Perhaps minim could help

Basicaly, you could do it in Minim, but it's all a bit more complicated. Notes ain't the music - beside of the pitches you have to have some sound sources and additional tools for composing music out of these pitches.

There is a lot of audio sythesis and music composition programming languages out there (like SuperCollider, CSound, ChucK, PureData...) created especially for this purpose. Maybe one of them it's a better choice?

Remember as well that you can easily communicate Processing with other software (written by you in other languages or ready ones, like Ardour, FrutyLoops, Logic etc.) via MIDI or OSC. I use this aproach a lot (actually starting to write such thing - parts in Processing control parts in SuperCollider - right now for the theatre piece).

Another way to do it is with the MidiBus or RWMidi libraries, which allow you to generate notes at a relatively high level, kind of like a player piano roll.  I have posted a number of music examples (from a class I taught on the subject) here:

Thanks all,

1. import krister.Ess.*;
2. AudioChannel myChannel;
   TriangleWave myWave;
   Envelope myEnvelope;
   int numNotes = 200;
   int noteDuration = 500;
   float[] rawSequence ={293.6648, 293.6648, 329.62756, 329.62756,
   391.9955, 369.99445, 293.6648, 293.6648, 329.62756, 293.6648,
   439.99997, 391.9955, 293.6648, 293.6648, 587.3294, 493.8834,
   391.9955, 369.99445, 392.62756, 523.25116, 523.25116, 493.8834,
   391.9955, 439.99997, 391.9955};
3. void setup()
   {
     size(100,100);
     Ess.start(this);
     myChannel = new AudioChannel();
     myChannel.initChannel(myChannel.frames(rawSequence.length * noteDuration));
     int current = 0;
     myWave = new TriangleWave(480, 0.3);
     EPoint[] myEnv = new EPoint[3];
     myEnv[0] = new EPoint(0,0);
     myEnv[1] = new EPoint(0.25,1);
     myEnv[2] = new EPoint(2,0);
     myEnvelope = new Envelope(myEnv);
     int time = 0;
     for(int i = 0; i<rawSequence.length; i++)
     {
       myWave.frequency = rawSequence[current];
       int begin = myChannel.frames(time);
       int e = int(noteDuration*0.8);
       int end = myChannel.frames(e);
       myWave.generate(myChannel, begin, end);
       myEnvelope.filter(myChannel, begin, end);
       current++;
       time += noteDuration;
     }
     myChannel.play();
   }
4. void draw() {}
5. public void stop()
   {
     Ess.stop();
     super.stop();
   }