cleanup, better explanations

notebooks/pitch_transcription_answer.ipynb

 {
  "metadata": {
   "name": "",
-  "signature": "sha256:192b3e3df17edf351eead6a15c46df3338b6faa3a8601240a7954615094c03e3"
+  "signature": "sha256:0c39aef785f81466fe4a14e5ae37752896439cc7ceb966b0f0cfcc61c8b8aff0"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -16,31 +16,99 @@
       "Pitch Transcription Exercise"
      ]
     },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Goal: Given an input signal, \n",
+      "\n",
+      "1. identify each note (including pitch, start time, and duration), and \n",
+      "2. render the transcription to be played back as audio."
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Imports:"
+     ]
+    },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "import essentia\n",
       "import essentia.standard as ess\n",
-      "loader = ess.MonoLoader(filename='../test/test.wav', sampleRate=44100)\n",
+      "import librosa"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Set figure size:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "rcParams['figure.figsize'] = (15, 6)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Read an input signal:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "fs = 44100.0\n",
+      "loader = ess.MonoLoader(filename='../test/test.wav', sampleRate=fs)\n",
       "signal_in = loader()"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 75
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Play the signal:"
+     ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "from IPython.display import Audio\n",
-      "#Audio(data=signal_in, rate=44100)"
+      "#Audio(data=signal_in, rate=44100) # may take a while to load"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 76
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Given a signal, return onset times:"
+     ]
     },
     {
      "cell_type": "code",
@@ -53,7 +121,14 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 77
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Given an audio segment, return pitch:"
+     ]
     },
     {
      "cell_type": "code",
@@ -63,7 +138,7 @@
       "spectrum = ess.Spectrum()\n",
       "\n",
       "def get_pitch(segment):\n",
-      "    if len(segment) < 4096:\n",
+      "    if len(segment) < 4096: # hack to get around Essentia error\n",
       "        N = len(segment) if len(segment) % 2 == 0 else len(segment) - 1\n",
       "    else:\n",
       "        N = 4096\n",
@@ -73,7 +148,14 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 78
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Given a pitch, return a sine wave:"
+     ]
     },
     {
      "cell_type": "code",
@@ -82,12 +164,19 @@
       "def generate_sine(pitch, n_duration):\n",
       "    #print midi, f0\n",
       "    n = arange(n_duration)\n",
-      "    return 0.2*sin(2*pi*pitch*n/44100.0)"
+      "    return 0.2*sin(2*pi*pitch*n/fs)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 79
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Given an input signal, transcribe it, and render the transcription using sine waves:"
+     ]
     },
     {
      "cell_type": "code",
@@ -102,7 +191,7 @@
       "    onsets = get_onsets(signal_in)\n",
       "    \n",
       "    # for each onset\n",
-      "    onsets = append(onsets, len(signal_in)/44100.0)\n",
+      "    onsets = append(onsets, len(signal_in)/fs)\n",
       "    for i in range(len(onsets)-1):\n",
       "        # pitch detect each segment\n",
       "        n0 = int(onsets[i]*44100)\n",
@@ -117,7 +206,14 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 80
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Transcribe:"
+     ]
     },
     {
      "cell_type": "code",
@@ -128,20 +224,93 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 81
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Write output to file:"
+     ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "#Audio(data=signal_out, rate=44100)\n",
-      "#Audio(data=sum([signal_out, signal_in], axis=0), rate=44100)\n",
+      "#Audio(data=signal_out, rate=fs)\n",
+      "#Audio(data=sum([signal_out, signal_in], axis=0), rate=fs)\n",
       "ess.MonoWriter(filename='../test/out.wav')(signal_out)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 82
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Plot the onsets:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plot(signal_in)\n",
+      "for onset in get_onsets(signal_in):\n",
+      "    axvline(onset*fs, color='r')"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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1/tQf0ksvNd/XbheqCy4w70LnpFV32zaRffdlXaUwU91da/Fi4zL1fWn1/ZH4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\nWpCxFA7CTvV4XlQ3c6buCII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+       "text": [
+        "<matplotlib.figure.Figure at 0x487c3d0>"
+       ]
+      }
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Plot the pitches:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "CQT = librosa.cqt(signal_in[fs:fs*8], fs, hop_length=4096, fmin=librosa.midi_to_hz(60), fmax=librosa.midi_to_hz(108))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stderr",
+       "text": [
+        "-c:1: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
+        "-c:1: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
+        "/usr/lib/python2.7/dist-packages/scipy/fftpack/basic.py:121: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
+        "  z = zeros(s,x.dtype.char)\n"
+       ]
+      }
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "librosa.display.specshow(librosa.logamplitude(CQT), sr=fs, y_axis='cqt_note', fmin=librosa.midi_to_hz(60), fmax=librosa.midi_to_hz(120))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
     },
     {
      "cell_type": "code",
@@ -149,8 +318,7 @@
      "input": [],
      "language": "python",
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 82
+     "outputs": []
     }
    ],
    "metadata": {}