MusicHMM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7aeb73ef",
   "metadata": {},
   "source": [
    "# <center> MusicHMM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4867c6ae",
   "metadata": {},
   "source": [
    "For this project, I decided to create a Hidden Markov Model (HMM) that in order to capture music distributions. By doing this, my goal was to create a bayesian model such that I could sample from it in order to generate new music. In order to do this, I utilized the `music21` python library in order to parse MIDI files and extract the note sequences. I then used the `hmmlearn` library in order to train HMMs on the note sequences. I created a variety of HMM models in order to fit certain assumptions about the data. By default, each observation state in the data / HMM sequences was a tuple of the note pitch and duration (in quarter notes); though some of the models separate the dependence between pitch and duration. After training the HMM models, I then used these models to generate new music sequences."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41b9b911",
   "metadata": {},
   "source": [
    "### Bach Dataset Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a80cb36",
   "metadata": {},
   "source": [
    "The `music21` library has a built-in corpus of Bach chorales, which I decided to use to train my models. Here, I load the dataset, transposing all the songs into the key of C, and analyze distributions of note states in the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "29f75237",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading bach dataset from bach_C_major.pkl\n"
     ]
    }
   ],
   "source": [
    "from musichmm import BachDataset\n",
    "\n",
    "data = BachDataset(transpose_key='C', major=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a80be19d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of songs in the dataset: 182\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of songs in the dataset:\", len(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "265a5549",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[list([NoteState(C4, 0.5), NoteState(D4, 0.5), NoteState(E4, 1.0), NoteState(F4, 1.0), NoteState(G4, 1.0), NoteState(F4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(D4, 0.5), NoteState(E4, 0.5), NoteState(F4, 0.5), NoteState(E4, 0.5), NoteState(D4, 1.0), NoteState(C4, 1.0), NoteState(D4, 1.0), NoteState(C4, 1.0), NoteState(C4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(F4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(F4, 1.0), NoteState(G4, 1.0), NoteState(F4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(D4, 0.5), NoteState(E4, 0.5), NoteState(F4, 0.5), NoteState(E4, 0.5), NoteState(D4, 1.0), NoteState(C4, 0.5), NoteState(A3, 0.5), NoteState(B3, 1.0), NoteState(C4, 1.0)])\n",
      " list([NoteState(G3, 1.0), NoteState(C4, 1.0), NoteState(C4, 1.0), NoteState(B3, 1.0), NoteState(A3, 0.5), NoteState(B3, 0.5), NoteState(C4, 1.0), NoteState(B3, 1.0), NoteState(C4, 1.0), NoteState(G3, 1.0), NoteState(A3, 1.0), NoteState(A3, 0.5), NoteState(G3, 0.5), NoteState(F3, 1.0), NoteState(G3, 1.0), NoteState(G3, 0.5), NoteState(C4, 1.0), NoteState(B3, 0.5), NoteState(G3, 1.0), NoteState(G3, 1.0), NoteState(G3, 1.0), NoteState(G3, 1.0), NoteState(F3, 0.5), NoteState(G3, 0.5), NoteState(A3, 1.0), NoteState(A3, 0.5), NoteState(G3, 0.5), NoteState(G3, 0.5), NoteState(F3, 0.25), NoteState(E3, 0.25), NoteState(F3, 1.0), NoteState(G3, 1.0), NoteState(G3, 1.0), NoteState(A3, 1.0), NoteState(B3, 1.0), NoteState(A3, 1.0), NoteState(G3, 1.0), NoteState(F3, 0.5), NoteState(A3, 0.25), NoteState(G#3, 0.25), NoteState(A3, 1.0), NoteState(G3, 1.0), NoteState(A3, 1.0), NoteState(A3, 0.5), NoteState(G3, 0.5), NoteState(F3, 1.0), NoteState(G3, 1.0), NoteState(G3, 0.5), NoteState(A3, 0.5), NoteState(G3, 1.0), NoteState(G3, 1.0)])\n",
      " list([NoteState(E3, 0.5), NoteState(F3, 0.5), NoteState(G3, 1.0), NoteState(A3, 1.0), NoteState(D3, 0.5), NoteState(E3, 0.5), NoteState(F3, 1.0), NoteState(G3, 1.0), NoteState(G3, 1.0), NoteState(G3, 1.0), NoteState(C3, 1.0), NoteState(C3, 3.0), NoteState(F3, 0.5), NoteState(D3, 0.5), NoteState(G3, 0.5), NoteState(F3, 0.25), NoteState(E3, 0.25), NoteState(F3, 1.0), NoteState(E3, 1.0), NoteState(E3, 1.0), NoteState(B2, 1.0), NoteState(C#3, 1.0), NoteState(D3, 1.0), NoteState(C#3, 1.0), NoteState(D3, 1.0), NoteState(C#3, 1.0), NoteState(A2, 1.0), NoteState(D3, 1.0), NoteState(C3, 1.0), NoteState(C3, 1.0), NoteState(D3, 1.0), NoteState(C3, 0.5), NoteState(D3, 0.5), NoteState(E3, 1.0), NoteState(A2, 0.5), NoteState(B2, 0.5), NoteState(C#3, 1.0), NoteState(C3, 1.0), NoteState(C3, 2.0), NoteState(D3, 1.0), NoteState(B2, 1.0), NoteState(C3, 0.5), NoteState(F3, 0.5), NoteState(D3, 1.0), NoteState(E3, 1.0)])\n",
