musical_analysis.ipynb

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    "## 1. Introduction\n",
    "<p>How do musicians choose the chords they use in their songs? Do guitarists, pianists, and singers gravitate towards different kinds of harmony?</p>\n",
    "<p>We can uncover trends in the kinds of chord progressions used by popular artists by analyzing the harmonic data provided in the <a href=\"http://ddmal.music.mcgill.ca/research/billboard\">McGill Billboard Dataset</a>. This dataset includes professionally tagged chords for several hundred pop/rock songs representative of singles that made the Billboard Hot 100 list between 1958 and 1991. Using the data-wrangling tools available in the <code>dplyr</code> package, and the visualization tools available in the <code>ggplot2</code> package, we can explore the most common chords and chord progressions in these songs, and contrast the harmonies of some guitar-led and piano-led artists to see where the \"affordances\" of those instruments may affect the chord choices artists make.</p>"
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      "\n",
      "Attaching package: ‘dplyr’\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n",
      "\n",
      "\u001b[1mRows: \u001b[22m\u001b[34m19198\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m9\u001b[39m\n",
      "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n",
      "\u001b[1mDelimiter:\u001b[22m \",\"\n",
      "\u001b[31mchr\u001b[39m (8): chord, root_integer, root_roman, quality, title_compressed, artist_...\n",
      "\u001b[32mdbl\u001b[39m (1): year\n",
      "\n",
      "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n",
      "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n"
     ]
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     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 6 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>year</th><th scope=col>chord</th><th scope=col>root_integer</th><th scope=col>root_roman</th><th scope=col>quality</th><th scope=col>title_compressed</th><th scope=col>artist_compressed</th><th scope=col>title</th><th scope=col>artist</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1961</td><td>A:min</td><td>9</td><td>VI</td><td>min</td><td>idon'tmind</td><td>jamesbrown</td><td>I Don't Mind</td><td>James Brown</td></tr>\n",
       "\t<tr><td>1961</td><td>C:maj</td><td>0</td><td>I </td><td>maj</td><td>idon'tmind</td><td>jamesbrown</td><td>I Don't Mind</td><td>James Brown</td></tr>\n",
       "\t<tr><td>1961</td><td>A:min</td><td>9</td><td>VI</td><td>min</td><td>idon'tmind</td><td>jamesbrown</td><td>I Don't Mind</td><td>James Brown</td></tr>\n",
       "\t<tr><td>1961</td><td>C:maj</td><td>0</td><td>I </td><td>maj</td><td>idon'tmind</td><td>jamesbrown</td><td>I Don't Mind</td><td>James Brown</td></tr>\n",
       "\t<tr><td>1961</td><td>A:min</td><td>9</td><td>VI</td><td>min</td><td>idon'tmind</td><td>jamesbrown</td><td>I Don't Mind</td><td>James Brown</td></tr>\n",
       "\t<tr><td>1961</td><td>C:maj</td><td>0</td><td>I </td><td>maj</td><td>idon'tmind</td><td>jamesbrown</td><td>I Don't Mind</td><td>James Brown</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 9\n",
       "\\begin{tabular}{lllllllll}\n",
       " year & chord & root\\_integer & root\\_roman & quality & title\\_compressed & artist\\_compressed & title & artist\\\\\n",
       " <dbl> & <chr> & <chr> & <chr> & <chr> & <chr> & <chr> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t 1961 & A:min & 9 & VI & min & idon'tmind & jamesbrown & I Don't Mind & James Brown\\\\\n",
       "\t 1961 & C:maj & 0 & I  & maj & idon'tmind & jamesbrown & I Don't Mind & James Brown\\\\\n",
       "\t 1961 & A:min & 9 & VI & min & idon'tmind & jamesbrown & I Don't Mind & James Brown\\\\\n",
