Transformational Theory-interactiveImage.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformational Theory - Draft"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some examples to test transformational functions with music21"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a Jupyter notebook created by [@musicenfanthen](https://github.com/musicEnfanthen) to work with some basic functions of transformational theory by David Lewin (and others; see e.g. Lewin, GMIT, 2007). \n",
    "\n",
    "For more information on Jupyter notebooks go to http://jupyter.org/. \n",
    "\n",
    "To execute a block of code in this notebook, click in the cell and press `Shift+Enter`.\n",
    "\n",
    "To get help on any music21 routine, click on it and press `Shift+Tab`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from music21 import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probably you have to set manually the correct file path to an Application that is able to open MusicXML files (like MuseScore). To do so, use the music21.environment module to set an musicxmlPath key.\n",
    "\n",
    "Make sure to change the string path/to/your/musicXmlApplication below to the correct file path (keep the quotation marks):\n",
    "\n",
    "    on Mac e.g.: /Applications/MuseScore 2.app/Contents/MacOS/mscore\n",
    "    or on Windows e.g.: C:/Program Files (x86)/MuseScore 2/bin/MuseScore.exe\n",
    "\n",
    "and uncomment the line (remove the # at the begin of the line).\n",
    "\n",
    "In the same way, you can also add a path to your lilypond installation, using env['lilypondPath']:\n",
    "\n",
    "    on Mac e.g.: Applications/Lilypond.app\n",
    "    on Windows e.g.: C:/Program Files (x86)/LilyPond/usr/bin/lilypond.exe\n",
    "\n",
    "Sometimes it's also necessary to adapt the musescoreDirectPNGPath. Check if it corresponds to your museScore path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Environment settings:\n",
      "musicXML:   /Applications/MuseScore 2.app/Contents/MacOS/mscore\n",
      "musescore:  /Applications/MuseScore 2.app/Contents/MacOS/mscore\n",
      "lilypond:   /Applications/Lilypond.app/Contents/Resources/bin/lilypond\n"
     ]
    }
   ],
   "source": [
    "# definition of environment settings is different from the settings \n",
    "# when this jupyter notebook runs locally on your machine.\n",
    "# Changes are necessary because jupyter notebook is running via Binder image\n",
    "\n",
    "env = environment.Environment()\n",
    "\n",
    "env['lilypondPath']='/usr/bin/lilypond'\n",
    "env['musescoreDirectPNGPath'] = '/usr/bin/musescore'\n",
    "env['musicxmlPath'] = '/usr/bin/musescore'\n",
    "\n",
    "environment.set('pdfPath', '/usr/bin/musescore')\n",
    "environment.set('graphicsPath', '/usr/bin/musescore')\n",
    "\n",
    "print('Environment settings:')\n",
    "print('musicXML:  ', env['musicxmlPath'])\n",
    "print('musescore: ', env['musescoreDirectPNGPath'])\n",
    "print('lilypond:  ', env['lilypondPath'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "Using jupyter notebook inside a Binder image causes some issues with music21's \".show()\"-method (see: https://github.com/cuthbertLab/music21/issues/260). Thanks to Tony Hirst (@psychemedia) there is a small workaround with a redefinition of the method:\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# re-definition of show()-method ---> \"HACK\" from https://github.com/psychemedia/showntell/blob/music/index_music.ipynb\n",
    "# see also this music21 issue: https://github.com/cuthbertLab/music21/issues/260\n",
    "%load_ext music21.ipython21\n",
    "\n",
    "from IPython.display import Image\n",
    "\n",
    "def render(s):\n",
