Note that, for a given n, we have split up the n^2 points in the square into a bunch of cycles (or orbits), of which the Fibonacci sequence forms the main part, or "melody". The other orbits provide the "accompaniment". Below are all the orbits for n = 2 to n = 8. We have turned these orbits into music using the following arbitrary substitution (and we have chosen a basepoint in each orbit):

Major: 0 = C, 1 = D, 2 = E, 3 = F, 4 = G, 5 = A, 6 = B, 7 = C

n = 2:    (0)    (0, 1, 1)

Listen mod 2

n = 3:    (0)    (0, 1, 1, 2, 0, 2, 2, 1)

Listen mod 3

n = 4:    (0)    (0, 1, 1, 2, 3, 1)    (2, 2, 0)    (0, 3, 3, 2, 1, 3)

Listen mod 4

n = 5:    (0)    (0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1)    (1, 3, 4, 2)

Listen mod 5

n = 6:    (0)    (0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1)    (0, 2, 2, 4, 0, 4, 4, 2)    (0, 3, 3)   

Listen mod 6

n = 7:    (0)    (0, 1, 1, 2, 3, 5, 1, 6, 0, 6, 6, 5, 4, 2, 6, 1)    (0, 2, 2, 4, 6, 3, 2, 5, 0, 5, 5, 3, 1, 4, 5, 2)    (0, 3, 3, 6, 2, 1, 3, 4, 0, 4, 4, 1, 5, 6, 4, 3)

Listen mod 7

n = 8:    (0)    (0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1)    (0, 4, 4)    (0, 2, 2, 4, 6, 2)    (0, 6, 6, 4, 2, 6)    (0, 3, 3, 6, 1, 7, 0, 7, 7, 6, 5, 3)    (1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2)    (1, 4, 5, 1, 6, 7, 5, 4, 1, 5, 6, 3)

Listen mod 8