Multiple tones with one piezo buzzer
First of all - You can drain max 20mA via pin, when one of the pins is HIGH and the other LOW, there is 5V between them, so there should be at least 250 Ohm resistor placed there, if you do not want damage your Arduino. I sugest add, to each of the red wires, at least a 200 Ohm resistor (to be safe).

For playing melody you have to save it somewhere, probabely easiest way is in arrays, and then play it note by note at regular intervals.

something like this (but insert your notes and set the length correctly):

int num_tones=6;
int tones1[] = {100,200,400,200,100,50};
int tones2[] = {262,131,131,262,131,524};

void loop() {
  for (int i=0;i&lt;num_tones;i++){
    analogWrite(buzzer1, tones1[i]);
    tone(buzzer2,tones2[i]);
    delay(250);
  }
}