       "\t 1961 & C:maj & 0 & I  & maj & idon'tmind & jamesbrown & I Don't Mind & James Brown\\\\\n",
       "\t 1961 & A:min & 9 & VI & min & idon'tmind & jamesbrown & I Don't Mind & James Brown\\\\\n",
       "\t 1961 & C:maj & 0 & I  & maj & idon'tmind & jamesbrown & I Don't Mind & James Brown\\\\\n",
       "\\end{tabular}\n"
      ],
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       "\n",
       "A tibble: 6 × 9\n",
       "\n",
       "| year &lt;dbl&gt; | chord &lt;chr&gt; | root_integer &lt;chr&gt; | root_roman &lt;chr&gt; | quality &lt;chr&gt; | title_compressed &lt;chr&gt; | artist_compressed &lt;chr&gt; | title &lt;chr&gt; | artist &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 1961 | A:min | 9 | VI | min | idon'tmind | jamesbrown | I Don't Mind | James Brown |\n",
       "| 1961 | C:maj | 0 | I  | maj | idon'tmind | jamesbrown | I Don't Mind | James Brown |\n",
       "| 1961 | A:min | 9 | VI | min | idon'tmind | jamesbrown | I Don't Mind | James Brown |\n",
       "| 1961 | C:maj | 0 | I  | maj | idon'tmind | jamesbrown | I Don't Mind | James Brown |\n",
       "| 1961 | A:min | 9 | VI | min | idon'tmind | jamesbrown | I Don't Mind | James Brown |\n",
       "| 1961 | C:maj | 0 | I  | maj | idon'tmind | jamesbrown | I Don't Mind | James Brown |\n",
       "\n"
      ],
      "text/plain": [
       "  year chord root_integer root_roman quality title_compressed artist_compressed\n",
       "1 1961 A:min 9            VI         min     idon'tmind       jamesbrown       \n",
       "2 1961 C:maj 0            I          maj     idon'tmind       jamesbrown       \n",
       "3 1961 A:min 9            VI         min     idon'tmind       jamesbrown       \n",
       "4 1961 C:maj 0            I          maj     idon'tmind       jamesbrown       \n",
       "5 1961 A:min 9            VI         min     idon'tmind       jamesbrown       \n",
       "6 1961 C:maj 0            I          maj     idon'tmind       jamesbrown       \n",
       "  title        artist     \n",
       "1 I Don't Mind James Brown\n",
       "2 I Don't Mind James Brown\n",
       "3 I Don't Mind James Brown\n",
       "4 I Don't Mind James Brown\n",
       "5 I Don't Mind James Brown\n",
       "6 I Don't Mind James Brown"
      ]
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   "source": [
    "# Loading individual Tidyverse packages\n",
    "library(dplyr)\n",
    "library(readr)\n",
    "library(ggplot2)\n",
    "# Reading in the McGill Billboard chord data\n",
    "bb <- read_csv(\"datasets/bb_chords.csv\")\n",
    "\n",
    "# Taking a look at the first rows in bb\n",
    "head(bb)"
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    "## 2. The most common chords\n",
    "<p>As seen in the previous task, this is a <em>tidy</em> dataset: each row represents a single observation, and each column a particular variable or attribute of that observation. Note that the metadata for each song (title, artist, year) is repeated for each chord -- like \"I Don't Mind\" by James Brown, 1961 -- while the unique attributes of each chord (chord symbol, chord quality, and analytical designations like integer and Roman-numeral notation) is included once for each chord change.</p>\n",
    "<p>A key element of the style of any popular musical artist is the kind of chords they use in their songs. But not all chords are created equal! In addition to differences in how they sound, some chords are simply easier to play than others. On top of that, some chords are easier to play on one instrument than they are on another. And while master musicians can play a wide variety of chords and progressions with ease, it's not a stretch to think that even the best musicians may choose more \"idiomatic\" chords and progressions for their instrument.</p>\n",
