Hexatonic Collections.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "thousand-market",
   "metadata": {},
   "source": [
    "# Hexatonic Collections\n",
    "\n",
    "## Included Collections\n",
    "\n",
    "- HEX<sub>0,1</sub> (<strong>P</strong>itch <strong>C</strong>lasses C, E, or G#) in 1-3 ordering\n",
    "- HEX<sub>1,2</sub> (<strong>PCs</strong> C#, F, A) in 1-3 ordering\n",
    "- HEX<sub>2,3</sub> (PCs D, F# Bb) in 1-3 ordering\n",
    "- HEX<sub>3,4</sub> (PCs Eb, G, B) in 1-3 ordering\n",
    "- HEX<sub>0,1</sub> (PCs C#, F, A) in 3-1 ordering (\"Augmented Scale\")\n",
    "- HEX<sub>1,2</sub> (PCs D, F#, Bb) in 3-1 ordering (\"Augmented Scale\")\n",
    "- HEX<sub>2,3</sub> (PCs Eb, G, B) in 3-1 ordering (\"Augmented Scale\")\n",
    "- HEX<sub>3,4</sub> (PCs E, Ab C) in 3-1 ordering (\"Augmented Scale\")\n",
    "\n",
    "## Remaining Collections\n",
    "\n",
    "- Prometheus Scale\n",
    "- Blues Scale\n",
    "- Tritone Scale\n",
    "\n",
    "## Hexatonic Collections with their own Notebook\n",
    "\n",
    "- Wholetone Scale"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "available-rehabilitation",
   "metadata": {},
   "source": [
    "## Importing Necessary Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "balanced-branch",
   "metadata": {},
   "outputs": [],
   "source": [
    "import music21, copy\n",
    "from IPython.display import Markdown, display"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sixth-advancement",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hungry-central",
   "metadata": {},
   "source": [
    "### Printing to Markdown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "living-madrid",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Printing to Markdown\n",
    "# ------------------------\n",
    "\n",
    "def print_md(string):\n",
    "    \"\"\"\n",
    "    Pretty print function to print to markdown.\n",
    "    \"\"\"\n",
    "    display(Markdown(string))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "universal-tiger",
   "metadata": {},
   "source": [
    "### Time Signature Fitting of Collection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "accredited-starter",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Finding a time signature based upon a pitch class collection's length\n",
    "# ----------------------------------------------------------------------\n",
    "\n",
    "def find_time_signature(scale):\n",
    "    \"\"\"\n",
    "    Finds the best fitting time signature of a given scale in a music21 \n",
    "    stream.\n",
    "    \"\"\"\n",
    "    \n",
    "    scale_stream = scale.flat.notes\n",
    "    m = music21.stream.Measure()\n",
    "    [m.insert(i.offset, i) for i in scale_stream]\n",
    "\n",
    "    return music21.meter.bestTimeSignature(m)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "silver-bowling",
   "metadata": {},
   "source": [
    "### Analyzing a Hexatonic Collection from a music21 Stream"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "outer-commonwealth",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Finding the mode and ordering of a hexatonic collection\n",