    "    s.show('lily.png')\n",
    "    return Image(filename=s.write('lily.png'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createMusic21NoteObjectFromIntervall(pitchArray):\n",
    "    n1 = note.Note(pitchArray[0])       \n",
    "    n2 = note.Note(pitchArray[1])\n",
    "    return [n1, n2]\n",
    "\n",
    "\n",
    "def showStream(prevNote, curNote, transformStr):    \n",
    "    # full name\n",
    "    prevFull = prevNote.pitch.unicodeNameWithOctave\n",
    "    curFull = curNote.pitch.unicodeNameWithOctave\n",
    "    \n",
    "    \n",
    "    # pitch class\n",
    "    prevPc = prevNote.pitch.pitchClass\n",
    "    curPc = curNote.pitch.pitchClass\n",
    "    \n",
    "    # frequency\n",
    "    prevFreq = prevNote.pitch.freq440\n",
    "    curFreq = curNote.pitch.freq440\n",
    "    \n",
    "    # midi\n",
    "    prevMidi = prevNote.pitch.midi\n",
    "    curMidi = curNote.pitch.midi\n",
    "    \n",
    "    curNote.offset = 1.0\n",
    "    \n",
    "    if not prevNote.lyrics:\n",
    "        prevNote.addLyric('full: ' + str(prevFull))\n",
    "        prevNote.addLyric('pc:   ' + str(prevPc))\n",
    "        prevNote.addLyric('midi: ' + str(prevMidi))\n",
    "        prevNote.addLyric('freq: ' + str(prevFreq))\n",
    "            \n",
    "    if not curNote.lyrics:\n",
    "        curNote.addLyric('full: ' + str(curFull))\n",
    "        curNote.addLyric('pc:   ' + str(curPc))\n",
    "        curNote.addLyric('midi: ' + str(curMidi))\n",
    "        curNote.addLyric('freq: ' + str(curFreq))\n",
    "           \n",
    "    intStream = stream.Score()           # create Score\n",
    "    intStream.append(prevNote)\n",
    "    intStream.append(curNote)\n",
    "    \n",
    "    # output\n",
    "    print(transformStr)\n",
    "    intStream.show('text')                     # output of the stream (using the .show()-method)\n",
    "\n",
    "    \n",
    "\n",
    "def getTransposition(prevNote, curNote):\n",
    "    #get pitch classes\n",
    "    curPc = curNote.pitch.pitchClass\n",
    "    prevPc = prevNote.pitch.pitchClass\n",
    "    \n",
    "    # transposition string\n",
    "    transStr = \"T\"\n",
    "    n = (curPc - prevPc) % 12\n",
    "    transStr += str(n)\n",
    "    \n",
    "    # output\n",
    "    showStream(prevNote, curNote, transStr)\n",
    "\n",
    "    \n",
    "def getInversion(prevNote, curNote):\n",
    "    #get pitch classes\n",
    "    curPc = curNote.pitch.pitchClass\n",
    "    prevPc = prevNote.pitch.pitchClass\n",
    "    \n",
    "    # inversion string\n",
    "    invStr = \"I\"\n",
    "    n = (curPc + prevPc) % 12\n",
    "    invStr += str(n)\n",
    "    \n",
    "    # output\n",
    "    showStream(prevNote, curNote, invStr)\n",
    "\n",
    "    \n",
    "def getTranspositionAndInversion(pitchArray):\n",
    "    # pitchArray = [pitch1, pitch2]\n",
    "    if len(pitchArray) > 2:\n",
    "        return\n",
    "    \n",
    "    noteArray = createMusic21NoteObjectFromIntervall(pitchArray)\n",
    "    print(noteArray)\n",
    "    \n",
    "    getTransposition(noteArray[0], noteArray[1])\n",
    "    getInversion(noteArray[0], noteArray[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[<music21.note.Note C#>, <music21.note.Note E>]\n",
      "T3\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 124,
       "width": 748
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 124,
       "width": 748
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example input (two pitches)\n",
    "# pitchArray = [pitch1, pitch2]\n",
    "\n",
    "pitchArray = ['C#4', 'E5']\n",
    "\n",
    "getTranspositionAndInversion(pitchArray)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}