A physical model was made of all the tunes in Deny Parsons’ Directory of Tunes. The Directory encodes tunes as a sequence of the letters, U, R, or D, according to whether the notes go up, repeat, or go down, with respect to the previous note. If we substitute +1, 0, -1 for U, R, D respectively, then let the Parsons number, S(n), be their sum up to the nth note. When the number of tunes with particular values of S for n = 1, 2, ...16, were counted for all the tunes in the Directory the results, seen in model form, showed a surprising checkerboard pattern. It is argued that the checkerboard is musically significant and arises because the distribution of repeating notes in tunes is non-random.