      " list([NoteState(C2, 1.0), NoteState(C3, 0.5), NoteState(B2, 0.5), NoteState(A2, 1.0), NoteState(G2, 1.0), NoteState(D2, 1.0), NoteState(E2, 0.5), NoteState(F2, 0.5), NoteState(G2, 1.0), NoteState(C2, 1.0), NoteState(C3, 0.5), NoteState(B2, 0.5), NoteState(A2, 0.5), NoteState(G2, 0.5), NoteState(F2, 0.5), NoteState(E2, 0.5), NoteState(D2, 0.5), NoteState(C2, 0.5), NoteState(B1, 1.0), NoteState(E2, 0.5), NoteState(C2, 0.5), NoteState(G2, 1.0), NoteState(C2, 1.0), NoteState(C2, 1.0), NoteState(G2, 1.0), NoteState(F2, 0.5), NoteState(E2, 0.5), NoteState(D2, 1.0), NoteState(G2, 0.5), NoteState(A2, 0.5), NoteState(B-2, 1.0), NoteState(A2, 1.0), NoteState(D2, 1.0), NoteState(B2, 1.0), NoteState(C3, 0.5), NoteState(B2, 0.5), NoteState(A2, 1.0), NoteState(G2, 1.0), NoteState(A2, 0.5), NoteState(B2, 0.5), NoteState(C3, 0.5), NoteState(C#3, 0.5), NoteState(D3, 1.0), NoteState(A2, 1.0), NoteState(C3, 0.5), NoteState(B2, 0.5), NoteState(A2, 0.5), NoteState(G2, 0.5), NoteState(F2, 0.5), NoteState(E2, 0.5), NoteState(D2, 0.5), NoteState(E2, 0.5), NoteState(F2, 1.0), NoteState(E2, 0.5), NoteState(F2, 0.5), NoteState(G2, 1.0), NoteState(C2, 1.0)])]\n"
     ]
    }
   ],
   "source": [
    "# Take a look at an example state sequence\n",
    "print(data[0].to_states())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c50aaef",
   "metadata": {},
   "source": [
    "#### Examine the note states in a single part of the song dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9a881f7d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of unique states: 129\n",
      "Number of non-singular states: 108\n",
      "Number of singular states: 21\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "part_sequences = data.to_states()   # (part, song, state sequence)\n",
    "part = part_sequences[0]            # (song, state sequence); only consider the first part\n",
    "\n",
    "unique_states, counts = np.unique(np.concatenate(part), return_counts=True)\n",
    "\n",
    "print(\"Number of unique states:\", len(unique_states))\n",
    "print(\"Number of non-singular states:\", np.sum(counts > 1))\n",
    "print(\"Number of singular states:\", np.sum(counts == 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8e87b8f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([NoteState(F3, 2.0), NoteState(G3, 4.0), NoteState(G#3, 1.0),\n",
       "       NoteState(G#3, 2.0), NoteState(A3, 0.25), NoteState(A3, 0.75),\n",
       "       NoteState(B3, 0.25), NoteState(B3, 1.5), NoteState(B3, 3.0),\n",
       "       NoteState(C#4, 2.0), NoteState(D4, 0.75), NoteState(F4, 0.75),\n",
       "       NoteState(F4, 4.0), NoteState(G#4, 2.0), NoteState(B-4, 4.0),\n",
       "       NoteState(B4, 0.125), NoteState(C5, 8.0), NoteState(D5, 0.75),\n",
       "       NoteState(G5, 0.25), NoteState(A5, 1.0), NoteState(REST, 0.5)],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Look at the states that only appear once in the data\n",
    "singular_states = unique_states[counts == 1]\n",
    "singular_states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cab53de2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([NoteState(F3, 1.0), NoteState(F3, 2.0), NoteState(F#3, 1.0),\n",
       "       NoteState(G3, 0.5), NoteState(G3, 1.0), NoteState(G3, 2.0),\n",
       "       NoteState(G3, 3.0), NoteState(G3, 4.0), NoteState(G#3, 1.0),\n",
       "       NoteState(G#3, 2.0), NoteState(A3, 0.25), NoteState(A3, 0.5),\n",
       "       NoteState(A3, 0.75), NoteState(A3, 1.0), NoteState(A3, 1.5),\n",
       "       NoteState(A3, 2.0), NoteState(A3, 3.0), NoteState(A3, 4.0),\n",
       "       NoteState(B-3, 0.5), NoteState(B-3, 1.0), NoteState(B3, 0.125),\n",
       "       NoteState(B3, 0.25), NoteState(B3, 0.5), NoteState(B3, 1.0),\n",
       "       NoteState(B3, 1.5), NoteState(B3, 2.0), NoteState(B3, 3.0),\n",
       "       NoteState(C4, 0.125), NoteState(C4, 0.5), NoteState(C4, 0.75),\n",
       "       NoteState(C4, 1.0), NoteState(C4, 1.5), NoteState(C4, 2.0),\n",
       "       NoteState(C4, 3.0), NoteState(C4, 4.0), NoteState(C#4, 0.5),\n",
       "       NoteState(C#4, 1.0), NoteState(C#4, 2.0), NoteState(D4, 0.25),\n",
       "       NoteState(D4, 0.5), NoteState(D4, 0.75), NoteState(D4, 1.0),\n",
       "       NoteState(D4, 1.5), NoteState(D4, 2.0), NoteState(D4, 3.0),\n",
       "       NoteState(E4, 0.25), NoteState(E4, 0.5), NoteState(E4, 0.75),\n",
       "       NoteState(E4, 1.0), NoteState(E4, 1.5), NoteState(E4, 2.0),\n",
       "       NoteState(E4, 3.0), NoteState(E4, 4.0), NoteState(F4, 0.25),\n",
       "       NoteState(F4, 0.5), NoteState(F4, 0.75), NoteState(F4, 1.0),\n",
       "       NoteState(F4, 1.5), NoteState(F4, 2.0), NoteState(F4, 3.0),\n",
       "       NoteState(F4, 4.0), NoteState(F#4, 0.5), NoteState(F#4, 1.0),\n",
       "       NoteState(F#4, 2.0), NoteState(G4, 0.25), NoteState(G4, 0.5),\n",
       "       NoteState(G4, 0.75), NoteState(G4, 1.0), NoteState(G4, 1.5),\n",
       "       NoteState(G4, 2.0), NoteState(G4, 3.0), NoteState(G4, 4.0),\n",
       "       NoteState(G#4, 1.0), NoteState(G#4, 2.0), NoteState(A4, 0.25),\n",
       "       NoteState(A4, 0.5), NoteState(A4, 0.75), NoteState(A4, 1.0),\n",
       "       NoteState(A4, 1.5), NoteState(A4, 2.0), NoteState(A4, 3.0),\n",
