Supplement SPD Code.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "498c649a",
   "metadata": {},
   "source": [
    "### This Supplementary material gives an implementation of Sequential Pitch Distributions (SPD) which is the core concept of the paper\n",
    "We have used a pitch file which is also added as part of Supplement, This file is of Raga Purya Dhanasri which was requested from CompMusic\n",
    "This file has an mbid: 930ae825-111c-4dd5-b8be-de609fd5202d and tonic frequency of 212.874556 Hz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "be24240f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "28a7a5ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = '930ae825-111c-4dd5-b8be-de609fd5202d.tsv'\n",
    "file_tonic = 212.874556"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16f789d6",
   "metadata": {},
   "source": [
    "### Function to get pitch data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6cb49cdf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_pitch_data(pitch_file_path):\n",
    "    data = pd.read_csv(pitch_file_path, sep='\\t')\n",
    "    return data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ff89a20",
   "metadata": {},
   "source": [
    "### Convert pitch frequency to an array of 60 pitch values with gaussian smooth with standard deviation 25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "36266eae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def freq_to_cents(freq, std=25):\n",
    "    frequency_reference = 10\n",
    "    c_true = 1200 * math.log((freq+1e-6) / frequency_reference, 2)\n",
    "\n",
    "    cents_mapping = np.linspace(0, 7180, 360) + 1997.3794084376191\n",
    "    target = np.exp(-(cents_mapping - c_true) ** 2 / (2 * std ** 2))\n",
    "\n",
    "    return np.sum(target.reshape([6, 60]), 0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9071d287",
   "metadata": {},
   "source": [
    "### Function to convert all pitche frequency to pitch value array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7c96e71f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_pitchvalues(pitches):\n",
    "    pitches_arr = pitches.values[:,0]\n",
    "    pitchvalue_prob = []\n",
    "    for idx, p in enumerate(pitches_arr):\n",
    "        if p==0:\n",
    "            continue\n",
    "        pitchvalue_prob.append(freq_to_cents(p))\n",
    "    return np.array(pitchvalue_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa6582d3",
   "metadata": {},
   "source": [
    "### Function to re-order the pitchvalue porbability array based on tonic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4d9a7b45",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reorder_tonic(pitchvalue_prob, tonic_freq):\n",
    "    tonic_pv_arr = freq_to_cents(tonic_freq)\n",
    "    tonic_pv = np.argmax(tonic_pv_arr) \n",
    "    return np.roll(pitchvalue_prob, -tonic_pv, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "036efc4d",
   "metadata": {},
   "source": [
    "### Function to normalize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "46be55bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(z):\n",
    "    z_min = np.min(z)\n",
    "    return (z - z_min)/(np.max(z)-z_min+0.001)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd8e8eb6",
   "metadata": {},
   "source": [
    "### Saw tooth wave with a period of 60\n",
    "    This is defined in Equation 1, Page 3 in the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b26f0dbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def modulo(x):\n",
    "    return x%60"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df05efde",
   "metadata": {},
   "source": [
    "### Modulo Add\n",
    "We define another function n which adds 60 to the modulo function\n",
    "whenever x is greater than y\n",
    "This function is defined in Equation 2; Page 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fae0a5fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def modulo_add(x,y):\n",
    "    mx = modulo(x)\n",
    "    my = modulo(y)\n",
    "    if mx>my:\n",
    "        return my+60\n",
    "    return my"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af911ad7",
   "metadata": {},
   "source": [
    "### Relax\n",
    "Function to relax a pitch value by +/- 2 pitch values (+/- 40 cents).\n",
    "\n",
    "This is defined in Equations 3-6; Page 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a0e2172f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def relax_fun(p,add,r=2):\n",
    "    if add:\n",
    "        return modulo(p+2)\n",
    "    return modulo(p-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2a0e436",
   "metadata": {},
   "source": [
    "### Compare\n",
    "We define function compare that evaluates to 1 when 'x' is at an equal or\n",
    "higher pitch than 'a' and at an equal or at a lower pitch than\n",
    "'b', else it evaluates to 0\n",
    "\n",
    "\n",
    "This function is defined in Equation 7; Page 4\n",
    "\n",
    "For the descending case refer line 268, 269 in the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c4d3ca98",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare(a,b,x,asc):\n",
    "    if not asc:\n",
    "        a, b = b, a\n",
    "    if a <= modulo_add(a,x) <= modulo_add(a,b):\n",
    "        return 1\n",
    "    return 0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e46023d1",
   "metadata": {},
   "source": [
    "### Get Pitch Distribution\n",
    "This function takes the mean across the time axis and normalizes\n",
    "\n",
