Yes, I am using a mixer for the sound effects. How would I link a MIDI device up to the Mixer, though? I don't see any "getTransmitter" or "getReceiver" methods (or any MIDI-related methods) for the Mixer or Line classes. I don't see "getMixer" or "setMixer" methods (or any Mixer or Line related methods) for the MIDIDevice, Sequencer, or Synthesizer classes either. The Mixer appears to be only used for mixing Lines, which are instances either of DataLine (SourceDataLine, TargetDataLine, or Clip) or Port (compact disks, headphones, audio input jacks, audio output jacks, microphones, or speakers).
I'll do some more searching on this though, to see if MIDI can somehow be routed through a mixer. At the moment, the only way I know how to do it is by converting the MIDI sequence into an AudioInputStream context (which is what Gervill does).