%matplotlib inline

import pylab as pl
import matplotlib as mpl

from pylab import cos, sin

def plot_circle():
    circle = mpl.patches.Circle((0, 0), radius=1, fill=False)
    a = pl.gca()
    a.add_patch(circle)
    pl.xlim(-1.1, 1.1)
    pl.ylim(-1.1, 1.1)
    a.set_aspect('equal')
    a.set_axis_off()

def annotate_and_label():
    note_labels = ['1', 'b2', '2', 'b3', '3', '4', 'b5', '5', 'b6', '6', 'b7', '7']
    
    for i in range(12):
        theta = pl.pi/2 - 2 * pl.pi / 12. * i
        x, y = cos(theta), sin(theta)
        #pl.plot((0, x), (0, y))
        pl.plot((x), (y), 'ok', )
        pl.annotate(note_labels[i], (x, y), (1.15 * x, 1.15 * y))

def plot_note(note, with_line=False):
    note = note % 12
    theta = pl.pi/2 - 2 * pl.pi / 12. * note
    x, y = cos(theta), sin(theta)
    # plot line before point
    if with_line:
        pl.plot((0, x), (0, y), '-k')
    # plot point
    pl.plot((x), (y), 'o', markeredgecolor='blue', markeredgewidth=10)
    

plot_circle()
annotate_and_label()
plot_note(2)
plot_note(7, with_line=True)

# setup diagram
plot_circle()
annotate_and_label()

# plot chord
major7_chord = [0, 4, 7, 11]
for note in major7_chord:
    plot_note(note, with_line=True)

pl.figure(figsize=(10, 10))
for i in range(4):
    pl.subplot(2, 2, i + 1)
    plot_circle()
    annotate_and_label()
    
    chord = map(lambda note: (note - major7_chord[i]) % 12, major7_chord)  
    for note in chord:
        plot_note(note, with_line=True)
    pl.title('Inversion %s' % (i + 1))
#pl.tight_layout(pad=0.8)