Using PIs - OPIs, UPIs, OPCIs, and UPCIs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "saved-attribute",
   "metadata": {},
   "source": [
    "# Using PIs - OPIs, UPIs, OPICs, and UPCIs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "atlantic-stevens",
   "metadata": {},
   "source": [
    "## Importing Required Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "together-garlic",
   "metadata": {},
   "outputs": [],
   "source": [
    "import music21, pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rapid-consultation",
   "metadata": {},
   "source": [
    "## Defining Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sustained-quantum",
   "metadata": {},
   "source": [
    "### Ordered Pitch Interval (OPI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "competent-portal",
   "metadata": {},
   "outputs": [],
   "source": [
    "# OPI\n",
    "def get_opi(x, y):\n",
    "    \"\"\"\n",
    "    Get the OPI from a music21 built-in function\n",
    "    \"\"\"\n",
    "\n",
    "    x = music21.note.Note(x)\n",
    "    y = music21.note.Note(y)\n",
    "\n",
    "    opi = music21.interval.notesToChromatic(x, y)\n",
    "    \n",
    "    return opi.semitones"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vocal-strip",
   "metadata": {},
   "source": [
    "### Unordered Pitch Interval (UPI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "restricted-philip",
   "metadata": {},
   "outputs": [],
   "source": [
    "# UPI\n",
    "def get_upi(x, y):\n",
    "    \"\"\"\n",
    "    Get the UPI from a music21 built-in function\n",
    "    \"\"\"\n",
    "    \n",
    "    x = music21.note.Note(x)\n",
    "    y = music21.note.Note(y)\n",
    "    \n",
    "    opi = music21.interval.notesToChromatic(x, y)\n",
    "    \n",
    "    return opi.undirected"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "powerful-highland",
   "metadata": {},
   "source": [
    "### Ordered Pitch Class Interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "legitimate-dutch",
   "metadata": {},
   "outputs": [],
   "source": [
    "# OPCI\n",
    "def get_opci(x, y):\n",
    "    \"\"\"\n",
    "    Use Straus' OPCI 'y - x mod12'\n",
    "    \n",
    "    \"\"\"\n",
    "    opci = (y - x) % 12\n",
    "    \n",
    "    return opci"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "suspended-genealogy",
   "metadata": {},
   "source": [
    "### Unordered Pitch Class Interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "otherwise-person",
   "metadata": {},
   "outputs": [],
   "source": [
    "# UPCI\n",
    "def get_upci(x, y):\n",
    "    \"\"\"\n",
    "    Use Straus' UPCI, a.k.a. 'interval class'.\n",
    "    'x - y mod12, whichever one is smaller'\n",
    "    \n",
    "    \"\"\"\n",
    "    z1 = (x - y) % 12 \n",
    "    z2 = (y - x) % 12\n",
    "    \n",
    "    if(z1 < z2):\n",
    "        upci = z1\n",
    "    \n",
    "    else:\n",
    "        upci = z2\n",
    "\n",
    "    return upci"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "isolated-democrat",
   "metadata": {},
   "source": [
    "### Take All Intervals and Place into a pandas Dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "altered-edmonton",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Collect all interval types and place them into pandas dataframe.\n",
    "def get_all_intervals(pitch_sequence):\n",
    "    \n",
    "    \"\"\"\n",
    "    Find all interval types (according to Straus) in a pitch sequence, and create a dataFrame.\n",
    "    \n",
    "    \"\"\"\n",
    "    df = pandas.DataFrame(columns=['PCs','opi','upi','opci','upci'])\n",
    "    \n",
    "    for i in range(len(pitch_sequence)):\n",
    "        \n",
    "        x_pitch = pitch_sequence[i].pitch.pitchClass\n",
    "        \n",
    "        if((i + 1) < len(pitch_sequence)):\n",
    "            y_pitch = pitch_sequence[i + 1].pitch.pitchClass\n",
    "        else:\n",
    "            break\n",
    "        \n",
    "        data = [\n",
    "                str(x_pitch) + ' to ' + str(y_pitch), \n",
    "                get_opi(x_pitch, y_pitch),\n",
    "                get_upi(x_pitch, y_pitch), \n",
    "                get_opci(x_pitch, y_pitch), \n",
    "                get_upci(x_pitch, y_pitch)\n",
    "        ]\n",
    "        \n",
    "        df.loc[i] = data\n",
