Last weekend I found about the aubio project. In their own words:
aubio is a library for audio labelling. Its features include segmenting a sound file before each of its attacks, performing pitch detection, tapping the beat and producing midi streams from live audio. [...]
In particular, one interesting piece of code is aubionotes. This script analyzes audio data and produces a midi output stream from it (what I was looking for!). I tried it out, but it turns that it wasn't as straightforward as I would have liked, because it works on top of the Jack audio server. What it does is to provide an audio input and a midi output, and transforms any audio data received into a midi stream.
I have been struggling against it until I realized how it was supposed to work (naturally, I came up with the idea on the way to work, so I had to wait the whole day to try it out). As it happens, I was on the (wrong) assumption that aubionotes would take the microphone input directly. It was after I fully understood how it wanted to interact with jack that I came to realize that I needed to use some software that would communicate with jack. So right after work I installed alsaplayer, recorded some audio, launched jack, launched aubionotes, connected mi midi keyboard, plugged everything together using qjackctl connections panel, and pressed 'play'. Oh what a joy! Midi notes were being played on my keyboard, trying to mimic what I had been singing. Even though a lot of extra notes were being played, I guess that's alright for a first experiment (and can be considered noise), the general idea of the tune I had sung could be heared being played in the keyboard.
Considering all the processing involved in order to convert voice to midi notes, I call this first experiment a success.
Now I have to figure out how to make jack use my microphone directly to capture live audio, so I don't have to pre-record it.