Find the values of these recursive functions to produce a three-part number-one pop hit. Embelish with percussion if desired.

Each value of n is a different eighth-note. There are four measures, so compute the values of base(n), tenor(n) and alto(n) for the first 32 values of n (0 through 31). These four measures repeat forever. It is a really annoying melody that will be stuck in your head for twelve days.

You can write a program to produce the right values, or you can do it by hand. Below are recursively defined math functions (not C code).

First, the base and tenor part numbers represent half steps, where 0 is middle C. Therefore, -3 is A and 5 is F. 3 is E flat.

foundation(0) = 0 foundation(n) = 5 + foundation(n-1) m(n) = foundation(RoundDownToInteger(n/8)) base(n) = (( m(n) + 6 ) % 12) - 6 c(0) = 0 c(n) = 2 + c(n - 1) t(n) = c(n) % 6 tenor(n) = if RoundDownToInteger(n/8) is even, t(n % 8) + base(n) else base(n)Second, the alto part numbers are not half steps, but rather are positions along a major scale,

q(0,i,j,x) = x q(n,i,j,x) = if (j==0), q(n-1, i+1, i+1, (-1)x) else q(n-1,i,j-1,x) arrow(n) = q(n,0,0,-1) a(0) = 2 a(n) = a(n - 1) + arrow(n - 1) alto(n) = if RoundDownToInteger(n/8) is odd, a(n % 8) else 5

**Show your work.**
You get one point for producing the sequence of notes, or you can get two
points for performing (voice, whistle, or playing a tape of) the correct
tune in class on the day it is due.

Good luck, may the Force be with you, and don't forget to wear ear plugs.