...
String note = gn.getGeneratedNote();
final int key = gn.getGeneratedKey();
                
ap.setMeasureArguments(note, 0, false); // класс extends JPanel
ap.repaint(); // нарисовать ноту
                
Thread t = new Thread(new Runnable() {
       public void run() {
        new PlayNote().play(key, instr); // проиграть ноту
    }
});
t.start();
...

import javax.sound.midi.*;

public class PlayNote {

	void play(int note, int instrument) {
		
		try {
			Sequencer sequencer = MidiSystem.getSequencer();
			sequencer.open();
			
			Sequence seq = new Sequence(Sequence.PPQ, 5);
			Track track = seq.createTrack();
			
			ShortMessage msg1 = new ShortMessage();
			msg1.setMessage(ShortMessage.PROGRAM_CHANGE, 0, instrument, 0);
			MidiEvent me1 = new MidiEvent(msg1, 1);
			track.add(me1);
			
			ShortMessage msg2 = new ShortMessage();
			msg2.setMessage(ShortMessage.NOTE_ON, note, 100);
			MidiEvent me2 = new MidiEvent(msg2, 1);
			track.add(me2);
			
			ShortMessage msg3 = new ShortMessage();
			msg3.setMessage(ShortMessage.NOTE_OFF, note, 100);
			MidiEvent me3 = new MidiEvent(msg3, 16);
			track.add(me3);
			
			sequencer.setSequence(seq);
			sequencer.start();
			Thread.sleep(2000);
			sequencer.close();
		} catch(Exception e) {
			e.printStackTrace();
		}
	}
}