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Orbifold.py

00001 '''
Copyright 2005 by Michael Gogins.

A concise geometric approach to common operations
in pragmatic music theory,
for use in score generating algorithms.

When run as a standalone program,
displays a model of the voice-leading space
for trichords and can orbit a chord through
the space, playing the results using Csound.

Voice-leading space is an orbifold of chords
with one dimension per voice, voices ordered by pitch,
pitch measured in tones per octave,
and a modulus equal to the range of the voices.
I.e., it is a complete Tonnetz.
Root progressions are motions more or less up and down
the 'columns' of identically structured chords.
The closest voice-leadings are between the closest chords in the space.
The 'best' voice-leadings are closest
first by 'smoothness,' and then by 'parsimony' (see below).

Based on: Dmitri Tymoczko, _The Geometry of Musical Chords_, 2005
(Princeton University).
'''
print __doc__
import gc
import operator
import sys
import traceback
import time
import random
import sets
import threading
import copy
import collections
from visual import *
from numpy import *
import Image
import ImageGrab
import ImageOps
import psyco

import csnd
import CsoundAC
'''
Represents operations on chords in a voice-leading orbifold.
Chords can actually have more dimensions than voices,
but voice-leading operations affect only the specified number of voices,
which can be a lower subspace of the orbifold.
This is to enable using the lower subspace of chords to represent pitches,
and the higher subspace to represent other properties of music;
e.g. [0:4] can be a tetrachord, [4:8] durations, [8:12] loudnesses, and so on.
'''
class Tonnetz(object):
    def __init__(self, voiceCount=3, cubeOctaveCount=2,octaveCount=3, tonesPerOctave=12, isCube=False, isPrism=False, isNormalPrism = False, debug=False):
        self.N = voiceCount
        self.octaveCount = octaveCount
        self.tonesPerOctave = tonesPerOctave
        self.isCube = isCube
        self.isPrism = isPrism
        self.isNormalPrism = isNormalPrism
        self.debug = debug
        self.R = self.tonesPerOctave * self.octaveCount
        self.NR = self.N * self.R
        self.cubeOctaveCount = cubeOctaveCount
        self.cubeTessitura = self.tonesPerOctave * self.cubeOctaveCount
        self.cubeRadius = 0.075
        self.prismRadius = self.cubeRadius * 2.0
        self.normalPrismRadius = self.prismRadius #* 2.0
    def getTessitura(self):
        if self.isCube:
            return self.cubeTessitura
        else:
            return self.R
    def sort(self, chord):
        c = array(chord, Float).copy()
        d = c[0:self.N]
        d.sort()
        c[0:self.N] = d
        return c
    def tones(self, chord):
        c = array(chord, Float).copy()
        for i in xrange(self.N):
           c[i] = c[i] % self.tonesPerOctave
        return self.sort(c)
    def zeroFormModulus(self, chord):
        c = array(chord, Float).copy()
        for i in xrange(self.N):
           c[i] = c[i] % self.tonesPerOctave
        m = min(c)
        for i in xrange(self.N):
            c[i] = c[i] - m
        return c
    def zeroForm(self, chord):
        c = array(chord).copy()
        m = min(c[:self.N])
        for i in xrange(self.N):
            c[i] = c[i] - m
        return c
    def range(self, chord):
        c = chord[0:self.N]
        return max(c) - min(c)
        #c = self.sort(chord).copy()
        #return c[self.N-1] - c[0]
    def firstInversion(self, chord):
        inversions = self.rotations(chord)
        inversionDistances = {}
        origin = []
        for i in xrange(self.N):
            origin.append(0.)
        for inversion in inversions:
            zi = self.zeroForm(inversion)
            #z = float(sum(zi)) / float(self.N)
            d = self.euclidean(zi, origin)
            if self.debug:
                print 'distance %f zeroform %s inversion %s' % (d, zi, inversion)
            inversionDistances[d] = inversion
        return inversionDistances[min(inversionDistances.keys())]
    def zeroFormFirstInversion(self, chord):
        return self.zeroForm(self.firstInversion(chord))
    def equalTones(self, a, b):
        a = self.tones(a)
        b = self.tones(b)
        if a == b:
            return True
        else:
            return False
    def inversions_(self, tones, iterating_chord, voice, inversions):
        if voice >= self.N:
            return
        if self.isPrism:
            beginning = -self.getTessitura() * 2
            end = self.getTessitura() * 2
        elif self.isCube:
            beginning = -self.getTessitura()
            end = self.getTessitura()
        p = beginning
        increment = 1.0
        while p < end:
            if self.pitchclass(p) == tones[voice]:
                iterating_chord[voice] = p
                increment = self.tonesPerOctave
                si = self.sort(iterating_chord)
                if self.isInside(si, self.getTessitura()):
                    ic = tuple(si.tolist())
                    inversions.add(ic)
                self.inversions_(tones, iterating_chord, voice + 1, inversions)
            p = p + increment
    def inversions(self, chord):
        inversions = sets.Set()
        tones = self.tones(chord)
        iterating_chords = self.rotations(tones)
        for iterating_chord in iterating_chords:
            voice = 0
            self.inversions_(tones, iterating_chord, voice, inversions)
        l = list(inversions)
        for i in xrange(len(l)):
            l[i] = array(l[i])
        return l
    def euclidean(self, a, b):
        ss = 0.0
        for i in xrange(self.N):
            ss += ((a[i] - b[i]) ** 2.0)
        return math.sqrt(ss)
    def voiceleading(self, a, b):
        v = []
        for i in xrange(self.N):
            v.append(b[i] - a[i])
        return v
    def areParallel(self, a, b):
        return CsoundAC.areParallel(a,b)
##        if self.debug:
##            v = self.voiceleading(a, b)
##        for i in xrange(self.N):
##            if v.count(v[i]) > 1:
##                for j in xrange(self.N):
##                    if i != j:
##                        if (math.fabs(a[i] - a[j]) == 7) and (math.fabs(b[i] - b[j]) == 7):
##                            if self.debug:
##                                print a, b, v, 'parallel fifth'
##                            return True
##        return false
00185     def smoothness(self, a, b):
        L1 = 0.0
        for i in xrange(self.N):
            L1 += math.fabs(b[i] - a[i])
        return L1
    def smoother(self, source, destination1, destination2, avoidParallels=False):
        s1 = self.smoothness(source, destination1)
        s2 = self.smoothness(source, destination2)
        if avoidParallels:
            if self.areParallel(source, destination1):
                return destination2
            if self.areParallel(source, destination2):
                return destination1
        if s1 <= s2:
            return destination1
        else:
            return destination2
    def simpler(self, source, destination1, destination2, avoidParallels=False):
        v1 = self.voiceleading(source, destination1)
        v1 = sort(v1)
        v2 = self.voiceleading(source, destination2)
        v2 = sort(v2)
        for i in xrange(self.N - 1, -1, -1):
            if v1[i] < v2[i]:
                return destination1
            if v2[i] < v1[i]:
                return destination2
        return destination1
    def closer(self, source, destination1, destination2, avoidParallels=False):
        if avoidParallels:
            if self.areParallel(source, destination1):
                return destination2
            if self.areParallel(source, destination2):
                return destination1
        s1 = self.smoothness(source, destination1)
        s2 = self.smoothness(source, destination2)
        if s1 < s2:
            return destination1
        if s1 > s2:
            return destination2
        return self.simpler(source, destination1, destination2, avoidParallels)
    def closest(self, source, destinations, avoidParallels=False):
        d = destinations[0]
        for i in xrange(1, len(destinations)):
            d = self.closer(source, d, destinations[i], avoidParallels)
        return d
    def isFirstInversion(self, chord):
        return tuple(self.zeroForm(chord)) == tuple(self.zeroFormFirstInversion(chord))
    def rotate(self, a, n=1):
        l = a.tolist()
        for i in xrange(n):
            tail = l.pop(self.N - 1)
            l.insert(0, tail)
        return array(l, Float)
    def invert(self, chord):
        chord = array(chord)
        c = chord[1:self.N].tolist()
        c.append(chord[0] + self.tonesPerOctave)
        d = chord.copy()
        d[0:self.N] = c
        return d
    def rotations(self, chord):
        chord = self.tones(chord)
        rotations = [chord]
        for i in xrange(1, self.N):
            #chord = self.rotate(chord, i)
            chord = self.invert(chord)
            rotations.append(chord)
        return rotations
    def isInside(self, chord, range):
        if self.isPrism:
            return self.isInFundamentalDomain(chord)
            #return self.isInsidePrism(chord, range)
        else:
            return self.isInsideCube(chord, range)
    def isInsideCube(self, chord, range):
        for i in xrange(self.N):
            if chord[i] < -range/2.0:
                return False
            if chord[i] >  range/2.0:
                return False
        return True
    def isInsideNormalPrism(self, chord, range):
        if not self.isInsidePrism(chord, range):
            return False
        if self.isFirstInversion(chord):
            return True
        return False
    def layer(self, chord):
        return sum(chord[0:self.N])
    def isInsidePrism(self, chord, range):
        if chord[0] < -range:
            return False
        elif chord[0] > range:
            return False
        for i in xrange(1, self.N):
            if chord[i] > chord[0] + range:
                return False
            elif chord[i] < chord[0]:
                return False
        s = sum(chord[0:self.N])
        if 0 <= s and s <= range:
            return True
        else:
            return False
    def isInFundamentalDomain(self, chord):
        if self.isInLayer(chord) and self.isInOrder(chord):
            if self.debug:
                print 'Chord',chord,'in F'
            return True
        else:
            if self.debug:
                print 'Chord',chord,'not in F'
            return False
    def isInLayer(self, chord):
        L = self.layer(chord)
        if not (0 <= L and L <= self.R):
            return False
        return True
    def isInOrder(self, chord):
        for i in xrange(self.N - 1):
            if not chord[i] <= chord[i + 1]:
                return False
        if not chord[self.N - 1] <= (chord[0] + self.R):
            return False
        return True
    def O(self, c):
        if self.debug:
            print "O: ",c,
        r = []
        for i in xrange(1, self.N):
            r.append(c[i] - (self.R / self.N))
        r.append(c[0] + (self.R - (self.R / self.N)))
        c[0:self.N] = r
        if self.debug:
            print c
        return c         
    def keepInside(self, chord):
        if self.isInFundamentalDomain(chord):
            return chord
        else:
            inversions = self.inversions(chord)
            if self.debug:
                print inversions
            for inversion in inversions:
                if self.isInOrder(inversion):
                    c = list(inversion)
                    for i in xrange(self.N):
                        if self.isInLayer(c):
                            return array(c)
                        c = self.O(c)
            return None
    def stayInside(self, chord):
        if self.isInside(chord, self.getTessitura()):
            return chord
        chord = self.sort(chord)
        if self.isPrism:
            inversions = self.inversions(chord)
            if self.debug:
                print 'inversions',inversions
            distances = {}
            for inversion in inversions:
                distances[self.euclidean(chord, inversion)] = inversion
            c = distances[max(distances.keys())]
            if self.debug:
                print 'keepInside:', 't =',self.getTessitura(), 'original =',chord, 'inside =',c
            return c
        else:
            c = array(chord)
            for i in xrange(self.N):
                while c[i] <  -self.getTessitura()/2:
                    c[i] += self.getTessitura()
                while c[i] >= self.getTessitura()/2:
                    c[i] -= self.getTessitura()
            c = self.sort(c)
            if self.debug:
                print chord,'keeps inside as',c
            return c
    def pitchclasses(self, chord):
        c = array(chord, Float).copy()
        for i in xrange(self.N):
            c[i] = self.pitchclass(chord[i])
        return c
    def pitchclass(self, pitch):
        return pitch % self.tonesPerOctave
    '''
    Returns the best bijective voice-leading,
    first by smoothness then by parsimony,
    optionally avoiding parallel fifths,
    from a given source chord of pitches
    to a new chord of pitches
    that belong to the pitch-class set of a target chord,
    and lie within a specified range.
    The algorithm makes an exhaustive search
    of potential target chords in the space.
    '''
    def voicelead(self, a, b, avoidParallels):
        if self.debug:
            print '   From:', a
            print '     To:', b
            print 'Through:'
        invs = self.inversions(b)
        if self.debug:
            for inv in invs:
                print '        ',inv
      c = self.closest(a, invs, avoidParallels)
        if self.debug:
            print '(%d inversions) is:' % len(invs)
            print '        ', c
            print 'Leading:', self.voiceleading(a,c)
        return c
    def label(self, chord):
        c = array(chord[0:self.N])
        return 'C   %s\nT   %s\n0   %s\n1   %s\n0-1 %s\nSum %f' % (c, self.tones(c), self.zeroForm(c), self.firstInversion(c), self.zeroFormFirstInversion(chord), sum(chord[0:self.N]))
        