       "       NoteState(B-4, 0.25), NoteState(B-4, 0.5), NoteState(B-4, 1.0),\n",
       "       NoteState(B-4, 4.0), NoteState(B4, 0.125), NoteState(B4, 0.25),\n",
       "       NoteState(B4, 0.5), NoteState(B4, 0.75), NoteState(B4, 1.0),\n",
       "       NoteState(B4, 1.5), NoteState(B4, 2.0), NoteState(B4, 3.0),\n",
       "       NoteState(B4, 4.0), NoteState(C5, 0.125), NoteState(C5, 0.25),\n",
       "       NoteState(C5, 0.5), NoteState(C5, 1.0), NoteState(C5, 1.5),\n",
       "       NoteState(C5, 2.0), NoteState(C5, 3.0), NoteState(C5, 8.0),\n",
       "       NoteState(C#5, 1.0), NoteState(D5, 0.125), NoteState(D5, 0.25),\n",
       "       NoteState(D5, 0.5), NoteState(D5, 0.75), NoteState(D5, 1.0),\n",
       "       NoteState(D5, 1.5), NoteState(D5, 2.0), NoteState(D5, 3.0),\n",
       "       NoteState(E5, 0.25), NoteState(E5, 0.5), NoteState(E5, 1.0),\n",
       "       NoteState(E5, 1.5), NoteState(E5, 2.0), NoteState(E5, 3.0),\n",
       "       NoteState(F5, 0.25), NoteState(F5, 0.5), NoteState(F5, 1.0),\n",
       "       NoteState(F5, 2.0), NoteState(G5, 0.25), NoteState(G5, 0.5),\n",
       "       NoteState(G5, 1.0), NoteState(G5, 1.5), NoteState(A5, 1.0),\n",
       "       NoteState(REST, 0.5), NoteState(REST, 1.0), NoteState(REST, 2.0)],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique_states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7893373f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of unique pitches: 26\n",
      "Number of unique durations: 10\n",
      "Number of singular pitches: 3\n",
      "Number of singular durations: 1\n"
     ]
    }
   ],
   "source": [
    "unique_pitches, pitch_counts = np.unique([state.pitch for state in unique_states if state.pitch is not None], return_counts=True)\n",
    "unique_durations, duration_counts = np.unique([state.duration for state in unique_states], return_counts=True)\n",
    "\n",
    "print(\"Number of unique pitches:\", len(unique_pitches))\n",
    "print(\"Number of unique durations:\", len(unique_durations))\n",
    "print(\"Number of singular pitches:\", np.sum(pitch_counts == 1))\n",
    "print(\"Number of singular durations:\", np.sum(duration_counts == 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "833e8014",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique pitches: ['A3' 'A4' 'A5' 'B-3' 'B-4' 'B3' 'B4' 'C#4' 'C#5' 'C4' 'C5' 'D4' 'D5' 'E4'\n",
      " 'E5' 'F#3' 'F#4' 'F3' 'F4' 'F5' 'G#3' 'G#4' 'G3' 'G4' 'G5' 'REST']\n",
      "Unique durations: [0.125 0.25  0.5   0.75  1.    1.5   2.    3.    4.    8.   ]\n"
     ]
    }
   ],
   "source": [
    "print(\"Unique pitches:\", unique_pitches)\n",
    "print(\"Unique durations:\", unique_durations)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "107a9043",
   "metadata": {},
   "source": [
    "#### Plot the counts for each NoteState"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "99a19413",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 454,
       "width": 571
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.hist(counts, bins=20)\n",
    "plt.xlabel(\"Number of occurrences\")\n",
    "plt.ylabel(\"Number of states\")\n",
    "plt.title(\"Number of occurrences of each state in the data\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a92fd60",
   "metadata": {},
   "source": [
    "# Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30c2aa8e",
   "metadata": {},
   "source": [
    "I look at implementing a variety of different HMM music generation models. These models vary in the number of supported parts of the music, and assumptions about the data. Often the assumptions that are made are about dependencies between different parts of the music or the pitch and duration of the notes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "213f8ea6",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_hidden_states = 20  # Number of hidden states to use in every model\n",
    "num_parts = 4           # Number of parts in the songs in the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "185f49dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "from musichmm import SongDataset\n",
    "\n",
    "# Define a simpler dataset that only contains the first part of each song\n",
    "simple_data = SongDataset([song.part(0) for song in data])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e8fd5dfe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[list([NoteState(C4, 0.5), NoteState(D4, 0.5), NoteState(E4, 1.0), NoteState(F4, 1.0), NoteState(G4, 1.0), NoteState(F4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(D4, 0.5), NoteState(E4, 0.5), NoteState(F4, 0.5), NoteState(E4, 0.5), NoteState(D4, 1.0), NoteState(C4, 1.0), NoteState(D4, 1.0), NoteState(C4, 1.0), NoteState(C4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(F4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(F4, 1.0), NoteState(G4, 1.0), NoteState(F4, 1.0), NoteState(E4, 1.0), NoteState(D4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(E4, 1.0), NoteState(D4, 0.5), NoteState(E4, 0.5), NoteState(F4, 0.5), NoteState(E4, 0.5), NoteState(D4, 1.0), NoteState(C4, 0.5), NoteState(A3, 0.5), NoteState(B3, 1.0), NoteState(C4, 1.0)])]\n"