    "# -------------------------------------------------------\n",
    "\n",
    "def analyze_hexatonic_collection(collection):\n",
    "    \"\"\"\n",
    "    Finding the hexatonic mode and ordering for chosen hexatonic collection \n",
    "    through analysis, meaning that a lookup table is not being used.\n",
    "    If you were to use it in a project consulting a lookup table would \n",
    "    benefit computing time.\n",
    "    \"\"\"\n",
    "    \n",
    "    # convert the hexatonic collection into a note name sequence\n",
    "    mode_notes = [n.name for n in collection]\n",
    "    \n",
    "    # converting notes in the hexatonic collection to pitch classes\n",
    "    pitch_classes = [music21.pitch.Pitch(n).pitchClass for n in mode_notes]\n",
    "    \n",
    "    # interval between the first and second note \n",
    "    order = music21.interval.notesToChromatic(collection[0],collection[1])\n",
    "    \n",
    "    # the range of possible hexatonic collections\n",
    "    the_range = 5\n",
    "    \n",
    "    if(order.directed == 1):\n",
    "        \n",
    "        # ordering of hexatonic collection with interval from first to second note\n",
    "        ordering = \"1-3\"\n",
    "        \n",
    "        # checking for discrete pitch classes in hexatonic collection\n",
    "        for x in range(the_range):\n",
    "            if(all(n in pitch_classes for n in [x, x + 1])):\n",
    "                hex_mode = x, x+1\n",
    "                break\n",
    "            \n",
    "    else:\n",
    "        \n",
    "        # ordering of hexatonic collection with interval from first to second note\n",
    "        ordering = \"3-1\"\n",
    "        \n",
    "        # checking for discrete pitch classes in hexatonic collection\n",
    "        for x in range(the_range):\n",
    "            if(all(n in pitch_classes for n in [x, x + 3])):\n",
    "                hex_mode = (x + 3) % 4, ((x + 3) % 4) + 1\n",
    "                break\n",
    "            \n",
    "    return hex_mode, mode_notes[0], pitch_classes[0], ordering  \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "theoretical-illness",
   "metadata": {},
   "source": [
    "### Creating a Hexatonic Collection Using music21's AbstractScale.buildNetworkFromPitches()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "formal-spanish",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hexatonic Collections\n",
    "# ----------------------------------------------------------------------\n",
    "# Since there is no pre-cooked hexatonic collection à la Straus in\n",
    "# music21, we have to create a new scale network to create a hexatonic\n",
    "# collection. HEX3,4 (starting on pitch class C) in 3-1 ordering is also\n",
    "# known as the \"Augmented scale.\"\n",
    "\n",
    "def get_hexatonic_collection(pc=\"C4\", ordering=\"1-3\"):\n",
    "    \"\"\"\n",
    "    Builds a hexatonic collection based on a pitch center and either 1-3 \n",
    "    or 3-1 ordering. The default pitch class for the pitch center in C4, \n",
    "    while the default ordering is 3-1.\n",