class TonnetzModel(Tonnetz):
    def __init__(self, octaveCount=1, tonesPerOctave=12, isCube=False, isPrism=True, isNormalPrism=False, doCycle=False, showFirstInversion=False, doConnect=False, enableCsound=False, debug=False, showUnordered=False):
        Tonnetz.__init__(self, 3, octaveCount=octaveCount, tonesPerOctave=tonesPerOctave, isCube=isCube, isPrism=isPrism, isNormalPrism=isNormalPrism, debug=debug)
        self.trichords = {}
        self.balls = {}
        self.ballsForChordTypes = {}
        self.doConnect = doConnect
        self.doCycle = doCycle
        self.showUnordered = showUnordered
        self.showFirstInversion = showFirstInversion
        self.firstInversions = []
        self.enableCsound = enableCsound
        if self.enableCsound:
            self.csound = csnd.CppSound()
        if self.isCube:
            for x in xrange(-self.cubeTessitura/2, self.cubeTessitura/2):
                for y in xrange(-self.cubeTessitura/2, self.cubeTessitura/2):
                    for z in xrange(-self.cubeTessitura/2, self.cubeTessitura/2):
                        trichord = (x,y,z)
                        radius = 0.125
                        if trichord not in self.trichords:
                            self.trichords[trichord] = trichord
                            ball = sphere(pos = trichord, radius = self.cubeRadius)
                            ball.trichord = trichord
                            self.balls[ball.trichord] = ball
                            self.setColor(ball)
                            ball.name = self.label(trichord)
                            ball.label = label(pos = trichord, text = ball.name, height = 11, box = 2, opacity = 0.3, linecolor=(0.5,0.5,0.5), visible = 0, line = 1, xoffset = 20, yoffset = 20)
        if self.isPrism or self.isNormalPrism:
            for x in xrange(-self.R, self.R+1):
                for y in xrange(x, x + self.R+1):
                    for z in xrange(x, x + self.R+1):
                        trichord = array((x,y,z), Float)
                        trichord = tuple(self.sort(trichord))
                        if self.isPrism and self.isInsidePrism(trichord, self.R):
                            if trichord not in self.trichords:
                                self.trichords[trichord] = trichord
                                tones = tuple(self.tones(trichord))
                                ball = sphere(pos = trichord, radius = self.prismRadius)
                                ball.trichord = trichord
                                self.balls[ball.trichord] = ball
                                self.setColor(ball)
                                ball.name = self.label(trichord)
                                ball.label = label(pos = trichord, text = ball.name, height = 11, box = 2, opacity = 0.3, linecolor=(0.5,0.5,0.5), visible = 0, line = 1, xoffset = 20, yoffset = 20)
                            else:
                                self.balls[trichord].radius = self.prismRadius
                        if self.isNormalPrism and self.isInsideNormalPrism(trichord, self.R):
                            if trichord not in self.trichords:
                                self.trichords[trichord] = trichord
                                tones = tuple(self.tones(trichord))
                                ball = sphere(pos = trichord, radius = self.normalPrismRadius)
                                ball.trichord = trichord
                                self.balls[ball.trichord] = ball
                                self.setColor(ball)
                                ball.name = self.label(trichord)
                                ball.label = label(pos = trichord,  text = ball.name, height = 11, box = 2, opacity = 0.3, linecolor=(0.5,0.5,0.5), visible = 0, line = 1, xoffset = -20, yoffset = 20)
        