    "        \n",
    "    return(df.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "injured-hammer",
   "metadata": {},
   "source": [
    "## Building a music21 Stream from a Pitch Sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "recognized-world",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 49,
       "width": 674
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "                <div id='midiPlayerDiv677'></div>\n",
       "                <link rel=\"stylesheet\" href=\"//cuthbertLab.github.io/music21j/css/m21.css\"\n",
       "                    type=\"text/css\" />\n",
       "                <script>\n",
       "                require.config({\n",
       "                    paths: {'music21': '//cuthbertLab.github.io/music21j/src/music21'}\n",
       "                });\n",
       "                require(['music21'], function() {\n",
       "                               mp = new music21.miditools.MidiPlayer();\n",
       "                               mp.addPlayer('#midiPlayerDiv677');\n",
       "                               mp.base64Load('data:audio/midi;base64,TVRoZAAAAAYAAQACBABNVHJrAAAAFAD/UQMHoSAA/1gEBAIYCIgA/y8ATVRyawAAAEQA/wMAAOAAQIgAkDxakACAPAAAkD5akACAPgAAkElakACASQAAkEBakACAQAAAkERakACARAAAkENakACAQwCIAP8vAA==');\n",
       "                        });\n",
       "                </script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
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   "source": [
    "# Decide on a Pitch Sequence\n",
    "# --------------------------\n",
    "\n",
    "# Can be written with pitch classes in integer notation\n",
    "# sequence_of_pitches = [0,2,1,4,8,7]\n",
    "\n",
    "# Can be written with traditional note names and pitch space specifiers\n",
    "sequence_of_pitches = ['C4','D4','C#5','E4','G#4','G4']\n",
    "\n",
    "# Creates music21 Stream to show and hear the pitches\n",
    "pitch_sequence = music21.stream.Stream()\n",
    "[pitch_sequence.append(music21.note.Note(x, type='half')) for x in sequence_of_pitches]\n",
    "\n",
    "# Showing a score\n",
    "pitch_sequence.show()\n",
    "\n",
    "# Listening...\n",
    "pitch_sequence.show('midi') # does not work on GitHub"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "listed-democrat",
   "metadata": {},
   "source": [
    "## Viewing the Dataframe of Intervals from the Pitch Sequence Stream"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "expired-finder",
   "metadata": {},
   "outputs": [
    {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "      <th></th>\n",
       "      <th>0</th>\n",
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       "      <th>2</th>\n",
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       "      <th>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PCs</th>\n",
       "      <td>0 to 2</td>\n",
       "      <td>2 to 1</td>\n",
       "      <td>1 to 4</td>\n",
       "      <td>4 to 8</td>\n",
       "      <td>8 to 7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>opi</th>\n",
       "      <td>2</td>\n",
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       "      <td>3</td>\n",
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       "    <tr>\n",
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       "      <th>opci</th>\n",
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       "      <td>4</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>upci</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "      <td>4</td>\n",
       "      <td>1</td>\n",
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       "           0       1       2       3       4\n",
       "PCs   0 to 2  2 to 1  1 to 4  4 to 8  8 to 7\n",
       "opi        2      -1       3       4      -1\n",
       "upi        2       1       3       4       1\n",
       "opci       2      11       3       4      11\n",
       "upci       2       1       3       4       1"
      ]
     },
     "execution_count": 8,
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    }
   ],
   "source": [
    "# Get All Intervals in Pitch Sequence and Place into pandas dataframe\n",
    "# -------------------------------------------------------------------\n",
    "\n",
    "get_all_intervals(pitch_sequence)"
   ]
  }
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