{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Harmonicity metrics"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is intended to demonstrate the use of the biotuner (https://github.com/antoineBellemare/biotuner/)\n",
    "\n",
    "The biotuner toolbox allows to extract harmonic information from biological time series, which in turn could both\n",
    "\n",
    "1. Inform the computation of musical structures\n",
    "2. Constitute the basis for the distinguishing states of consciousness (when applied to M/EEG signal).\n",
    "\n",
    "In this notebook we will go through different metrics of harmonicity that can be derived from time series.\n",
    "\n",
    "As a first step, we will identify spectral peaks of interest in the signal (see the *peaks extraction* notebook for more details).\n",
    "\n",
    "Then, each metric can be computed on any pair of frequencies. When used on a set of more than two frequencies, some metrics (harmonic similarity, inter-harmonic concordance) will average the values for all possible pairs of frequencies, while others (euler, sub-harmonic tension) will incorporate all the frequencies in their computation by more complex ways than averaging the harmonicity of all pairs of frequencies."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Harmonic similarity\n",
    "\n",
    "The harmonic similarity, a measure developed by [Gill and Purves (2008)](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0008144), corresponds to ''the percentage of harmonic frequencies that the dyad held in common with a harmonic series defined by the greatest common divisor of the harmonic frequencies in the dyad''.\n",
    "\n",
    "The formula to derive the harmonic similarity, which is called by the function *dyad_similarity*, is\n",
    "\n",
    "*HS* = ((x + y - 1) / (x * y)) * 100\n",
    "\n",
    "We will visualize this metric by defining a ratio of two frequencies, computing the harmonic series of each frequency, and comparing them with the harmonic series of the fundamental frequency, defined as the greatest common divisor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reduced fraction : 3/2\n",
      "Reduced fraction : 33/20\n",
      "Harmonic similarity : 66.67\n",
      "Fundamental frequency : 100\n",
      "Harmonic similarity : 7.88\n",
      "Fundamental frequency : 10\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from biotuner.vizs import viz_harmsim\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from fractions import Fraction\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore', category=DeprecationWarning)\n",
    "# define two harmonic frequencies\n",
    "harm_ratio = [300, 200]\n",
    "print('Reduced fraction : {}'.format(Fraction(harm_ratio[0]/harm_ratio[1])))\n",
    "\n",
    "# define two non-harmonic frequencies\n",
    "nonharm_ratio = [330, 200]\n",
    "print('Reduced fraction : {}'.format(Fraction(nonharm_ratio[0]/nonharm_ratio[1]).limit_denominator(1000)))\n",
    "\n",
    "# plot the harmonic similarity of the two pairs of frequencies\n",
    "viz_harmsim(harm_ratio[0], harm_ratio[1], n_fund=10)\n",
    "viz_harmsim(nonharm_ratio[0], nonharm_ratio[1], n_fund = 40)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inter-harmonic concordance\n",
    "\n",
    "This metric takes a pair of frequency peaks and compares their harmonics pairwise to find concordances.\n",
    "\n",
    "We will use a function that plot a visual representation of the inter-harmonic concordance for a pair of high-consonant and a pair of low-consonant frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[36, 6, 12, 18, 24, 30]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[56, 28]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from biotuner.vizs import viz_interharm_conc\n",
    "# Define number of harmonics\n",
    "n_harms = 20\n",
    "\n",
    "# High-consonant frequencies\n",
    "x = 3\n",
    "y = 2\n",
    "viz_interharm_conc(x, y, n_harms)\n",
    "\n",
    "# Low-consonant frequencies\n",
    "x2 = 7\n",
    "y2 = 4\n",
    "viz_interharm_conc(x2, y2, n_harms)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Euler Gradus Suavitatis\n",
    "\n",
    "The Euler metric of harmonicity refers to the ''sweetness'' of a musical chord.\n",
    "The first step is to find the least common multiple (LCM) of the reduced form of the set of frequencies.\n",
    "Then, the prime factors of the LCM is added, and finally the number of prime factors is subtracted to give the final result.\n",
    "\n",
    "Here, we use a function to plot the LCM of the set of frequencies and compare a case of low- and high-harmonicity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Euler Gradus Suavitatis = 9\n",