                            else:
                                self.balls[trichord].radius = self.normalPrismRadius
        if self.doConnect:
            for trichord in self.trichords.values():
                self.connect(trichord, self.sort((trichord[0] + 1.0, trichord[1], trichord[2])))
                self.connect(trichord, self.sort((trichord[0], trichord[1] + 1.0, trichord[2])))
                self.connect(trichord, self.sort((trichord[0], trichord[1], trichord[2] + 1.0)))
                self.connect(trichord, self.sort((trichord[0] - 1.0, trichord[1], trichord[2])))
                self.connect(trichord, self.sort((trichord[0], trichord[1] - 1.0, trichord[2])))
                self.connect(trichord, self.sort((trichord[0], trichord[1], trichord[2] - 1.0)))                  
    def setColor(self, ball):
        z = tuple(self.zeroFormFirstInversion(ball.trichord))
        if z in self.ballsForChordTypes:
            ball.color = self.ballsForChordTypes[z].color
        else:
            # Color major triads red.
            if   z == (0, 4, 7):
                ball.color = (1.0,0.0,0.0)
            # Color augmented triads white.
            elif z == (0, 4, 8):
                ball.color = (1.0,1.0,1.0)
            # Color minor triads blue.
            elif z == (0, 3, 7):
                ball.color = (0.67,0.67,1.0)
            else:
                hue = (z[0] + z[1] * 2.0 + z[2]) / 44.0
                saturation = 1.0
                value = 1.0
                ball.color = color.hsv_to_rgb((hue, saturation, value))
    def showAsFirstInversion(self, trichord):
        if not self.showFirstInversion:
            return False
        elif self.isFirstInversion(trichord):
            return True
        else:
            return False
    def connect(self, origin, neighbor):
        o = tuple(origin)
        n = tuple(neighbor)
        if n in self.trichords:
            curve(pos = [o, n], color = (0.65, 0.65, 0.65))
    def runGrab(self, filename, bbox=None):
        while scene.visible:
            if scene.mouse.clicked:
                print 'CURRENT POINT:'
                print 'center =',scene.center
                print 'forward =',scene.forward
                print 'up =',scene.up
                print 'scale =',scene.scale
                print 'fov = ',scene.fov
                print
                try:
                    if bbox:
                        image = ImageGrab.grab(bbox)
                    else:
                        image = ImageGrab.grab()
                    #image = ImageOps.grayscale(image)
                    image.save(filename)
                    print 'Captured screen shot in "%s".' % (filename)
                except:
                    traceback.print_exc()
                scene.mouse.events = 0

