20130917_Extracting the notes from the melody of MusicXML file.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In one of the last posts, we extracted the chords from a MusicXML formatted file. In this post, we're going to do two things:\n",
      "\n",
      "- extract notes from the melody\n",
      "- check on which chord they happen\n",
      "\n",
      "First of all, let's concentrate on the first item\n",
      "\n",
      "# Extracting the melodic line of a MusicXML file"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first question to ask is: how is a note coded? In our case, we're going to work with Autumn Leaves as our sample file. After analyzing the tune, I've noticed that the whole lead sheet is a sequence of measures. Let's look at the first measure to see how the first note in the melody, a B, is embedded with its chord."
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "<measure width=\"270.27\" number=\"1\">\n",
      "            <print>\n",
      "                <system-layout>\n",
      "                    <system-margins>\n",
      "                        <left-margin>69.92</left-margin>\n",
      "                        <right-margin>0.00</right-margin>\n",
      "                    </system-margins>\n",
      "                    <top-system-distance>201.04</top-system-distance>\n",
      "                </system-layout>\n",
      "            </print>\n",
      "            <attributes>\n",
      "                <divisions>4</divisions>\n",
      "                <key>\n",
      "                    <fifths>1</fifths>\n",
      "                    <mode>major</mode>\n",
      "                </key>\n",
      "                <time>\n",
      "                    <beats>6</beats>\n",
      "                    <beat-type>8</beat-type>\n",
      "                </time>\n",
      "                <clef>\n",
      "                    <sign>G</sign>\n",
      "                    <line>2</line>\n",
      "                </clef>\n",
      "            </attributes>\n",
      "            <harmony print-frame=\"no\">\n",
      "                <root>\n",
      "                    <root-step>E</root-step>\n",
      "                </root>\n",
      "                <kind text=\"m\">minor</kind>\n",
      "            </harmony>\n",
      "            <note>\n",
      "                <rest/>\n",
      "                <duration>2</duration>\n",
      "                <voice>1</voice>\n",
      "                <type>eighth</type>\n",
      "            </note>\n",
      "            <note default-y=\"-20.00\" default-x=\"118.77\">\n",
      "                <pitch>\n",
      "                    <step>B</step>\n",
      "                    <octave>4</octave>\n",
      "                </pitch>\n",
      "                <duration>2</duration>\n",
      "                <voice>1</voice>\n",
      "                <type>eighth</type>\n",
      "                <stem>down</stem>\n",
      "                <beam number=\"1\">begin</beam>\n",
      "            </note>\n",
      "            <note default-y=\"-15.00\" default-x=\"149.21\">\n",
      "                <pitch>\n",
      "                    <step>C</step>\n",
      "                    <alter>1</alter>\n",
      "                    <octave>5</octave>\n",
      "                </pitch>\n",
      "                <duration>2</duration>\n",
      "                <voice>1</voice>\n",
      "                <type>eighth</type>\n",
      "                <accidental>sharp</accidental>\n",
      "                <stem>down</stem>\n",
      "                <beam number=\"1\">end</beam>\n",
      "            </note>\n",
      "            <note default-y=\"-10.00\" default-x=\"179.65\">\n",
      "                <pitch>\n",
      "                    <step>D</step>\n",
      "                    <alter>1</alter>\n",
      "                    <octave>5</octave>\n",
      "                </pitch>\n",
      "                <duration>2</duration>\n",
      "                <voice>1</voice>\n",
      "                <type>eighth</type>\n",
      "                <accidental>sharp</accidental>\n",
      "                <stem>down</stem>\n",
      "                <beam number=\"1\">begin</beam>\n",
      "            </note>\n",
      "            <note default-y=\"0.00\" default-x=\"209.32\">\n",
      "                <pitch>\n",
      "                    <step>F</step>\n",
      "                    <alter>1</alter>\n",
      "                    <octave>5</octave>\n",
      "                </pitch>\n",
      "                <duration>2</duration>\n",
      "                <voice>1</voice>\n",
      "                <type>eighth</type>\n",
      "                <stem>down</stem>\n",
      "                <beam number=\"1\">continue</beam>\n",
      "            </note>\n",
      "            <note default-y=\"-5.00\" default-x=\"239.00\">\n",
      "                <pitch>\n",
      "                    <step>E</step>\n",
      "                    <octave>5</octave>\n",
      "                </pitch>\n",
      "                <duration>2</duration>\n",
      "                <voice>1</voice>\n",
      "                <type>eighth</type>\n",
      "                <stem>down</stem>\n",
      "                <beam number=\"1\">end</beam>\n",
      "            </note>\n",
      "        </measure>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So what we need to do is to parse each measure by finding all blocks containing an harmonic part, the chords that's followed by notes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import xml.etree.cElementTree as ET"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xml = file(\"files/autumn_leaves.xml\", 'r').readlines()\n",
      "tree = ET.fromstringlist(xml)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "first_measure = tree.find(\".//measure\")\n",
      "first_measure"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<Element 'measure' at 0x462b350>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chords = first_measure.findall(\"harmony/root/root-step\")\n",
      "chords"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "[<Element 'root-step' at 0x462b910>]"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chords[0].text"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "'E'"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for note in first_measure.findall(\"note/pitch/step\"):\n",
      "    print note.text"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "B\n",
        "C\n",
        "D\n",
        "F\n",
        "E\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This allows us to easily get the notes. However, there are two sorts of alterations that need to be taken into account:\n",
      "\n",
      "- the key alterations (here we're in the key of E minor / G major, therefore F is sharp)\n",
      "- the accidental alterations\n",
      "\n",
