Arduino? If yes, how do I install it?
2.How can the signals from the 72 keys be converted to MIDI signals? What is the source code for this purpose? (I don't expect anybody to sit and write the whole code for me. That would be called "audacity". I just need some information, in order to learn how to do it on my own. Of course, I would refuse to accept any code...)
3.Is it possible to just convert MIDI to USB, without using any extra equipment? This site: http://arduino.cc/en/Hacking/MidiWith8U2Firmware put thoughts into my mind...
And I said previously: "Keep in mind that I want to be able to play chords (press two or more keys simultaneously) and I also want to hear the note produced for as long as I keep the key pressed, but fading a little bit as time passes" (this probably has to do with the source code - part)