02_plot_pitch_differences_whole_set_p3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. MusicNet pitch differences\n",
    "\n",
    "This tutorial demontrates the data using one recording as example. It depends on the NumPy, matplotlib, and intervaltree packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os,sys,shutil,mmap\n",
    "import numpy as np                      # fast vectors and matrices\n",
    "import matplotlib.pyplot as plt         # plotting\n",
    "\n",
    "from IPython.display import Audio\n",
    "\n",
    "from intervaltree import Interval,IntervalTree\n",
    "\n",
    "import pickle\n",
    "\n",
    "import sys\n",
    "\n",
    "sys.path.insert(0,'lib/')\n",
    "import config\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constants\n",
    "\n",
    "A recording of a musical performance is a real-valued time series. The values of this time series represent sound pressure variations sampled at regular intervals, in this case 44,100Hz. The human ear interprets pressure periodicities as musical notes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "fs = 44100      # samples/second\n",
    "sz_float = 4\n",
    "window = 16384\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Import\n",
    "Import the recordings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(config.labels_path, 'rb') as f:\n",
    "    labels = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dict()\n",
    "for record in os.listdir(config.records_path):\n",
    "    fd = os.open(config.records_path + record, os.O_RDONLY)\n",
    "    buff = mmap.mmap(fd, 0, mmap.MAP_SHARED, mmap.PROT_READ)\n",
    "    data[int(record[:-4])] = (buff, len(buff)/sz_float)\n",
    "    os.close(fd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "recording 2494\n",
      "Python-Type of Labels: <class 'intervaltree.intervaltree.IntervalTree'>\n",
      "Length of recording: 13100544.0\n"
     ]
    }
   ],
   "source": [
    "rec_id = 2494\n",
    "print( \"recording\", rec_id)\n",
    "print (\"Python-Type of Labels:\",type(labels[rec_id]))\n",
    "print (\"Length of recording:\", data[rec_id][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Intervals\n",
    "Extract frames of window size 16384 in every music sample and count the jumps of different semitones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# count jumps of 0 to 128 semitones\n",
    "jumps = np.zeros(128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Music sample 2560 contains 1021 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1792 contains 1272 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2562 contains 889 windows of length 0.37151927437641724 seconds.\n",
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      "Music sample 2588 contains 1407 windows of length 0.37151927437641724 seconds.\n"
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     "name": "stdout",
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      "Music sample 2218 contains 538 windows of length 0.37151927437641724 seconds.\n",
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      "Music sample 2411 contains 347 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2415 contains 613 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2416 contains 374 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2417 contains 612 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2147 contains 1350 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2451 contains 1135 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2420 contains 637 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2422 contains 650 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2423 contains 801 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2424 contains 545 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1916 contains 1816 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2538 contains 571 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1918 contains 988 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2431 contains 862 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2432 contains 521 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2433 contains 1242 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1922 contains 1082 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1923 contains 1058 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2436 contains 1842 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2441 contains 2139 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2442 contains 471 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1931 contains 1269 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1932 contains 673 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2626 contains 1598 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1735 contains 1924 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2285 contains 608 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1859 contains 1057 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2628 contains 335 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2247 contains 218 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2117 contains 716 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2288 contains 516 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2466 contains 822 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2444 contains 2074 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2289 contains 547 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2472 contains 579 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2473 contains 902 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2476 contains 1277 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2477 contains 594 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2478 contains 859 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2480 contains 1064 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2481 contains 954 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2482 contains 1528 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2483 contains 989 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2462 contains 1317 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2486 contains 1206 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2487 contains 914 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2488 contains 1187 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2490 contains 1397 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2463 contains 833 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2492 contains 1293 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2494 contains 799 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2555 contains 602 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2497 contains 791 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1822 contains 1239 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2501 contains 988 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2502 contains 720 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2504 contains 1239 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2505 contains 1317 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2078 contains 958 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2507 contains 586 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2509 contains 1303 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2510 contains 1216 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2512 contains 1139 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2514 contains 1092 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2516 contains 1044 