owengc/MAT240E homework2 Secret

## MAT240E homework2
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      "# Owen Campbell\n",
      "# MAT 240E Homework 2\n",
      "#\n",
      "# For the purposes of this assignment, key modulations will be defined (rather naively) as follows: \n",
      "#     'parallel minor' - The first chord and the last chord are of the same scale degree, but change from major to\n",
      "#                        major to minor\n",
      "#     'parallel major' - The first chord and the last chord are of the same scale degree, but change from major to\n",
      "#                        minor to major\n",
      "#     'relative minor' - The root of the last chord is 9 semitones above the root of the first chord and\n",
      "#                        there is a shift from major to minor tonality\n",
      "#     'relative major' - The root of the last chord is 3 semitones above the root of the first chord and\n",
      "#                        there is a shift from minor to major tonality\n",
      "#     'submediant'     - The root of the last chord is 9 semitones above the root of the first chord but\n",
      "#                        there is no shift in tonality\n",
      "#     'mediant'        - The root of the last chord is 3 semitones above the root of the first chord but\n",
      "#                        there is no shift in tonality\n",
      "#     'subdominant'    - The root of the last chord is 5 semitones above the root of the first chord\n",
      "#     'dominant'       - The root of the last chord is 7 semitones above the root of the first chord\n",
      "#     'unknown'        - The first chord in the work differs from the last chord but the modulation does\n",
      "#                        not fall into any of the above categories\n",
      "#     'none'           - The first chord in the work does not differ from the last chord\n",
      "# Hypothesis: Since these are classical works, it is very likely that the majority of the pieces will \n",
      "#             involve a fairly predictable key modulation; specifically, one to a parallel, relative, \n",
      "#             dominant or subdominant key. I originally intended to process all the works in the corpus,\n",
      "#             but due to time constraints I am only using the Bach Chorales"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 131
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from music21 import *\n",
      "import ntpath\n",
      "import string"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# this function attempts to determine the interval, in semitones (+/-) between two pitches\n",
      "def degree_dif(start, end):\n",
      "    if start == end:\n",
      "        return 0\n",
      "    if end - start < 0:\n",
      "        return end - start + 12\n",
      "    else:\n",
      "        return end - start"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 129
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "core = corpus.CoreCorpus()\n",
      "modulations = {'parallel minor': 0, 'parallel major': 0, 'relative minor': 0, 'relative major': 0, \n",
      "                'submediant': 0, 'mediant': 0, 'subdominant': 0, 'dominant': 0, 'unknown': 0, 'none': 0}\n",
      "works = core.getBachChorales()\n",
      "#print ntpath.basename(works[0])\n",
      "for work in works:\n",
      "    #name = ntpath.basename(work)\n",
      "    work = corpus.parse(work)\n",
      "    excerpt = work.measures(0,5)\n",
      "    reduction = work.chordify().stripTies(retainContainers=True)\n",
      "    chords = reduction.flat.getElementsByClass('Chord')\n",
      "    nchords = len(chords)\n",
      "    try:\n",
      "        # attempt to get pitch class of first real chord\n",
      "        first = harmony.chordSymbolFigureFromChord(chords[0], True)\n",
      "        if first[0] == 'Chord Symbol Cannot Be Identified':\n",
      "            idx = 2\n",
      "            while first == 'Chord Symbol Cannot Be Identified':\n",
      "                first = harmony.chordSymbolFigureFromChord(chords[nchords + idx], True)\n",
      "                idx += 1\n",
      "        fc_name = first[0].split('/', 1)[0]\n",
      "        fc_color = first[1]\n",
      "        fc_num = pitch.Pitch(str(fc_name).translate(None, string.ascii_lowercase)).pitchClass\n",
      "        ft = first[1]\n",
      "\n",
      "        # attempt to get pitch class of last chord\n",
      "        last = harmony.chordSymbolFigureFromChord(chords[nchords - 1], True)\n",