    "This is defined in Equation 9; Page 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "32b8aeb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_pitch_distribution(pitchvalue_prob):\n",
    "    s_mean = normalize(np.mean(pitchvalue_prob, axis=0))\n",
    "    return s_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7924a1a0",
   "metadata": {},
   "source": [
    "### Get Mean (Pitch distribution) and Standard Deviation across time axis\n",
    "This is deined in equation 10; Page 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9a11f30b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_pitch_histograms(pitchvalue_prob):\n",
    "    s_mean = get_pitch_distribution(pitchvalue_prob)\n",
    "    s_std = normalize(np.std(pitchvalue_prob, axis=0))\n",
    "\n",
    "    s = np.stack([s_mean, s_std], axis=-1)\n",
    "    return s\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "427317f5",
   "metadata": {},
   "source": [
    "### Get pitch distribution between start and end pitch values\n",
    "This is defined in Equation 11; Page 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "739b2024",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_pd_between_pspe(pitchvalue_prob, ps, pe, asc, relax=2):\n",
    "    if asc:\n",
    "        relax_sign = relax\n",
    "    else:\n",
    "        relax_sign = -relax\n",
    "    pd = get_pitch_distribution(pitchvalue_prob)\n",
    "    w = np.zeros(60)\n",
    "    for i in range(60):\n",
    "        w[i] = pd[i]*compare(ps-relax_sign,pe+relax_sign,i, asc)\n",
    "    return normalize(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a39a016",
   "metadata": {},
   "source": [
    "### Function to compute Sequential Pitch Distributions\n",
    "The below functions compute SPD for a given start pitch value (ps) and end pitch value (pe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "73e61b8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_spd_ps_pe(pitchvalue_prob, ps, pe, asc, relax=2):\n",
    "    default_hist = get_pd_between_pspe(pitchvalue_prob, ps, pe, asc)  # Default values to be filled when SPD is not available; line 254, 255 in the paper\n",
    "    lim = 55\n",
    "    pitches_arg = np.argmax(pitchvalue_prob,1) # pitch value with the highest probability\n",
    "    \n",
    "    if asc:\n",
    "        relax_sign = relax\n",
    "    else:\n",
    "        relax_sign = -relax\n",
    "    prev_dist = np.zeros(60)\n",
    "    cum_pitch_dist = np.zeros(60)\n",
    "    n = len(pitches_arg)\n",
    "    k=0\n",
    "    start = False\n",
    "    end = False\n",
    "    for idx in range(n):\n",
    "        p = pitches_arg[idx]\n",
    "        \n",
    "        \n",
    "        if compare(ps-relax_sign, ps+relax_sign, p, asc):\n",
    "            start = True  # This verifies Equation 12; Page 4\n",
    "        \n",
    "        if start and compare(pe-relax_sign, pe+relax_sign, p, asc):\n",
    "            end = True  # This verifies Equation 14; Page 4\n",
    "            k=1\n",
    "        \n",
    "        if start and (compare(ps-relax_sign, pe+relax_sign, p, asc)): # This verifies Equation 15; Page 4\n",
    "            prev_dist[p] = prev_dist[p] + 1  # Equation 16; Page 4\n",
    "            k=1\n",
    "        \n",
    "        if start and end and not (compare(ps-relax_sign, pe+relax_sign, p, asc)):\n",
    "            # This verfies Equation 13; Page 4\n",
    "            cum_pitch_dist = cum_pitch_dist + prev_dist\n",
    "            prev_dist = np.zeros(60)\n",
    "            start = False\n",
    "            end = False\n",
    "            k=0\n",
    "        if not (compare(ps-relax_sign, pe+relax_sign, p, asc)):\n",
    "            prev_dist = np.zeros(60)\n",
    "            start = False\n",
    "            end = False\n",
    "            k=0\n",
    "    \n",
    "    if k==1:\n",
    "        # This handles an edge case where prev_dist is not empty but not yet been added to cum_pitch_dist\n",
    "        cum_pitch_dist = cum_pitch_dist + prev_dist\n",
    "    \n",
    "    if np.sum(cum_pitch_dist)==0:\n",
    "        return normalize(default_hist)  # Return simple pitch distributin incase SPD is empty lines 254, 255\n",
    "    return normalize(cum_pitch_dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56a2fa79",
   "metadata": {},
   "source": [
    "### Get pitch data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "afd5682b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(167664, 1)\n"
     ]
    }
   ],
   "source": [
    "pitches = get_pitch_data(file_name)\n",
    "print(pitches.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dd640bd",
   "metadata": {},
   "source": [
    "### Convert to Pitch Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "038a6cd0",
   "metadata": {},
   "outputs": [],
   "source": [
    "pitchvalue_prob = get_pitchvalues(pitches)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceca87f4",
   "metadata": {},
   "source": [
    "### Reorder pitch value array for the given tonic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d6d40a1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "pitchvalue_prob = reorder_tonic(pitchvalue_prob, file_tonic)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99129d4a",
   "metadata": {},
   "source": [
    "### Utils to Gaussian smooth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1b9ecb87",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_all_smooth_pitch_values(std=25):\n",
    "    c_note = freq_to_cents(31.7 * 2, std)\n",
