17_01_17 music is math.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nmeasures_to_successes = {}\n",
    "for nmeasures in range(1, 13):\n",
    "    subdivs_total = nmeasures * 16\n",
    "    successes = []\n",
    "    for seqlen in range(1, 13):\n",
    "        for nrepeats in range(1, 3):\n",
    "            seq_total = 0\n",
    "            seq_current = seqlen\n",
    "            niter = 0\n",
    "            while seq_total < subdivs_total:\n",
    "                seq_total += seq_current * nrepeats\n",
    "                seq_current += 1\n",
    "                niter += 1\n",
    "            if seq_total == subdivs_total and niter > 1:\n",
    "                successes.append((seqlen, nrepeats))\n",
    "    nmeasures_to_successes[nmeasures] = successes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nmeasures_to_successes = {x: y for x, y in filter(lambda x: len(x[1]) > 0, nmeasures_to_successes.items())}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------------3----------------------------------------\n",
      "[0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8]\n",
      "----------------------------------------5----------------------------------------\n",
      "[0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
      "----------------------------------------7----------------------------------------\n",
      "[0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
      "----------------------------------------9----------------------------------------\n",
      "[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n",
      "----------------------------------------11----------------------------------------\n",
      "[0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n"
     ]
    }
   ],
   "source": [
    "nmeasures_to_sequences = {}\n",
    "for nmeasures, sequences in sorted(nmeasures_to_successes.items(), key=lambda x: x[0]):\n",
    "    print '-' * 40 + str(nmeasures) + '-' * 40\n",
    "    nmeasures_to_sequences[nmeasures] = []\n",
    "    for seq_len_current, nrepeats in sequences:\n",
    "        subdivs_total = nmeasures * 16\n",
    "        sequence = []\n",
    "        while len(sequence) < subdivs_total:\n",
    "            for _ in xrange(nrepeats):\n",
    "                sequence += xrange(seq_len_current)\n",
    "            seq_len_current += 1\n",
    "        nmeasures_to_sequences[nmeasures].append(sequence)\n",
    "        print sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def accumu(lis):\n",
    "    total = 0\n",
    "    for x in lis:\n",
    "        total += x\n",
    "        yield total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 81, 84]\n"
     ]
    }
   ],
   "source": [
    "seq_tonal_intervals = [0, 4, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3]\n",
    "seq_tonal_start = 53\n",
    "\n",
    "seq_tonal_rel = accumu(seq_tonal_intervals)\n",
    "seq_tonal = [seq_tonal_start + x for x in seq_tonal_rel]\n",
    "print seq_tonal\n",
    "\n",
    "seq_drums = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 53, 57, 60, 62, 64, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 53, 57, 60, 62, 53, 57, 60, 62, 53, 57, 60, 62, 64, 53, 57, 60, 62, 64, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 81, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 81, 53, 57, 60, 53, 57, 60, 53, 57, 60, 62, 53, 57, 60, 62, 53, 57, 60, 62, 64, 53, 57, 60, 62, 64, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 81, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 81, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 81, 84, 53, 57, 60, 62, 64, 67, 69, 71, 74, 76, 79, 81, 84]\n",
      "35\n"
     ]
    }
   ],
   "source": [
    "seq_tonal_final = []\n",
    "nmeasures_total = 0\n",
    "for nmeasures, sequences in sorted(nmeasures_to_sequences.items(), key=lambda x: x[0]):\n",
    "    for sequence in sequences:\n",
    "        if max(sequence) < len(seq_tonal_intervals):\n",
    "            seq_tonal_final += [seq_tonal[i] for i in sequence]\n",
    "            nmeasures_total += nmeasures\n",
    "print seq_tonal_final\n",
    "print nmeasures_total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from midiutil.MidiFile import MIDIFile\n",
    "\n",
    "def sequence_to_midi(sequence, output_name):\n",
    "    # create your MIDI object\n",
    "    mf = MIDIFile(1)     # only 1 track\n",
    "    track = 0   # the only track\n",
    "\n",
    "    time = 0    # start at the beginning\n",
    "    mf.addTrackName(track, time, \"mathmusic\")\n",
    "    mf.addTempo(track, time, 160)\n",
    "\n",
    "    channel = 0\n",
    "    volume = 127\n",
    "    time = 0\n",
    "    duration = 0.25\n",
    "    for note in sequence:\n",
    "        if note > 0:\n",
    "            mf.addNote(track, channel, note, time, duration, volume)\n",
    "        time += duration\n",
    "\n",
    "    # write it to disk\n",
    "    with open(output_name, 'wb') as outf:\n",
    "        mf.writeFile(outf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/midiutil/MidiFile.py:848: FutureWarning: Please explicitly set adjust_origin. Default behaviour will change in a future version.\n",
      "  FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "sequence_to_midi(seq_tonal_final, 'seq_tonal.mid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 54, 60, 62, 59, 54, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 54, 60, 62, 59, 54, 60, 62, 59, 54, 60, 62, 59, 54, 54, 60, 62, 59, 54, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 60, 54, 60, 62, 54, 60, 62, 54, 60, 62, 59, 54, 60, 62, 59, 54, 60, 62, 59, 54, 54, 60, 62, 59, 54, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 60, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 60, 59, 54, 60, 62, 59, 54, 53, 60, 62, 57, 60, 62, 60, 59]\n",
      "35\n"
     ]
    }
   ],
   "source": [
    "seq_drums_rel = [1, 7, 9, 6, 1, 0, 7, 9, 4, 7, 9, 7, 6]\n",
    "seq_drums_start = 53\n",
    "\n",
    "seq_drums = [seq_drums_start + x for x in seq_drums_rel]\n",
    "\n",
    "seq_drums_final = []\n",
    "nmeasures_total = 0\n",
    "for nmeasures, sequences in sorted(nmeasures_to_sequences.items(), key=lambda x: x[0]):\n",
    "    for sequence in sequences:\n",
    "        if max(sequence) < len(seq_drums):\n",
    "            seq_drums_final += [seq_drums[i] for i in sequence]\n",
    "            nmeasures_total += nmeasures\n",
    "print seq_drums_final\n",
    "print nmeasures_total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "mask_to_seq = {}\n",
    "for select in set(seq_drums):\n",
    "    mask_to_seq[select] = [x if x == select else 0 for x in seq_drums_final]\n",
    "print mask_to_seq[53]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for mask, seq in mask_to_seq.items():\n",
    "    sequence_to_midi(seq, 'drums_{}.mid'.format(mask))\n",
    "sequence_to_midi(seq_drums_final, 'drums.mid')"
   ]
  }
 ],
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