In the formula, the result of dividing the riddle answer by the element the arrow is pointing to is approximately the same than dividing the width of the card (red line) by the height (black line).
The card was designed with the golden ratio (1.618), this number can be calculated by dividing two consecutive Fibonacci numbers.
The melody is a sequence of 7 elements, numbers to be exact. The notes increase their duration following the Fibonacci sequence. The sixteenth note has a value of 1 (which is its usual value in computer music), therefore the 7 notes will be equivalent to 1, 1, 2, 3, 5, 8, 13.
The next fibonacci number is 13 + 8 = 21