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2300 contains 641 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2283 contains 517 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2521 contains 2024 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2522 contains 979 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2523 contains 1503 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2607 contains 1814 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2527 contains 1039 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2528 contains 1248 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1872 contains 1371 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2530 contains 1512 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2531 contains 2670 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2532 contains 1476 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2533 contains 2874 windows of length 0.37151927437641724 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Music sample 2537 contains 772 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1933 contains 946 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2471 contains 1220 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2540 contains 709 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2542 contains 1752 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2284 contains 612 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2550 contains 485 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2217 contains 501 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1876 contains 959 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1791 contains 946 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2556 contains 407 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 2557 contains 2051 windows of length 0.37151927437641724 seconds.\n",
      "Music sample 1824 contains 680 windows of length 0.37151927437641724 seconds.\n"
     ]
    }
   ],
   "source": [
    "for rec_id in labels.keys():\n",
    "    frames =  int(data[rec_id][1] / window )\n",
    "    print(\"Music sample {} contains {} windows of length {} seconds.\".format(rec_id, frames, float(window)/fs))\n",
    "\n",
    "    YY_per_window = np.zeros((frames, 128))\n",
    "    Y = labels[rec_id]\n",
    "    for i in range(frames):\n",
    "        labels_tmp = Y[i*window]\n",
    "        for label in labels_tmp:\n",
    "            YY_per_window[i,label.data[1]] = 1\n",
    "      \n",
    "    # count the number of apearances of the different pitch jumps.\n",
    "    \n",
    "    #register first window\n",
    "    pitches = YY_per_window[0]\n",
    "\n",
    "    for i in range(1,frames):\n",
    "        tmp = YY_per_window[i]\n",
    "        for j in np.where(pitches==1)[0]:\n",
    "            for k in np.where(tmp==1)[0]:\n",
    "                jumps[np.abs(j-k)] += 1\n",
    "        pitches = tmp\n",
    "    \n",
    "jumps = jumps / sum(jumps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots shows that there are more and less probable pitch differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20,10))\n",
    "plt.rcParams['xtick.labelsize']=24\n",
    "plt.rcParams['ytick.labelsize']=24\n",
    "for i in range(128):\n",
    "    plt.plot([i,i],[0,100*jumps[i]], c='cornflowerblue', linewidth = 6)\n",
    "plt.xlabel('Pitch Differences in Semitones',fontsize=24)\n",
    "plt.ylabel('Frequency (in %)',fontsize=24)\n",
    "\n",
    "plt.savefig(\"pictures/pitch_differences_in_music_net.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most probable pitch differences (in half tones) are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "chords = [\"Perfect unison\", \"Minor second\", \"Major second\", \"Minor third\", \"Major third\", \"Perfect fourth\", \n",
    "          \"Tritone\", \"Perfect fifth\", \"Minor sixth\", \"Major sixth\", \"Minor seventh\", \"Major seventh\", \n",
    "          \"Perfect octave\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \n",
    "         \"Double octave\", \"\"]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Semitones\t Chord\t\t\tFrequency of Pitch Difference \n",
      "0 \t\t Perfect unison \t\t 14.16 %\n",
      "12 \t\t Perfect octave \t\t 8.0 %\n",
      "3 \t\t Minor third \t\t 5.68 %\n",
      "7 \t\t Perfect fifth \t\t 5.41 %\n",
      "5 \t\t Perfect fourth \t\t 5.32 %\n",
      "4 \t\t Major third \t\t 4.28 %\n",
      "9 \t\t Major sixth \t\t 4.23 %\n",
      "2 \t\t Major second \t\t 4.06 %\n",
      "8 \t\t Minor sixth \t\t 3.49 %\n",
      "24 \t\t Double octave \t\t 3.18 %\n",
      "19 \t\t  \t\t\t 3.11 %\n",
      "17 \t\t  \t\t\t 2.84 %\n",
      "16 \t\t  \t\t\t 2.79 %\n",
      "1 \t\t Minor second \t\t 2.77 %\n",
      "15 \t\t  \t\t\t 2.67 %\n",
      "10 \t\t Minor seventh \t\t 2.56 %\n",
      "6 \t\t Tritone \t\t 2.41 %\n",
      "21 \t\t  \t\t\t 1.93 %\n",
      "14 \t\t  \t\t\t 1.83 %\n",
      "20 \t\t  \t\t\t 1.62 %\n",
      "28 \t\t  \t\t\t 1.39 %\n",
      "22 \t\t  \t\t\t 1.31 %\n",
      "29 \t\t  \t\t\t 1.23 %\n",
      "31 \t\t  \t\t\t 1.23 %\n",
      "27 \t\t  \t\t\t 1.22 %\n",
      "11 \t\t Major seventh \t\t 1.19 %\n",
      "18 \t\t  \t\t\t 1.16 %\n",
      "36 \t\t  \t\t\t 0.96 %\n",
      "26 \t\t  \t\t\t 0.91 %\n",
      "13 \t\t  \t\t\t 0.89 %\n"
     ]
    }
   ],
   "source": [
    "print(\"Semitones\\t Chord\\t\\t\\tFrequency of Pitch Difference \")\n",
    "sorting = np.argsort(-jumps)\n",
    "for i in range(30):\n",
    "    if chords[min(sorting[i],25)] == \"\":\n",
    "        print (sorting[i],\"\\t\\t\",chords[min(sorting[i],25)],\"\\t\\t\\t\",np.round(jumps[sorting[i]]*100,2),\"%\")\n",
    "    else:\n",
    "        print (sorting[i],\"\\t\\t\",chords[min(sorting[i],25)],\"\\t\\t\",np.round(jumps[sorting[i]]*100,2),\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print the table to file in LATEX-Style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "F = open(\"pictures/interval_frequencies_music_net.txt\",\"w\")\n",
    "\n",
    "F.write(\"Semitones & Chord & Frequency of Pitch Difference \\\\\\\\ \\n  \\\\hlineB{2} \\n\")\n",
    "sorting = np.argsort(-jumps)\n",
    "for i in range(30):\n",
    "    \n",
    "    if i%2 == 0:\n",
    "        F.write('\\\\rowcolor{lightlightgray}')\n",
    "    \n",
    "    F.write ('{} & {} & {}\\% \\\\\\\\ \\n'.format(sorting[i],chords[min(sorting[i],25)],np.round(jumps[sorting[i]]*100,2)))\n",
    "    \n",
    "F.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00020611964921889015\n",
      "1.052181455436743e-05\n",
      "1.9155098291284297e-05\n",
      "2.7518591911422508e-05\n",
      "3.210502389665959e-05\n",
      "1.6726987240276425e-05\n",
      "2.9676912845651727e-06\n",
      "1.699677735705508e-05\n",
      "2.6979011677865206e-06\n",
      "2.9676912845651727e-06\n",
      "2.4281110510078686e-06\n",
      "2.6979011677865206e-07\n",
      "4.0468517516797805e-06\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "2.6979011677865206e-07\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "\n",
      "(array([ 73,  74,  75,  76,  77,  78,  79,  81,  82,  83,  84,  85,  86,\n",
      "        87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,  98,  99,\n",
      "       100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112,\n",
      "       113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
      "       126, 127]),)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for i in range(60,128):\n",
    "    print (jumps[i])\n",
    "print()\n",
    "print(np.where(jumps==0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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