How can I start playing several wave-sounds at the same time? (e.g. playing a chord by playing 3 notes at the same time)

I want to write a program that plays different chords that are built up by 3 or 4 notes. For each note I have one wave-file. After clicking on a button the wave will be played at the same time so I can hear a full chord.

My first attempt was to use 3 different mediaplayer-components. It works, i will hear 3 different sounds at the same time, but they are not synchronized (it sounds like an arpeggio). The sounds don't start to play at exactly the same time. I suppose the problem is because of the "queue" im my procedure:

procedure play_chords;
begin
  ...
  mediaplayer1.play;
  mediaplayer2.play;
  mediaplayer3.play;
  ...
end;

Do you know any other (easy way) possibility?

It would be also okay, if someone could tell me how I can play several MIDI-Notes, but I don't really know how to use MIDI in delphi...