    "    \"\"\"\n",
    "    \n",
    "    # container for custom scale based on a pitch sequence model\n",
    "    new_scale = music21.scale.AbstractScale()\n",
    "\n",
    "    # deciding what ordering the new scale will have: 1-3 (default)\n",
    "    # or 3-1\n",
    "    if(ordering == '3-1'):\n",
    "        new_scale.buildNetworkFromPitches(\n",
    "            [\"C#4\", \"E4\", \"F4\", \"G#4\", \"A4\", \"C5\"])\n",
    "    else:\n",
    "        new_scale.buildNetworkFromPitches(\n",
    "            [\"C4\", \"C#4\", \"E4\", \"F4\", \"G#4\", \"A4\"])\n",
    "\n",
    "    # creating a hexatonic collection based on a given pitch center\n",
    "    hex_col = new_scale._net.realizePitch(pc)\n",
    "\n",
    "    # opening a stream to hold a hexatonic collection\n",
    "    hexatonic_collection = music21.stream.Stream()\n",
    "\n",
    "    # filling the stream with pitch class\n",
    "    [hexatonic_collection.append(music21.note.Note(p)) for p in hex_col]\n",
    "\n",
    "    # pitch centet\n",
    "    pitch_center = music21.note.Note(pc).name \n",
    "    \n",
    "    # return the collection\n",
    "    return hexatonic_collection, pitch_center, ordering\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nuclear-albuquerque",
   "metadata": {},
   "source": [
    "## Example Creating a Hexatonic Collection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "demanding-houston",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "### F# Hexatonic Collection in 3-1 Ordering"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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x7wLgaMq/M5IkSVLfGdPGvv9KfPGrZjHwIYYmQyGKU7yePO+1wkqbE8WUalmtG4FIkrpqGdEj9LsV619j6MiGccQQzSwzgHk0ngwtGUP8vZTyMEAk2tcmku3XA9tXtGl1/vZFwF7AAy1HJ0mSJPWAVnuIziEmM6/lcODajPXLiGHyO9B7PUSPaKBNo5UtJUn9YxmRJMqaFqVab9C0qcDVxJD7VrS6n7QqsCeR9NwheSzdsD4meXwPcHtqnxeBmU2e51HgUOCWVgOVJEmSesU4YK0W9juN2r1LvwH8rsax/x/xoX02sAXwFjEXUNHzc76/gTazae3frN+smTyuwuj4eTUyTE4evWbVrHFED9Gsa6dy3ZiMdWfT/k0+r1s1YhrwYcrzgJ7fwD4rM/T6eon43LV8dvNhfkaMDFqI16mKUUryV17LUi9bKXmcQRRTlPrBOGAivteqf6RHca/O0Gt3Wq0dB3AOKEmSJEmSJEmjxAD1q8RX2ocYmpXlFeAUsocXLk9U092JxgoTvQZcRgzN6kbS9jTKd/FquQM4r8Ox9IJVif/L/8DhcSreADGkeBdgfeIuUKmX+ttEsbZriB7newCfLiBG9bcvEHODHl+xfk3gn1OvrwEurWjzCYbP0disrwOPt3kMjQ4fo7kq8YPAjxg6F+6RxPvoKZRHC00i5h59BXiVKJ7kTXP1iknAt4CLiSJ0Uj/4AFFg+FhiRKTUD/6VmCbnJ0UHIjVoQ+K7HMRnhYdT26YBJ+d1ogHil2OwynJQlf02rrNfreUGIjnXSRObiOdpeqfS/Ltor1JsLTOJn7eReVWlTjqQmHe43u/mEuC3xFyQUrOuB57KWP9lytfYYobPI70R8BzN/V2rXK6jd/6uqPedRe3r6VmieOV8YHdi6ptKlzE0QSr1utWI6/uYeg2lHnIicd2uWHQgUhPmE1PlSP1iV8qfg3es2LYxNT43N1tUaRawbpVt1wOXZKx/Z7Kt5tj9GuYCtyaPT7Z4jHrWb6LtCfROj4mziJ60cwuOQ+qEqcQ13mjF7rHEnXipFaWketqKwOdSr88lbu6lbUTMVdOqBcDR9M7fFfW+yps+txJFLO8E5hGfle4gPh9c1d3QJEmSpP7QbEL0PTW2fY3hX+hWJHohtJoMLZkN/CY5/6ttHivLFg22O5sYQt5NmwAnAd8B7uryuaWizABupvnK2/ayU6uWMTQhOkAMY18jeT2f4cPp27UI2At4IOfjamQ7D7gNmJA8PxW4stCIJEmSpD5Tq1J8lmoJ0fnA/2asP50Yz5+HLYDv53SsSls30OZ24PMdOn8t04BDsMqbRo+pwNU0nwwteTPHWDR6VCZEj6M8NPMlYuqGrPmxW/Uo0aPZOZrVrD8CPwUeKToQSZIkqV81mxCtnDut5ByG9w7dADiqweO+Qsx3Vc/Hqd1LtVX1imG8CHwEJ8OWuuFsYNM29r8vr0A0qqQTop8hJuQGeB7YjfrzLd7fxLl+AmxO9IKWJEmSJHVZswnR1TLWLQEuyFj/GaoPX/09Uaii5ESieuQqwIeBy2vEcGr9MJsyGXh3je2DxByGj+V8XknDbUH14myN+mMegWjUKc3LeCYxdy1EL865NFZ85tPE1CbVepE+Sfz92gD4ezoz/YskSZIkqQHNziGaVTjifqLCbtpyZFcnfwn4JPBfRDL2JGKe0TnJ9gVEMvRyokfOLzLOuTOwDVE8IA9zqf3v8E/ANcnzrZP25wALczq/pLJ/yOEYWcXdpHqWEnM2b5K8vgL4O+LvViPeBL5I3OzbiJj6YRzRw/R54u9kZTEcSZIkSVIBmk2IrpSxbn7Gui2AlSvWLSSSmQ8mr5cBdwM7Uk6Ipt0AvJeolLpcxbaPkF9CdI8a234FfCN5vjtwKbACsA7FzCcqjXSbt7n/9ZRvYEjNKCUrXwT+kago30rl97dx2gZJkiRJ6mnNDpnP6inzUMa6d2Ws+zjlZGhJaWjrHLKH199LduJxn2oBNmk8kVzNcjdwOPEl+aNEb6EVkm3Tczp/HlYihvR/neiRJPWzmW3suwA4mtaSWNLXgUOJazBrXmypn1wAXFR0EJIkSVKvaraH6NNE78i0v2S0q6yIfi9wWUa7u5PHVYAZxBxrlX5EDKPdKrXuHcAEoidOO95P9jQAzxFzmb5GFIb6AdXnQ+2WAWBdYrqAbYBtgc2I3rOlLz3XJYvUr55i+HtMIxYBewEP5BuORpHbk0UaCc4sOgBJkiSpl7WSEK2U1ct0+YrXF5Dd2yZd/GQO2QnRQeBnDE2IjiEq3mcN12/G4Rnr3gb2J4oofQX4WpvnaNUUYHtgv+T1xQz/d61UdNJWatelwA5N7vMo0bPvlvzDkaSe9QdgJ4aPvpEkSZJUxzjggCbaZyU1/4YYqpq2ZsXr1aucZ7nkmAPA3xIFlrIsyVj3Udr7ErAa2cPlzyHi/wHROzTL2jT379aKc4mkaEm9ZCjALgyfu7WeMcSw+8XAG5T/j9dIHrcBXmnymFKrHiN6nc9usP11wPnANDr/Oyll2SZ53I3WejdL7WplGp8ZxOcF3zfVLyYnj1vgdav+sVny+GHgrSIDkZowifhM63ut+sU7U8/nMvSz8YxaOw7gPGmSJEmSJEmSRokBYMsm2o8BrgZWTa37C8N7Wk4hem6VhtN/i+qT+3+TqOD+ENHrM8vKwI0V6/YBnmgk6AzTiaG56V6X/00MkS8liI8neq1muQr4UovnbtRdDbQZBF4g/m0fAm6lXCk5y/uAI4EN6hx3GfDjpO2/kD3/q9Rp44g7OpOI95JXU0ut61zqpvcAZwCHYXV59Y9/I+Z7P6joQKQGTQFuAE4nptKS+sEngGOAHYn57qV+cDlRl6HT+Q4pL9sQI6wB/o5yrSKIgrm/yvNkPyQScell/Yx2V6S230z1+S1PTNq8RVR9zzK94nwLgLGthQ/AryuOdz0xfD/tewz/OUvLz9s4d6Mqz/k4cAnxxvQ+oqL8PIYnirNMJZKm1X6erGVp8nhETj+PJI1EexPvldsXHYjUhMuAe4oOQmrCasR77TFFByI1ofQ9t9q0cFIvmo83ntRfdqWcx9qxYtvG1Mh7ZRVEqud0hs+BktWT8iTKvbh2AvatcrxSYaUJwIZV2lT2aLyJSNi14kPJUnI/UUSp1+Z1+RJwCnBy8voooifuN4FrgZcaPM4MInF6cJPnb+XakCRJkiRJknpas1XmAf5K9J48MbXueGKI9XOpdfck67+TvL6ISIpeVXG8dHfWOUT37Eo7V7y+oqmIyyYA369Y9yiRZKy0U43jbAf8qGLdIuBUYgh7Hk5LHue2cYypxBQHs9qORpIkSZIkSRrFViaGcKe7m56T0W6A6OlYGn69jJi3qrJi+jPJ9lOqnO/m1Hmezdi/UevQ3LDxZpdDWoyrlrnJsffO2FZvyPwvaO/neQaHgUpSLQ6ZVz9yyLz6jUPm1Y8cMq9+5JB59ZuuDpkHeIX4Evhaat3fA5+saDdI9L58N3AlkSA9luHJ09Kw+TkZ59qaob01vwu82VLUUYTpmhb3redt4JEOHbsVeRRLuAK4PYdYJEmSJEmSpJ7QypD5kruBjxFVyEqJ1R8Ck4leoOkq0LcTVeHXJTK2lZV4/0hUmq9MiI4Fzkq9vo1IiLZqMDlPIwWZTgc+X2XbJQyfN7VUiKhXVGbGW3FJDseQJEmSpNHmV8BDtN6ZRyrCZ4CXiw5C6oZ2EqIAvyEKEl0IrEQkGr8NvJcod/9cRfvHkqVSqYfoLCKhupDoTXo60bsUolfqwcDiNmMeBJY00G5ZnW2NHKNIM9rc/3o615tWkiRJkkayh5JF6idXFx2A1C15VBL/NbAtQ3t9fpDoQfohIrFZT7qw0qbAJODfgS8k6xYmx+ylIem9bmob+y4AjiaSx5IkSZIkSdKIkUdCFGLi3XcBF6TWrUkkS+cBHwdWqbH/Q0SVdojK9POBf0hev0AMc/99TrGOFANEj9y1gTOIHp0zU9tfbfG4i4C9gAfaCU6SJEmSJEnqRe0OmU97nRgmfwbwVWDfZP3WwPnEEPO7iWTnX4ih85OJxOl0ykPU908d89dEoabKofd5+yXDq7iPr9H+IMo/X8kiInHbqSJEqwJ7EpWMd0geS71ASxU3ZwN/TZ6ne9026lHgUOCWlqOUJEmSJEmSRqktiLlFX6BGmfuMZSlwMbAzjQ23z8MjTcZYbTkkx5jmEFMG/LaJ878vtf84oghVo/ueS8wDK0lq3N7Ee+j2RQciNeEy4J6ig5CasBrxXntMvYaSJGlU2ZVyXquyuPjG1MiDDQDf6nBwA0Qv0PWBNYAVgBWJhN3rqWVi0uZNhlaW74Y5wLptHmMJcDPxs+Thc9TupZrlEqKXZ8l4YCciOZ11rNeIuV/vJYpWSZKaswGwH/BT4OmCY5EatS8whRjBI/WDiUTl4+uBPxQciyRJ6h3rAB9Nnl8EPJXaNhU4otqOA8AbnYurKWOA5ZLnb2JBn4kt7PMW5akHKo0h/r8HkjalrLgkqXVjgQnUfv+Ves0E4vPAW0UHIjVoAFgeWEx0QpAkSYKhucTK72Slzw89byXKSbrdC46lF9Qb4v4s0Rt1PvHvVatolSSpMxwyr37kkHn1G4fMS5KkXOVVZT4Pr1Ie7j2nyEB6xNKK17cCpxBDM9chpiF4EHgSuAp4uavRSZIkSZIkSX0ozyrzebgXWA8TohCV7CcSw9rOA04Friw0IkmSJEmSJKnP9VIPUYgCPwCzC42iN1xKFOl4pOhAJEmSJEmSpJGiF3uIAswqNApJkiRJvWIh8AngtqIDkSRJI0OvJUQfTB6nE5Wg3iwwFkmSJEnFews4v+ggJEnSyNHJIfMTgc2AXYgh8AMN7PNM6vnMDsQkSZIkSZIkaRTrREJ0JeB7wFPEEPibgPnAi8BpwNQa+z6fej6zA7FJkiRJkiRJGsXyHjK/NnA1sEnGtlWAE4D9gd2AJzLaLCESp6sS1eZV2wXEECJJkiRJkiRJDcgzITqWqIqelQxNmw1cCLwXGMzY/hyREB2fY2wj1ZlFByBJkvrOZdQesSNJkiSpQR8lEpyNLptWOc5NyfajOhxvv1gV2BuYVnQgkqRh9ib+Zm1fdCCSJEmSpMbkOYfooU22/0CV9Sskj0vaiGUkeRG4Eni26EAkSZIkSZKkfpdnQvRvmmw/pcr6VZLHpW3EIkmSJEmSJEnD5JUQXY5yz85GvZaxbhKwTvLcHpGSJEmSJEmScpVXQnSA5nt03pyxblfKxZTubCsiSZI67zngv4EFRQciSZIkSeq+O2m8oNIdRBI1bQD4n2T7A90JWZIkSZIkSZJacxKNJUNfADbJ2P9jqTbHdiFeSZIkSZIkSWrZROBRaidD7wI2zdj3MGBx0uZhYHIX4pUkSZIkSZKktmwNvMjwROgvgPcDYyva7whcm2r3RrJOkiRJkiRJknJXOY9nHjYDfgpsnlr3DHA7UTn+TWADYEtgRqrN08ABwO87EJMkSZIkSZIkdcx44BjgQRorsHQYsFwhkUqSJEmSJEkaNTrRQ7Ty+FsB2xM9RlcBFhLzhD5MJEzvIxKjkiRJkiRJktRR/x8AiC4yLUqjBgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 49,
       "width": 674
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a hexatonic collection, providing the pitch center, and ordering\n",
    "hexatonic_collection_1 = get_hexatonic_collection('f#4', '3-1')\n",
    "\n",
    "# Creating a (backup) copy of the music21 stream\n",
    "hexatonic_collection_2 = copy.deepcopy(hexatonic_collection_1[0])\n",
    "\n",
    "# Finding a time signature that can hold the collection\n",
    "hexatonic_collection_1[0].insert(0, find_time_signature(hexatonic_collection_1[0]))\n",
    "\n",
    "# Print a header\n",
    "print_md(\"### \" + hexatonic_collection_1[1] + \" Hexatonic Collection in \" + \n",
    "         hexatonic_collection_1[2] + \" Ordering\")\n",
    "\n",
    "# Printing the collection in Common Music Notation (CMN) format\n",
    "hexatonic_collection_1[0].show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "humanitarian-salon",
   "metadata": {},
   "source": [
    "## Example Analyzing a Hexatonic Collection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "third-disorder",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1, 2), 'F#', 6, '3-1')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# analyzing mode, pitch center, and ordering of a given hexatonic collection\n",
    "analysis_results = analyze_hexatonic_collection(hexatonic_collection_2)\n",
    "analysis_results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "korean-branch",
   "metadata": {},
   "source": [
    "### Formatting Analysis Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "sized-might",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "*Mode*: HEX<sub>1,2</sub><br /> *Pitch Center*: F# (6)<br /> *Ordering*: 3-1"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pretty printing results\n",
    "print_md(\"*Mode*: HEX<sub>{},\".format(analysis_results[0][0]) + \n",
    "         \"{}</sub><br /> \".format(analysis_results[0][1]) + \n",
    "         \"*Pitch Center*: {} \".format(analysis_results[1]) + \n",
    "         \"({})<br /> \".format(analysis_results[2]) +\n",
    "         \"*Ordering*: {}\".format(analysis_results[3]))\n"
   ]
  }
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