    def run(self):
        pickedBall = None
        oldBall = None
        movingChord = ( 0, 4, 7)
        movingChord = tuple(self.sort(movingChord))
        translation = (1,1,1)
        while scene.visible:
            if scene.mouse.clicked:
                try:
                    m = scene.mouse.getclick()
                    if oldBall:
                        oldBall.label.visible = 0
                    if pickedBall:
                        pickedBall.label.visible = 0
                    oldBall = pickedBall
                    pickedBall = m.pick
                    if pickedBall:
                        pickedBall.label.visible = 1
                        note1 = "i 2 0 4 %d 70 0 -.75" % (60 + pickedBall.pos[0])
                        note2 = "i 2 0 4 %d 70 0  .0"  % (60 + pickedBall.pos[1])
                        note3 = "i 2 0 4 %d 70 0  .75" % (60 + pickedBall.pos[2])
                        print '%s\n%s\n%s' % (note1, note2, note3)
                        if self.enableCsound:
                            self.csound.inputMessage(note1)
                            self.csound.inputMessage(note2)
                            self.csound.inputMessage(note3)
                        print
                except:
                    traceback.print_exc()
                    print self.label(movingChord)
                scene.mouse.events = 0
            elif self.doCycle:
                try:
                    movingBall = self.balls[movingChord]
                    movingBall.label.visible=1
                    print movingBall.name
                    time.sleep(2)
                    movingBall.label.visible=0
                    a = (movingChord[0], movingChord[1], movingChord[2])
                    print 'Old chord',a
                    movingChord = (movingChord[0] + translation[0], movingChord[1] + translation[1], movingChord[2] + translation[2])
                    print 'New chord',movingChord
                    #movingChord = self.voiceLead(a, b, True)
                    movingChord = tuple(self.keepInside(movingChord))
                    print 'New chord inside',movingChord
                    note1 = "i  2 0 4 %d 70 0 -.75" % (60 + movingBall.pos[0])
                    note2 = "i  2 0 4 %d 70 0  .0"  % (60 + movingBall.pos[1])
                    note3 = "i  2 0 4 %d 70 0  .75" % (60 + movingBall.pos[2])
                    print note1
                    print note2
                    print note3
                    if self.enableCsound:
                        self.csound.inputMessage(note1)
                        self.csound.inputMessage(note2)
                        self.csound.inputMessage(note3)
                    print
                except:
                    traceback.print_exc()
                    print self.label(movingChord)
                    return
        print "Finished."