      "        if last[0] == 'Chord Symbol Cannot Be Identified':\n",
      "            idx = 2\n",
      "            while last[0] == 'Chord Symbol Cannot Be Identified':\n",
      "                last = harmony.chordSymbolFigureFromChord(chords[nchords - idx], True)\n",
      "                idx += 1\n",
      "        lc_name = last[0].split('/', 1)[0]\n",
      "        lc_color = last[1]\n",
      "        lc_num = pitch.Pitch(str(lc_name).translate(None, string.ascii_lowercase)).pitchClass\n",
      "        lt = last[1]\n",
      "       \n",
      "        distance = degree_dif(fc_num, lc_num)\n",
      "        \n",
      "        #print '~~~~~'\n",
      "        #print 'first: {} ({})'.format(fc_num, fc_name)\n",
      "        #print 'last:  {} ({})'.format(lc_num, lc_name)\n",
      "        #print 'dist:  {}'.format(distance)\n",
      "        \n",
      "        \n",
      "        if distance == 0:\n",
      "            if fc_color == lc_color:\n",
      "                modulations['none'] += 1\n",
      "                #print 'conclusion: none'\n",
      "            elif fc_color == 'minor' and lc_color == 'major':\n",
      "                modulations['parallel major'] += 1\n",
      "                #print 'conclusion: parallel major'\n",
      "            elif fc_color == 'major' and lc_color == 'minor':\n",
      "                modulations['parallel minor'] += 1\n",
      "                #print 'conclusion: parallel minor'\n",
      "            else: # this will happen with less common chord labels like 'Gpedal' or 'Gsus'\n",
      "                modulations['none'] += 1\n",
      "                #print 'conclusion: none'\n",
      "        elif distance == 9:\n",
      "            if fc_color == 'major' and lc_color == 'minor':\n",
      "                modulations['relative minor'] += 1\n",
      "                #print 'conclusion: relative minor'\n",
      "            else: # modulating to MAJOR 6\n",
      "                modulations['submediant'] += 1\n",
      "                #print 'conclusion: submediant'\n",
      "        elif distance == 3:\n",
      "            if fc_color == 'minor' and lc_color == 'major':\n",
      "                modulations['relative major'] += 1\n",
      "                #print 'conclusion: relative major'\n",
      "            else: # modulating to MINOR 3\n",
      "                modulations['mediant'] += 1\n",
      "                #print 'conclusion: mediant'\n",
      "        elif distance == 5:\n",
      "            modulations['subdominant'] += 1\n",
      "            #print 'conclusion: subdominant'\n",
      "        elif distance == 7:\n",
      "            modulations['dominant'] += 1\n",
      "            #print 'conclusion: dominant'\n",
      "        else:\n",
      "            modulations['unknown'] += 1\n",
      "            #print 'conclusion: unknown'     \n",
      "        #print\n",
      "    except:\n",
      "        continue"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 144
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib as mpl\n",
      "mpl.rcParams['figure.figsize'] = (16, 4)\n",
      "\n",
      "pyplot.bar(range(len(modulations)), modulations.values(), align='center')\n",
      "pyplot.xticks(range(len(modulations)), modulations.keys(), rotation='vertical')\n",
      "pyplot.title('Modulations in Bach Chorales')\n",
      "pyplot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "output_type": "display_data",
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AZI9Scw+JBh8AAAD4DU2IkGtoWuHkLR+p/SSxr5zFfnIeTYicw2vKOYxLACC3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\nORowYIAmT57ssK/uLFkzatQ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       "text": [
        "<matplotlib.figure.Figure at 0x10b923cd0>"
       ]
      }
     ],
     "prompt_number": 149
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Conclusion:\n",
      "# Though modulation to the parallel major was very common, the vast majority of the Bach Chorales ended\n",
      "# in the same key they began in, undermining my hypothesis that modulations would be most common. Perhaps\n",
      "# if the same analysis was performed on other Bach works or works by another composer we would see \n",
      "# different results. Furthermore, this analysis method has obvious limitations, and I would suspect that\n",
      "# many of the pieces which returned to the original key included some sort of modulation part way through\n",
      "# the work. "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 148
    }
   ],
   "metadata": {}
  }
 ]
}