      "Prime factors are [2, 2, 3, 5]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Euler Gradus Suavitatis = 17\n",
      "Prime factors are [3, 5, 11]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from biotuner.vizs import viz_euler\n",
    "\n",
    "# high-harmonicity chord\n",
    "chord_harm = [3, 4, 5]\n",
    "viz_euler(chord_harm)\n",
    "\n",
    "# low-harmonicity chord\n",
    "chord_lowharm = [3, 5, 11]\n",
    "viz_euler(chord_lowharm)\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sub-harmonic tension\n",
    "\n",
    "The subharmonic tension is derived from the [article on transitional harmony](https://downloads.spj.sciencemag.org/research/2019/2369041.pdf) from Chan, Dong and Li (2019). The subharmonic tension refers to the level of alignment between the sets of subharmonics of each note constituting a chord.\n",
    "\n",
    "Here we will visualize harmonic tension by plotting all the subharmonics of each chord's notes and finding where they align."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\user\\github\\biotuner\\biotuner\\metrics.py:656: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  harm_temp.append(1 / delta_norm)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Subharmonic tension of chord [3, 4] is 0.0\n",
      "Subharmonic tension of chord [3, 4.6] is 0.0069694349009638955\n",
      "Subharmonic tension of chord [3.2, 4.3] is 0.00778210116731511\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from biotuner.metrics import compute_subharmonic_tension, compute_subharmonics\n",
    "from biotuner.biotuner_utils import frequency_to_note\n",
    "from matplotlib.pyplot import figure\n",
    "\n",
    "# define the chords\n",
    "chords = [[3, 4], [3, 4.6], [3.2, 4.3]]\n",
    "\n",
    "# define the number of subharmonics\n",
    "n_harmonics = 30\n",
    "\n",
    "# define the delta limit (ms)\n",
    "delta_lim = 15\n",
    "\n",
    "# compute subharmonic tension for all chords\n",
    "subharms_tot = []\n",
    "common_subs_tot = []\n",
    "delta_t_tot = []\n",
    "sub_tension = []\n",
    "for c in chords:\n",
    "    subharms, common_subs, delta_t = compute_subharmonics(c, n_harmonics, delta_lim)\n",
    "    subharms_tot.append(subharms)\n",
    "    common_subs_tot.append(common_subs)\n",
    "    delta_t_tot.append(delta_t)\n",
    "    _, _, subtens, _ = compute_subharmonic_tension(c, n_harmonics, delta_lim,\n",
    "                                min_notes=2)\n",
    "    sub_tension.append(subtens)\n",
    "common_subs = []\n",
    "for i in range(len(common_subs_tot)):\n",
    "    common_subs.append([np.mean(x) for x in common_subs_tot[i]])\n",
    "\n",
    "# print subharmonic tension values\n",
    "for chord in range(len(chords)):\n",
    "    print('Subharmonic tension of chord {} is {}'.format(str(chords[chord]),\n",
    "                                                  str(sub_tension[chord][0])))                                                                 \n",
    "\n",
    "# plot subharmonics and their delta values\n",
    "fig, ax = plt.subplots(figsize=(4, 6))\n",
    "colors = ['orange', 'turquoise', 'purple']\n",
    "for i in range(len(subharms_tot)):\n",
    "    m=0\n",
    "    for note, color in zip(subharms_tot[i], colors):\n",
    "        \n",
    "        x = [i+1+m]*len(note)\n",
    "        ax.scatter(x, note, color=color, s=25)\n",
    "        if len(common_subs_tot[i]) > 0:\n",
    "            x_fit = [i+1+0.25]*len(common_subs_tot[i])\n",
    "            y_fit = [np.average(x) for x in common_subs_tot[i]]\n",
    "            ax.scatter(x_fit, y_fit, color='black',\n",
    "                       marker='^', s=150, alpha=0.6)\n",
    "            for z, txt in enumerate(delta_t_tot[i]):\n",
    "                ax.annotate(str(np.round(txt, 1)), (x_fit[z], y_fit[z]),\n",
    "                            bbox=dict(boxstyle=\"square\", alpha=0.1,color='deeppink'), \n",
    "                            xytext=(x_fit[z]+0.1, y_fit[z]))\n",
    "                #ax.annotate(str(frequency_to_note(y_fit[z])), (2.5, y_fit[z]),\n",
    "                #            bbox=dict(boxstyle=\"square\", alpha=0.1,color='turquoise'), \n",
    "                #           xytext=(x_fit[z]+0.1, y_fit[z]+5))\n",
    "        m = m+0.05\n",
    "ax.annotate('delta values', (0.95, 100), bbox=dict(alpha=0.1, color='deeppink'))\n",
    "plt.xlabel('Chord number', size=14)\n",
    "plt.ylabel('Subharmonic cycle (ms)', size=14)\n",
    "plt.xticks(np.arange(1, len(subharms_tot)+1, 1))\n",
    "plt.ylim(0, 2500)\n",
    "plt.gca().invert_yaxis()\n",
    "#plt.savefig('transitional_subharmonics_5notes_IF.png', dpi=300)"
   ]
  }
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