      "First, let's see if we can take into account the accidental alterations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for note in first_measure.findall(\"note/pitch\"):\n",
      "    if note.find(\"alter\") != None:\n",
      "        alter = note.find(\"alter\").text\n",
      "        print note.find(\"step\").text, alter\n",
      "    else:\n",
      "        print note.find(\"step\").text\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "B\n",
        "C 1\n",
        "D 1\n",
        "F 1\n",
        "E\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can easily take into account this sort of alteration by using a function already coded in a previous notebook that shifts a note by a required number of semitones."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def increment_note(note, half_tones):\n",
      "    notes = ['C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A', 'A#', 'B']\n",
      "    ind = notes.index(note)\n",
      "    return notes[(ind + half_tones) % 12]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for note in first_measure.findall(\"note/pitch\"):\n",
      "    if note.find(\"alter\") != None:\n",
      "        alter = note.find(\"alter\").text\n",
      "        print increment_note(note.find(\"step\").text, int(alter))\n",
      "    else:\n",
      "        print note.find(\"step\").text\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "B\n",
        "C#\n",
        "D#\n",
        "F#\n",
        "E\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "After seing the output of this function, it turns out that the key alteration is in fact already coded within the note. That's a good point for us because then we don't need to take into account a behaviour of the style: \"if this note is in the key accidentals then make it sharp or flat\". We can just use the notes right away."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Parsing harmony and melody at the same time"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From what we've seen before, it seems logical to parse the song on a per-measure way. Using what we learnt before, we can loop over each child of each measure. If the child is a harmony element, we can set the active chord to be the one extracted from there. If it is a note element, we can increment the note count over a given chord."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def get_chord_from_harmony_tag(harmony_tag):\n",
      "    root = harmony_tag.find('root/root-step').text\n",
      "    alter_elem = harmony_tag.find('root/root-alter')\n",
      "    if alter_elem != None:\n",
      "        root = increment_note(root, int(alter_elem.text))\n",
      "    kind_attrib = harmony_tag.find('kind').attrib['text']\n",
      "    return \" \".join([root, kind_attrib])\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "get_chord_from_harmony_tag(first_measure.find(\"harmony\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "'E m'"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def get_note_from_note_tag(note_tag):\n",
      "    pitch = note_tag.find(\"pitch\")\n",
      "    if pitch != None: #in case the note is a rest\n",
      "        note = pitch.find(\"step\").text\n",
      "        if pitch.find(\"alter\") != None:\n",
      "            note = increment_note(note, int(pitch.find(\"alter\").text))\n",
      "        return note\n",
      "    else:\n",
      "        return None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "note_tag = first_measure.findall(\"note\")[1]\n",
      "get_note_from_note_tag(note_tag)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "'B'"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "we now have the needed helper functions and can turn to the main loop."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def write_note_to_dict(note, current_chord, note_chord_dict):\n",
      "    if not current_chord in note_chord_dict:\n",
      "        note_chord_dict[current_chord] = [0] * 12\n",
      "    ind = ['C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A', 'A#', 'B'].index(note)\n",
      "    note_chord_dict[current_chord][ind] += 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "current_chord = None\n",
      "note_chord_dict = {}\n",
      "for measure in tree.findall(\".//measure\"):\n",
      "    for child in measure:\n",
      "        if child.tag == 'harmony':\n",
      "            current_chord = get_chord_from_harmony_tag(child)\n",
      "        if child.tag == 'note':\n",
      "            note = get_note_from_note_tag(child)\n",
      "            if current_chord != None and note != None:\n",
      "                write_note_to_dict(note, current_chord, note_chord_dict)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "note_chord_dict"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "{'A ': [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0],\n",
        " 'A 7': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],\n",
        " 'A m': [1, 0, 1, 0, 3, 0, 8, 9, 0, 7, 0, 0],\n",
        " 'A m7': [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],\n",
        " 'B 7': [1, 1, 0, 1, 2, 0, 20, 8, 0, 8, 0, 4],\n",
        " 'B 7#5': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],\n",
        " 'C 7': [0, 0, 0, 0, 5, 0, 1, 4, 0, 0, 1, 0],\n",
        " 'C Maj7': [2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2],\n",
        " 'D 7': [4, 0, 5, 0, 3, 0, 2, 0, 0, 1, 0, 0],\n",
        " 'E 7': [4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4],\n",
        " 'E 7b9': [2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2],\n",
        " 'E m': [0, 1, 0, 1, 5, 0, 5, 4, 0, 0, 0, 6],\n",
        " 'E m7': [0, 0, 0, 1, 8, 0, 6, 10, 0, 0, 0, 2],\n",
        " 'F# 7': [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
        " 'F# m7b5': [4, 0, 1, 0, 2, 0, 3, 1, 0, 5, 0, 1],\n",
        " 'G ': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3],\n",
        " 'G 7': [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
        " 'G Maj7': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6]}"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(10, 10))\n",
      "note_arr = array([note_chord_dict[key] for key in note_chord_dict])\n",
      "matshow(note_arr, fignum=False, cmap=cm.gray)\n",
      "xticks(arange(0, 12), ['C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A', 'A#', 'B']);\n",
      "yticks(arange(0, len(note_chord_dict.keys())), note_chord_dict.keys());\n",
      "colorbar(shrink=0.75)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 79,
       "text": [
        "<matplotlib.colorbar.Colorbar instance at 0x07AB9AF8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FFXK73Ro8ePB5NapBE+Yej0eZmZmSpMzMTNup9t69e2vAgAFyuVwaMGCArrnmGklSYmKi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\n8ccfa8iQIWrXrp1CQ0OVnp6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       "text": [
        "<matplotlib.figure.Figure at 0x7833d90>"
       ]
      }
     ],
     "prompt_number": 79
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}