     ]
    }
   ],
   "source": [
    "# Take a look at an example simple state sequence\n",
    "print(simple_data[0].to_states())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cecc7d4e",
   "metadata": {},
   "source": [
    "## SimpleMusicHMM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65ae9a7a",
   "metadata": {},
   "source": [
    "The SimpleMusicHMM model only trains on songs with a single part, and therefore a single sequence of NoteState objects. It assumes note pitch and duration are dependent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "36133093",
   "metadata": {},
   "outputs": [],
   "source": [
    "from musichmm import SimpleMusicHMM\n",
    "\n",
    "simple_hmm = SimpleMusicHMM(n_components=num_hidden_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fe56bf61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[28],\n",
       "       [39],\n",
       "       [48],\n",
       "       ...,\n",
       "       [54],\n",
       "       [43],\n",
       "       [30]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_hmm.initialize_states(simple_data)[0]    # Encoded NoteState sequences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7fa515c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<musichmm.models.SimpleMusicHMM.SimpleMusicHMM at 0x7fee9defdf10>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_hmm.fit(simple_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a7446ca0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[30],\n",
       "       [30],\n",
       "       [36],\n",
       "       [48],\n",
       "       [56],\n",
       "       [41],\n",
       "       [32],\n",
       "       [46],\n",
       "       [30],\n",
       "       [54]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example of sampling from the model\n",
    "simple_samples = simple_hmm.sample(num_notes=10)\n",
    "simple_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "caad3555",
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_song = simple_hmm.generate_song(num_notes=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "dd5e092d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <div id=\"midiPlayerDiv27740\"></div>\n",
       "        <link rel=\"stylesheet\" href=\"https://cuthbertLab.github.io/music21j/css/m21.css\">\n",
       "        \n",
       "        <script\n",
       "        src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"\n",
       "        ></script>\n",
       "    \n",
       "        <script>\n",
       "        function midiPlayerDiv27740_play() {\n",
       "            const rq = require.config({\n",
       "                paths: {\n",
       "                    'music21': 'https://cuthbertLab.github.io/music21j/releases/music21.debug',\n",
       "                }\n",
       "            });\n",
       "            rq(['music21'], function(music21) {\n",
       "                mp = new music21.miditools.MidiPlayer();\n",
       "                mp.addPlayer(\"#midiPlayerDiv27740\");\n",
       "                mp.base64Load(\"data:audio/midi;base64,TVRoZAAAAAYAAQACJ2BNVHJrAAAAFAD/UQMHoSAA/1gEBAIYCM5g/y8ATVRyawAAAQYA/wMAAOAAQM5gkDxazmCAPAAAkD5apzCAPgAAkDxazmCAPAAAkEBapzCAQADOYJBAWs5ggEAAAJA8Ws5ggDwAzmCQQFrOYIBAAACQPlqBnUCAPgAAkDxapzCAPAAAkEVak1iARQAAkEBazmCAQAAAkD5azmCAPgDOYJBAWs5ggEAAAJA+WoGdQIA+AACQQFqnMIBAAACQPlqTWIA+AACQPlrOYIA+AACQQFrOYIBAAACQPlrOYIA+AACQQ1rOYIBDAACQQVrOYIBBAACQQFqnMIBAAACQQVrOYIBBAACQQFqnMIBAAACQN1rOYIA3AACQPFrOYIA8AACQPFqnMIA8AM5g/y8A\");\n",
       "            });\n",
       "        }\n",
       "        if (typeof require === 'undefined') {\n",
       "            setTimeout(midiPlayerDiv27740_play, 2000);\n",
       "        } else {\n",
       "            midiPlayerDiv27740_play();\n",
       "        }\n",
       "        </script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simple_song.play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "fc9cd3a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_song.save('songs/simple.mid')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89d87a24",
   "metadata": {},
   "source": [
    "## SimpleIndependentMusicHMM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db031c62",
   "metadata": {},
   "source": [
    "The SimpleIndependentMusicHMM model only trains on songs with a single part; however, it separates the pitch and duration states into two separate HMMs.\n",
    "While this makes the assumption that pitch and duration are independent, it takes advantage of the smaller state space for each, making the problem easier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ed0842e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from musichmm import SimpleIndependentMusicHMM\n",
    "\n",
    "simple_indep_hmm = SimpleIndependentMusicHMM(n_components=num_hidden_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "01ab06c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9,  2],\n",
