#!/usr/bin/env python
# Calculate frequency intervals for Bach tuning for Aeolus.
# Aeolus's temperament specifications start on C (element 9 is A).
# Based on the chart on:
#  http://www-personal.umich.edu/~bpl/larips/index.html

comma = ((3.0/2)**12) / (2.0**7)
rc = comma**(1.0/12)
# Rotated left one position to start on C.
adj = [-2, -2, -2, -2, 0, 0, 0, -1, -1, -1, 1, -2, -2]

out = [0] * 12

f = 1.0
for i in range(12):
	print "fifth", i, "=", f
	out[(7 * i) % 12] = f
	f = f * (3.0/2) * (rc**adj[i])
print "octave =", f

for i in range(12):
	while out[i] > 2.0:
		out[i] /= 2

for i in range(12):
	print "freq", i, "=", out[i] * (440.0 / out[9])

print "{"
print "    " + ",\n    ".join(map(str, out))
print "};"