Sitting in on some undergraduate composition lectured this year, using it as a chance to brush up on some things I was never formally taught. This is particularly beneficial to my knowledge of acoustic contemporary composition (as opposed to the electroacoustic side of things). Yesturday I sat in on a lecture on Maxwell Davies’ use of Magic Square number patterns in *Ave Maris Stella* (1975; chamber ensemble). I wrote a little python script to generate any odd-order sized square (*n*), and a the values with modulo wrap (where modulo = *n*):

`# MAGIC SQUARES CALCULATOR`

# solves magic square for odd-ordered grid sizes

# owmtxy 17/10/2012

# for python v.2.6.6

```
```n = int(input("Enter (odd) order size (n): "))

square = []

def calculateSquare(row,col):

val = n*((row+col-1+(n/2))%n) + ((row + (2*col)-2)%n)+1;

return val

#Create Array

print "Magic",n,"*",n,"Square Array:"

for i in range(n):

for j in range(n):

square.append(calculateSquare(i+1,j+1))

# Print array in a nice n*n grid

for k in range(n):

print square[k*n:(k*n)+n]

print "n Modulo",n,"Array:

#Create Array of modulo values

modSquare = []

for i in range(n):

for j in range(n):

modulo = (calculateSquare(i+1,j+1)%n)

modSquare.append(modulo)

`# Print array in a nice n*n grid`

for k in range(n):

print modSquare[k*n:(k*n)+n]

To model Maxwell Davies’ use somewhat, a regular *n *x *n *grid is drawn up, and a melody of length *n* is written to the top row of the grid. Each row is then transposed (using the interval of that top-line melody), the pitch of cell *i* comes from cell *i-(n-1)*. In a 7×7 grid, the starting pitch of the second row (cell 8), comes from cell 2. Our magic square layout is then used to re-map these cells into a new order, giving us a magic square of pitch classes.

My plan is to use this grid in conjunction with some form of cellular automata to select or ‘activate’ cells of the magic square.