       "       [11,  2],\n",
       "       [13,  4],\n",
       "       ...,\n",
       "       [18,  2],\n",
       "       [11,  6],\n",
       "       [ 9,  4]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example of state sequence input to the model(s)\n",
    "simple_indep_hmm.initialize_states(simple_data)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "64b21d3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<musichmm.models.SimpleIndependentMusicHMM.SimpleIndependentMusicHMM at 0x7fee8b0d8980>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_indep_hmm.fit(simple_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "06b554f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9,  2],\n",
       "       [ 7,  2],\n",
       "       [11,  3],\n",
       "       [ 9,  2],\n",
       "       [ 5,  4],\n",
       "       [13,  7],\n",
       "       [18,  4],\n",
       "       [23,  4],\n",
       "       [18,  4],\n",
       "       [13,  6]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_indep_hmm.sample(num_notes=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1de4eaef",
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_indep_song = simple_indep_hmm.generate_song(num_notes=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7fdaf629",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <div id=\"midiPlayerDiv23177\"></div>\n",
       "        <link rel=\"stylesheet\" href=\"https://cuthbertLab.github.io/music21j/css/m21.css\">\n",
       "        \n",
       "        <script\n",
       "        src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"\n",
       "        ></script>\n",
       "    \n",
       "        <script>\n",
       "        function midiPlayerDiv23177_play() {\n",
       "            const rq = require.config({\n",
       "                paths: {\n",
       "                    'music21': 'https://cuthbertLab.github.io/music21j/releases/music21.debug',\n",
       "                }\n",
       "            });\n",
       "            rq(['music21'], function(music21) {\n",
       "                mp = new music21.miditools.MidiPlayer();\n",
       "                mp.addPlayer(\"#midiPlayerDiv23177\");\n",
       "                mp.base64Load(\"data:audio/midi;base64,TVRoZAAAAAYAAQACJ2BNVHJrAAAAFAD/UQMHoSAA/1gEBAIYCM5g/y8ATVRyawAAARQA/wMAAOAAQM5gkEBapzCAQAAAkDdapzCANwAAkEBapzCAQAAAkEBapzCAQAAAkEFazmCAQQAAkEBazmCAQAAAkD5azmCAPgAAkDxazmCAPAAAkD5azmCAPgAAkD5apzCAPgCnMJA+Ws5ggD4AAJBBWs5ggEEAAJBAWqcwgEAAAJBDWqcwgEMAAJBDWs5ggEMAAJBKWs5ggEoAAJBGWs5ggEYAAJBCWs5ggEIAAJBBWrsIgEEAAJBDWqcwgEMAAJBAWs5ggEAAAJBBWs5ggEEAAJBAWs5ggEAAAJA7Ws5ggDsAAJBAWs5ggEAAAJBDWs5ggEMAAJA+WqcwgD4AAJBBWqcwgEEAAJBDWs5ggEMAzmD/LwA=\");\n",
       "            });\n",
       "        }\n",
       "        if (typeof require === 'undefined') {\n",
       "            setTimeout(midiPlayerDiv23177_play, 2000);\n",
       "        } else {\n",
       "            midiPlayerDiv23177_play();\n",
       "        }\n",
       "        </script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simple_indep_song.play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "944ed7fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_indep_song.save(\"songs/simple_indep.mid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37a4bcff",
   "metadata": {},
   "source": [
    "## NaiveMusicHMM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7081c1b2",
   "metadata": {},
   "source": [
    "With the NaiveMusicHMM model, we move into models that take multiple parts of the music into account. In this naive model, we train on all 4 parts of the songs in the Bach chorales dataset, but for simplicity we assume that the parts are independent of each other. This means that we train a separate HMM for each part of the music. Note that we still assume that pitch and duration are dependent variables within each part."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "118a8bd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from musichmm import NaiveMusicHMM\n",
    "\n",
    "naive_hmm = NaiveMusicHMM(num_parts, n_components=num_hidden_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "5e9f1701",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[28],\n",
       "        [39],\n",
       "        [48],\n",
       "        ...,\n",
       "        [54],\n",
       "        [43],\n",
       "        [30]]),\n",
       " array([[32],\n",
       "        [74],\n",
       "        [74],\n",
       "        ...,\n",
       "        [51],\n",
       "        [68],\n",
       "        [32]]),\n",
       " array([[57],\n",
       "        [65],\n",
       "        [79],\n",
       "        ...,\n",
       "        [56],\n",
       "        [66],\n",
       "        [59]]),\n",
       " array([[18],\n",
       "        [95],\n",
       "        [89],\n",
       "        ...,\n",
       "        [17],\n",
       "        [63],\n",
