Update: This page:
MIDIUSB - Arduino Reference
Says "This library allows any microcontroller with native USB capabilities (atmega32u4 based boards or ARM boards) to appear as a MIDI peripheral over USB to a connected computer."
It does list compatibility with a much wider range of boards (including Nano) but I think that is a bit misleading because, although it will compile on those boards, it won't actually work! It goes on to say "
Note: while the library is supposed to compile correctly on these architectures, it might require specific hardware features that may be available only on some boards."
A Teensy 2.0 should work, and it appears ARM boards should also.