Ok, thanks to you I found the problem ! The 6n138 and 137 don't have the same wiring . I got it working with by correcting the connection of the opto isolator
(basically, it's pin 5 to ground, 6 to Rx , 1,5kO res between 6and 7, and 7,8 to +5Vcc, the other pins are the same as 138)

I still have speed issues. The datas are received, but at a very slow pace(about a good midi pack by second). Do you see any way to improve the speed, to get a more "real-time" application ?