Before posting I did a bit of research in the forum and I already read the MiniMonome page (you linked it somewere in the past forum). It was useful!
So I thought that my connection was ok, the three cathodes of each led are connected to the TLC5940 outputs. As I am trying a single column and three rows I have connected all my cathodes together (divised by colour: all the blue cathodes are connected to TLC output pin 0, all the green ones to output pin 1 and the red to 2) and the 3 positive are connected to arduino digital pins.
I am checking again your schematic but the only thing I miss is the mosfet on the positive line that I am not using because, for now, I am driving only a led at once...
I am going to post a picture of my actual connection. Or could it be a software related problem...
(Or the problem it's me 
)