       "        [18]])]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example of state sequence input to the model\n",
    "naive_hmm.initialize_states(data)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "0901af55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<musichmm.models.NaiveMusicHMM.NaiveMusicHMM at 0x7fee8ac41880>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_hmm.fit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "48b6d557",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[30],\n",
       "        [23],\n",
       "        [30],\n",
       "        [30],\n",
       "        [67],\n",
       "        [30],\n",
       "        [67],\n",
       "        [30],\n",
       "        [12],\n",
       "        [28]]),\n",
       " array([[ 86],\n",
       "        [ 32],\n",
       "        [ 32],\n",
       "        [ 30],\n",
       "        [ 74],\n",
       "        [ 32],\n",
       "        [  7],\n",
       "        [ 68],\n",
       "        [100],\n",
       "        [ 86]]),\n",
       " array([[57],\n",
       "        [59],\n",
       "        [89],\n",
       "        [79],\n",
       "        [49],\n",
       "        [30],\n",
       "        [45],\n",
       "        [91],\n",
       "        [68],\n",
       "        [79]]),\n",
       " array([[95],\n",
       "        [89],\n",
       "        [78],\n",
       "        [79],\n",
       "        [90],\n",
       "        [96],\n",
       "        [96],\n",
       "        [90],\n",
       "        [78],\n",
       "        [45]])]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_hmm.sample(num_notes=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "73938b99",
   "metadata": {},
   "outputs": [],
   "source": [
    "naive_song = naive_hmm.generate_song(num_notes=30, truncation=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "713b54f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <div id=\"midiPlayerDiv29226\"></div>\n",
       "        <link rel=\"stylesheet\" href=\"https://cuthbertLab.github.io/music21j/css/m21.css\">\n",
       "        \n",
       "        <script\n",
       "        src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"\n",
       "        ></script>\n",
       "    \n",
       "        <script>\n",
       "        function midiPlayerDiv29226_play() {\n",
       "            const rq = require.config({\n",
       "                paths: {\n",
       "                    'music21': 'https://cuthbertLab.github.io/music21j/releases/music21.debug',\n",
       "                }\n",
       "            });\n",
       "            rq(['music21'], function(music21) {\n",
       "                mp = new music21.miditools.MidiPlayer();\n",
       "                mp.addPlayer(\"#midiPlayerDiv29226\");\n",
       "                mp.base64Load(\"data:audio/midi;base64,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\");\n",
       "            });\n",
       "        }\n",
       "        if (typeof require === 'undefined') {\n",
       "            setTimeout(midiPlayerDiv29226_play, 2000);\n",
       "        } else {\n",
       "            midiPlayerDiv29226_play();\n",
       "        }\n",
       "        </script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "naive_song.play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "ea86c50e",
   "metadata": {},
   "outputs": [],
   "source": [
    "naive_song.save(\"songs/naive.mid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9539d5e",
   "metadata": {},
   "source": [
    "## NaiveIndependentMusicHMM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3017a9b1",
   "metadata": {},
   "source": [
    "This model is the independent extension of the NaiveMusicHMM model. It trains on all 4 parts of the songs in the Bach chorales dataset, assuming that each part is independent of the other parts, but further separates the pitch and duration states into two separate HMMs for each part. This makes the assumption that pitch and duration are independent variables within each part."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "25eb7a3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from musichmm import NaiveIndependentMusicHMM\n",
    "\n",
    "naive_indep_hmm = NaiveIndependentMusicHMM(num_parts, n_components=num_hidden_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "5d678c12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 9,  2],\n",
       "        [11,  2],\n",
       "        [13,  4],\n",
       "        ...,\n",
       "        [18,  2],\n",
       "        [11,  6],\n",
       "        [ 9,  4]]),\n",
       " array([[27,  3],\n",
       "        [11,  3],\n",
       "        [11,  3],\n",
       "        ...,\n",
       "        [ 1,  0],\n",
       "        [ 6,  3],\n",
       "        [27,  3]]),\n",
       " array([[19,  1],\n",
       "        [25,  1],\n",
       "        [30,  3],\n",
       "        ...,\n",
       "        [19,  0],\n",
       "        [25,  3],\n",
       "        [19,  3]]),\n",
       " array([[13,  2],\n",
       "        [14,  1],\n",