def runModel(model):
    began = time.clock()
    scene.background = (1,1,1)
    scene.background = (0,0,0)
    scene.autocenter = 1
    sort(model.firstInversions)
    if model.enableCsound:
        model.csound.setPythonMessageCallback()
        model.csound.setOrchestra('''
sr=44100
ksmps=100
nchnls=2

iafno ftgen 3,          0,    4097,       10,   1, .4, .2, .1, .1, .05
iafno ftgen 41,   0,    65537,      10,   1 ; Sine wave.
iafno ftgen 42,   0,    65537,      11,   1 ; Cosine wave. Get that noise down on the most widely used table!

instr 2 ; Heavy metal model, Perry Cook
; INITIALIZATION
ioctave                 =                       p4 / 12.0 + 3.0
iattack           =                 0.01
idecay                  =                 2.0
isustain          =                 p3
irelease          =                 0.125
p3                =                 iattack + idecay + isustain + irelease
iindex                  =                 1
icrossfade        =                 3
ivibedepth        =                 0.02
iviberate         =                 4.8
ifn1              =                 41
ifn2              =                 3
ifn3              =                 3
ifn4              =                 41
ivibefn           =                 42
ifrequency        =                 cpsoct(ioctave)
iamplitude        =                 ampdb(p5) * 20.0
ijunk6                  =                 p6
; Constant-power pan.   
ipi               =                 4.0 * taninv(1.0)
iradians          =                 p7 * ipi / 2.0
itheta                  =                 iradians / 2.0
; Translate angle in [-1, 1] to left and right gain factors.
irightgain        =                 sqrt(2.0) / 2.0 * (cos(itheta) + sin(itheta)) * iamplitude
ileftgain         =                 sqrt(2.0) / 2.0 * (cos(itheta) - sin(itheta)) * iamplitude
ijunk8                  =                 p8
ijunk9                  =                 p9
ijunk10           =                 p10
ijunk11           =                 p11
; AUDIO
adecay0           expsegr           1.0, iattack, 2.0, idecay, 1.1, isustain, 1.001, irelease, 1.0, irelease, 1.0
adecay                  =                 adecay0 - 1.0
asignal                 fmmetal           0.1, ifrequency, iindex, icrossfade, ivibedepth, iviberate, ifn1, ifn2, ifn3, ifn4, ivibefn
                  outs              ileftgain * asignal * adecay, irightgain * asignal * adecay
endin
            ''')
        model.csound.setScore('''
            f1 0 8192 10 1
            f0 600
            e
            ''')
        model.csound.setCommand('csound -h -d -r 44100 -k 441 -m128 -b100 -B100 -odac6 temp.orc temp.sco')
        model.csound.exportForPerformance()
        gc.disable()
        model.csound.compile()
        performanceThread = csnd.CsoundPerformanceThread(model.csound)
        performanceThread.Play()
    fg = (1,1,1)
    arrowcolor = (0.7,0.7,0.7)
    size = model.getTessitura() * 1.125
    shaftwidth = model.cubeRadius * 1.0
    arrow(pos = (0,0,0), axis=(size/3,0,0), fixedwidth=1, shaftwidth=shaftwidth, color = arrowcolor)
    label(pos = (size/3,0,0), text = 'Voice 1', color=fg, height = 20, box = 0, linecolor=(0.5,0.5,0.5), opacity = 0.1, visible = 1, line = 0, xoffset =  5, yoffset =  5, zoffset = 5)
    arrow(pos = (0,0,0), axis=(0,size/1.5,0), fixedwidth=1, shaftwidth=shaftwidth, color = arrowcolor)
    label(pos = (0,size/1.5,0), text = 'Voice 2', color=fg, height = 20, box = 0, linecolor=(0.5,0.5,0.5), opacity = 0.1, visible = 1, line = 0, xoffset =   5, yoffset = 5, zoffset = 5)
    arrow(pos = (0,0,0), axis=(0,0,size), fixedwidth=1, shaftwidth=shaftwidth, color = arrowcolor)
    label(pos = (0,0,size), text = 'Voice 3', color=fg, height = 20, box = 0, linecolor=(0.5,0.5,0.5), opacity = 0.1, visible = 1, line = 10, xoffset = 5, yoffset = 5, zoffset = 5)
    arrow(pos = (0,0,0), axis=(size/2.5,size/2.5,size/2.5), fixedwidth=1, shaftwidth=shaftwidth, color=arrowcolor)
    label(pos = (size/2.5,size/2.5,size/2.5), text = 'Orthogonal axis', color=fg, height = 20, box = 0, linecolor=(0.5,0.5,0.5), opacity = 0.1, visible = 1, line = 0, xoffset = 5, yoffset = 5, zoffset = 5)
    ended = time.clock()
    elapsed = ended - began
    print 'elapsed: %f' % (elapsed)
    model.run()
    print 'Visual finished.'
    if model.enableCsound:
        performanceThread.Stop()
        print 'Csound finished.'
print 'Program finished.'
    

if __name__ == '__main__':
    scene.fullscreen = True
    # Tonnetz for trichords
    model = TonnetzModel(octaveCount=1, doCycle=False, doConnect=True, isPrism=True, enableCsound=True)
    # Ranged chord space
    #model = TonnetzModel(octaveCount=2, doCycle=False, doConnect=False, isCube=True, isPrism=False)
    # Tonnetz in ranged chord space
    #model = TonnetzModel(octaveCount=1, doCycle=True, doConnect=False, isPrism=True, isCube=True)
    # Voice-leading space
    #model = TonnetzModel(octaveCount=3, doCycle=True, doConnect=False, isPrism=True, isNormalPrism=False)
    # Normal chord space
    #model = TonnetzModel(octaveCount=3, doCycle=False, doConnect=False, isPrism=False, isNormalPrism=True)
    # Normal chord space in voice-leading space
    #model = TonnetzModel(octaveCount=3, doCycle=False, doConnect=False, isPrism=True, isNormalPrism=True)
    runModel(model)


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