    "    all_notes = np.zeros([60, 60])\n",
    "    for p in range(60):\n",
    "        all_notes[p] = get_smooth_pitch_value(c_note, p)\n",
    "\n",
    "    return all_notes, c_note\n",
    "\n",
    "def get_smooth_pitch_value(c_note, note):\n",
    "    return np.roll(c_note, note, axis=-1)\n",
    "\n",
    "def gauss_smooth(raga_feat):\n",
    "    all_notes, c_note = get_all_smooth_pitch_values(std=25)\n",
    "    smooth = np.zeros([12,12,60,2])\n",
    "    for i in range(12):\n",
    "        for j in range(12):\n",
    "            if i==j:\n",
    "                continue\n",
    "            for k in range(0,2):\n",
    "                smooth[i,j,:,k] = gauss_smooth_util(raga_feat[i,j,:,k], all_notes)\n",
    "    return smooth\n",
    "                \n",
    "def gauss_smooth_util(arr1, all_notes):\n",
    "    smooth = 0\n",
    "    for i in range(60):\n",
    "        smooth = smooth + all_notes[i]*arr1[i]\n",
    "    \n",
    "#     smooth = np.power(normalize(smooth), 0.8)\n",
    "    smooth = normalize(smooth)\n",
    "    return smooth"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d46690ce",
   "metadata": {},
   "source": [
    "### Generate full SPD (All ps, pe pairs and both ascending and descending)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "87b29d76",
   "metadata": {},
   "outputs": [],
   "source": [
    "def full_spd(pitchvalue_prob):\n",
    "    lim = 55\n",
    "    spd_array = np.zeros([12,12,60,2])\n",
    "    \n",
    "    for i in range(0, 60, 5):\n",
    "        for j in range(0, lim + 1, 5):\n",
    "            s = i\n",
    "            e = j\n",
    "            if s==e:\n",
    "                continue\n",
    "            spd_asc = compute_spd_ps_pe(pitchvalue_prob, s, e, asc=True)\n",
    "            spd_dsc = compute_spd_ps_pe(pitchvalue_prob, e, s, asc=False)\n",
    "            \n",
    "            spd_array[i//5, j//5, :, 0] = spd_asc\n",
    "            spd_array[i//5, j//5, :, 1] = spd_dsc\n",
    "                    \n",
    "    return spd_array\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cfab2b6",
   "metadata": {},
   "source": [
    "### Generate full SPD and Smooth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "81fcfe83",
   "metadata": {},
   "outputs": [],
   "source": [
    "spd_array = full_spd(pitchvalue_prob)  # Can take several minutes\n",
    "spd_array = gauss_smooth(spd_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad80c6a9",
   "metadata": {},
   "source": [
    "## Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "201b7d79",
   "metadata": {},
   "source": [
    "SPD for a transition of notes from Ma' (30) to Ni (55) in an ascending order; As shown in Figure 1 (Blue) Top left in the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "688edf6f",
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(spd_array[6,11,:,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "824a7426",
   "metadata": {},
   "source": [
    "SPD for a transition of notes from Ni (55) to Ma' (30) in a descending order; As shown in Figure 1 (Blue) Top Middle in the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7bcd5380",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1743014d438>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(spd_array[6,11,:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07f361e0",
   "metadata": {},
   "source": [
    "SPD for a transition of notes from Komal Dha (40) to Ga (20) in a ascending order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5e7aacd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x174301c44a8>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(spd_array[8,4,:,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abc56f2d",
   "metadata": {},
   "source": [
    "SPD for a transition of notes from Ga (20) to Komal Dha (40) to in a descending order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4df20759",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17430227550>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(spd_array[8,4,:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5602dd5a",
   "metadata": {},
   "source": [
    "### Generates features used for KNN model\n",
    "See Equation 18, 19; Page 4\n",
    "\n",
    "Also see lines 270-272, 299-302"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1a4e46e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_knn_features(pitchvalue_prob, spd_array):\n",
    "    \n",
    "    hist = get_pitch_histograms(pitchvalue_prob)\n",
    "    print(hist.shape)\n",
    "    \n",
    "    v1 = np.zeros([11,12,60,2])\n",
    "    for j in range(5,60,5):\n",
    "        for i in range(0,60,5):\n",
    "            v1[(j//5)-1,i//5,:,:] = spd_array[i//5,modulo(j+i)//5,:,:]  # Equation 18; Page 4\n",
    "    \n",
    "    print(v1.shape)\n",
    "    \n",
    "    v2 = np.zeros([12,11,60,2])\n",
    "    for i in range(0,60,5):\n",
    "        for j in range(5,60,5):\n",
    "            v2[i//5,(j//5)-1,:,:] = spd_array[i//5,modulo(j+i)//5,:,:]  # Equation 19; Page 4\n",
    "    \n",
    "    print(v2.shape)\n",
    "    \n",
    "    return hist, v1, v2\n",
    "            \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ff26940d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60, 2)\n",
      "(11, 12, 60, 2)\n",
      "(12, 11, 60, 2)\n"
     ]
    }
   ],
   "source": [
    "knn_f = get_knn_features(pitchvalue_prob, spd_array)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
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