       "        [ 8,  1],\n",
       "        ...,\n",
       "        [13,  1],\n",
       "        [37,  4],\n",
       "        [13,  2]])]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_indep_hmm.initialize_states(data)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "f40a76ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<musichmm.models.NaiveIndependentMusicHMM.NaiveIndependentMusicHMM at 0x7fee8b0cc7d0>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_indep_hmm.fit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 1,  4],\n",
       "        [ 6,  2],\n",
       "        [12,  4],\n",
       "        [10,  2],\n",
       "        [10,  4],\n",
       "        [14,  5],\n",
       "        [ 6,  2],\n",
       "        [14,  6],\n",
       "        [12,  4],\n",
       "        [10,  4]]),\n",
       " array([[19,  3],\n",
       "        [27,  1],\n",
       "        [27,  1],\n",
       "        [ 6,  3],\n",
       "        [11,  5],\n",
       "        [11,  1],\n",
       "        [20,  3],\n",
       "        [22,  3],\n",
       "        [20,  0],\n",
       "        [28,  1]]),\n",
       " array([[16,  3],\n",
       "        [ 6,  1],\n",
       "        [10,  1],\n",
       "        [ 6,  0],\n",
       "        [20,  1],\n",
       "        [ 1,  1],\n",
       "        [ 6,  5],\n",
       "        [16,  1],\n",
       "        [10,  1],\n",
       "        [ 6,  1]]),\n",
       " array([[38,  2],\n",
       "        [14,  2],\n",
       "        [14,  2],\n",
       "        [13,  2],\n",
       "        [ 2,  2],\n",
       "        [37,  2],\n",
       "        [37,  2],\n",
       "        [ 5,  2],\n",
       "        [ 5,  1],\n",
       "        [31,  2]])]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_indep_hmm.sample(num_notes=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "naive_indep_song = naive_indep_hmm.generate_song(num_notes=30, truncation=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "86c31136",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <div id=\"midiPlayerDiv30731\"></div>\n",
       "        <link rel=\"stylesheet\" href=\"https://cuthbertLab.github.io/music21j/css/m21.css\">\n",
       "        \n",
       "        <script\n",
       "        src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"\n",
       "        ></script>\n",
       "    \n",
       "        <script>\n",
       "        function midiPlayerDiv30731_play() {\n",
       "            const rq = require.config({\n",
       "                paths: {\n",
       "                    'music21': 'https://cuthbertLab.github.io/music21j/releases/music21.debug',\n",
       "                }\n",
       "            });\n",
       "            rq(['music21'], function(music21) {\n",
       "                mp = new music21.miditools.MidiPlayer();\n",
       "                mp.addPlayer(\"#midiPlayerDiv30731\");\n",
       "                mp.base64Load(\"data:audio/midi;base64,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\");\n",
       "            });\n",
       "        }\n",
       "        if (typeof require === 'undefined') {\n",
       "            setTimeout(midiPlayerDiv30731_play, 2000);\n",
       "        } else {\n",
       "            midiPlayerDiv30731_play();\n",
       "        }\n",
       "        </script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "naive_indep_song.play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "6ec334c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "naive_indep_song.save(\"songs/naive_indep.mid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c179457",
   "metadata": {},
   "source": [
    "## ConditionalMusicHMM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a248a1c",
   "metadata": {},
   "source": [
    "For this final part, we implement a model that conditions the note pitch in each part on the concurrent pitch in the bass part of the music. Thus, our pitch note states are tuples of the form (pitch, bass_pitch). In order to take advantage of the reduced state space, we also separate the pitch and duration states into two separate HMMs for each part. When sampling from the model, we sample the bass part first, and then condition sampling of the other parts on the bass pitch at that time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "08c49513",
   "metadata": {},
   "outputs": [],
   "source": [
    "from musichmm import ConditionalMusicHMM\n",
    "\n",
    "conditional_hmm = ConditionalMusicHMM(num_parts, n_components=num_hidden_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "12b58c60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 93,   2],\n",
       "        [ 95,   2],\n",
       "        [112,   4],\n",
       "        ...,\n",
       "        [189,   2],\n",
       "        [279,   6],\n",
       "        [ 93,   4]]),\n",
       " array([[123,   3],\n",
       "        [132,   3],\n",
       "        [ 19,   3],\n",
       "        ...,\n",
       "        [317,   0],\n",
       "        [320,   3],\n",
