#! /usr/bin/env python

# Create JI scales based on divisions

import sys

from math import gcd

def fractions(n):
    """ Return all irreducible fractions between 1 and 2 with denominator n """
    return[(x,n) for x in range(n+1,2*n) if gcd(x,n) == 1]

def rational(x):
    """ Map a pitch to a rational number """
    return float(x[0])/float(x[1])

try:
    limit = int(sys.argv[1]) + 1
except IndexError:
    print(f"Usage: {sys.argv[0]} <integer>")
    sys.exit(1)
except ValueError:
    print(f"Could not parse {sys.argv[1]} as integer")
    sys.exit(2)

# fractions(n) excludes the octave, so we add it manually
pitches = [(2,1)]
for denominator in range(limit):
    pitches += fractions(denominator)

# Print scala file
print(f"{len(pitches)} tone ji scale")
print(len(pitches))
for (x,y) in sorted(pitches, key=rational):
    print(str(x) + "/" + str(y))