Use a boolean: when reaching the size, if boolean is false, play the note and set the boolean to true. Reset it to false when the shape decreases.

Ok, so that makes sense. I understand the concept (kinda). I do not really know how to construct a boolean. Any good guides for this or can anybody explain please?

Well, I would search boolean word in the Reference...

It's like this :

1. Square square = new Square(10.0,10.0,10,10,76.0,true);
2. class Square { 
3.   float ex, wy;
4.   int nex, nwy;
5.   float area;
6.   boolean runonce;
7.   Square(float W, float H) {
8.     area = 50;
9.     ex = W;
10.     wy = H;
11.   }
12.   void display() {
13.     if (runonce) {
14.       starttime=millis();
15.       if (starttime+millis()<5000) {
16.         area = area + sin(frameCount/16);       
17.         fill(0);
18.         strokeWeight(10);
19.         stroke(130);
20.         rectMode(CENTER);
21.         rect(ex, wy, area, area);
22.         myBus.sendNoteOn(1, 36, 70);
23.       }
24.     }
25.     fill(0, 121, 184);
26.     strokeWeight(10);
27.     stroke(130);
28.     rectMode(CENTER);
29.     rect(ex, wy, area, area);
30.   }
31. }
32. void setup() {
33.   square.display();
34. }

I can't run this code because the constructor is wrong and i miss several other things. But i think you understand what i mean.