Now, I transformed my attic keyboard rig in a small-but-slowly-growing-up project studio, so I bought all the things I need, including Ableton Live.
I connected the MIDI ports of the Phatty to the audio interface's ones, and generally it works fine, but (omitting the sustained note problem) the Phatty plays only one of three notes.
Yes, if I (or Ableton) play three notes, only one of these will actually sound.
This is as interesting as annoying

I disconnected the MIDI cables... and... it's still so!!

Because I live in Italy, I'm dying to send my synthesizer to the Moog factory, I hope there will be a solution...
Thank you so much, have a nice day everybody!