       "        [123,   3]]),\n",
       " array([[118,   1],\n",
       "        [120,   1],\n",
       "        [141,   3],\n",
       "        ...,\n",
       "        [347,   0],\n",
       "        [350,   3],\n",
       "        [118,   3]]),\n",
       " array([[13,  2],\n",
       "        [14,  1],\n",
       "        [ 8,  1],\n",
       "        ...,\n",
       "        [13,  1],\n",
       "        [37,  4],\n",
       "        [13,  2]])]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conditional_hmm.initialize_states(data)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "82d51e6e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of pitch states in part 0 : 306\n",
      "Number of pitch states in part 1 : 351\n",
      "Number of pitch states in part 2 : 371\n",
      "Number of pitch states in part 3 : 40\n",
      "Number of duration states in part 0 : 10\n",
      "Number of duration states in part 1 : 9\n",
      "Number of duration states in part 2 : 9\n",
      "Number of duration states in part 3 : 8\n"
     ]
    }
   ],
   "source": [
    "# Basic analysis of pitch states\n",
    "for i, pitches in enumerate(conditional_hmm.pitches):\n",
    "    print(\"Number of pitch states in part\", i, \":\", len(pitches))\n",
    "for i, durations in enumerate(conditional_hmm.durations):\n",
    "    print(\"Number of duration states in part\", i, \":\", len(durations))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2f0bc439",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<musichmm.models.ConditionalMusicHMM.ConditionalMusicHMM at 0x7fee8b2779b0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conditional_hmm.fit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "775e18e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[108,   4],\n",
       "        [ 73,   4],\n",
       "        [ 64,   4],\n",
       "        [ 73,   6],\n",
       "        [186,   4],\n",
       "        [186,   4],\n",
       "        [275,   2],\n",
       "        [284,   2],\n",
       "        [186,   6],\n",
       "        [305,   4]]),\n",
       " array([[132,   3],\n",
       "        [ 81,   1],\n",
       "        [ 90,   0],\n",
       "        [ 90,   0],\n",
       "        [ 90,   3],\n",
       "        [ 81,   5],\n",
       "        [217,   3],\n",
       "        [214,   3],\n",
       "        [328,   3],\n",
       "        [217,   3]]),\n",
       " array([[129,   3],\n",
       "        [ 74,   1],\n",
       "        [ 89,   3],\n",
       "        [ 89,   3],\n",
       "        [ 89,   1],\n",
       "        [ 20,   1],\n",
       "        [ 25,   1],\n",
       "        [228,   1],\n",
       "        [235,   3],\n",
       "        [235,   3]]),\n",
       " array([[14,  1],\n",
       "        [ 8,  5],\n",
       "        [ 2,  2],\n",
       "        [26,  2],\n",
       "        [31,  1],\n",
       "        [26,  1],\n",
       "        [20,  1],\n",
       "        [37,  1],\n",
       "        [31,  1],\n",
       "        [26,  1]])]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conditional_hmm.sample(num_notes=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "08cecf50",
   "metadata": {},
   "outputs": [],
   "source": [
    "conditional_song = conditional_hmm.generate_song(num_notes=30, truncation=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "b8046428",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <div id=\"midiPlayerDiv28477\"></div>\n",
       "        <link rel=\"stylesheet\" href=\"https://cuthbertLab.github.io/music21j/css/m21.css\">\n",
       "        \n",
       "        <script\n",
       "        src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"\n",
       "        ></script>\n",
       "    \n",
       "        <script>\n",
       "        function midiPlayerDiv28477_play() {\n",
       "            const rq = require.config({\n",
       "                paths: {\n",
       "                    'music21': 'https://cuthbertLab.github.io/music21j/releases/music21.debug',\n",
       "                }\n",
       "            });\n",
       "            rq(['music21'], function(music21) {\n",
       "                mp = new music21.miditools.MidiPlayer();\n",
       "                mp.addPlayer(\"#midiPlayerDiv28477\");\n",
       "                mp.base64Load(\"data:audio/midi;base64,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\");\n",
       "            });\n",
       "        }\n",
       "        if (typeof require === 'undefined') {\n",
       "            setTimeout(midiPlayerDiv28477_play, 2000);\n",
       "        } else {\n",
       "            midiPlayerDiv28477_play();\n",
       "        }\n",
       "        </script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "conditional_song.play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "6bc12e69",
   "metadata": {},
   "outputs": [],
   "source": [
    "conditional_song.save(\"songs/conditional.mid\")"
   ]
  }
 ],
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