    "<p>To start to explore that, let's look at the most common chords in the McGill Billboard Dataset.</p>"
   ]
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      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 20 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>chord</th><th scope=col>n</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>C:maj </td><td>1183</td></tr>\n",
       "\t<tr><td>G:maj </td><td>1140</td></tr>\n",
       "\t<tr><td>A:maj </td><td>1071</td></tr>\n",
       "\t<tr><td>D:maj </td><td>1054</td></tr>\n",
       "\t<tr><td>F:maj </td><td> 859</td></tr>\n",
       "\t<tr><td>E:maj </td><td> 839</td></tr>\n",
       "\t<tr><td>Bb:maj</td><td> 718</td></tr>\n",
       "\t<tr><td>B:maj </td><td> 503</td></tr>\n",
       "\t<tr><td>Ab:maj</td><td> 375</td></tr>\n",
       "\t<tr><td>Eb:maj</td><td> 360</td></tr>\n",
       "\t<tr><td>A:min </td><td> 328</td></tr>\n",
       "\t<tr><td>E:min </td><td> 298</td></tr>\n",
       "\t<tr><td>Db:maj</td><td> 293</td></tr>\n",
       "\t<tr><td>D:min </td><td> 250</td></tr>\n",
       "\t<tr><td>B:min </td><td> 236</td></tr>\n",
       "\t<tr><td>N     </td><td> 201</td></tr>\n",
       "\t<tr><td>E:min7</td><td> 186</td></tr>\n",
       "\t<tr><td>C:min </td><td> 176</td></tr>\n",
       "\t<tr><td>D:7   </td><td> 176</td></tr>\n",
       "\t<tr><td>A:min7</td><td> 170</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 20 × 2\n",
       "\\begin{tabular}{ll}\n",
       " chord & n\\\\\n",
       " <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t C:maj  & 1183\\\\\n",
       "\t G:maj  & 1140\\\\\n",
       "\t A:maj  & 1071\\\\\n",
       "\t D:maj  & 1054\\\\\n",
       "\t F:maj  &  859\\\\\n",
       "\t E:maj  &  839\\\\\n",
       "\t Bb:maj &  718\\\\\n",
       "\t B:maj  &  503\\\\\n",
       "\t Ab:maj &  375\\\\\n",
       "\t Eb:maj &  360\\\\\n",
       "\t A:min  &  328\\\\\n",
       "\t E:min  &  298\\\\\n",
       "\t Db:maj &  293\\\\\n",
       "\t D:min  &  250\\\\\n",
       "\t B:min  &  236\\\\\n",
       "\t N      &  201\\\\\n",
       "\t E:min7 &  186\\\\\n",
       "\t C:min  &  176\\\\\n",
       "\t D:7    &  176\\\\\n",
       "\t A:min7 &  170\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 20 × 2\n",
       "\n",
       "| chord &lt;chr&gt; | n &lt;int&gt; |\n",
       "|---|---|\n",
       "| C:maj  | 1183 |\n",
       "| G:maj  | 1140 |\n",
       "| A:maj  | 1071 |\n",
       "| D:maj  | 1054 |\n",
       "| F:maj  |  859 |\n",
       "| E:maj  |  839 |\n",
       "| Bb:maj |  718 |\n",
       "| B:maj  |  503 |\n",
       "| Ab:maj |  375 |\n",
       "| Eb:maj |  360 |\n",
       "| A:min  |  328 |\n",
       "| E:min  |  298 |\n",
       "| Db:maj |  293 |\n",
       "| D:min  |  250 |\n",
       "| B:min  |  236 |\n",
       "| N      |  201 |\n",
       "| E:min7 |  186 |\n",
       "| C:min  |  176 |\n",
       "| D:7    |  176 |\n",
       "| A:min7 |  170 |\n",
       "\n"
      ],
      "text/plain": [
       "   chord  n   \n",
       "1  C:maj  1183\n",
       "2  G:maj  1140\n",
       "3  A:maj  1071\n",
       "4  D:maj  1054\n",
       "5  F:maj   859\n",
       "6  E:maj   839\n",
       "7  Bb:maj  718\n",
       "8  B:maj   503\n",
       "9  Ab:maj  375\n",
       "10 Eb:maj  360\n",
       "11 A:min   328\n",
       "12 E:min   298\n",
       "13 Db:maj  293\n",
       "14 D:min   250\n",
       "15 B:min   236\n",
       "16 N       201\n",
       "17 E:min7  186\n",
       "18 C:min   176\n",
       "19 D:7     176\n",
       "20 A:min7  170"
      ]
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   ],
   "source": [
    "# Counting the most common chords\n",
    "bb_count <- bb %>%\n",
    "    count(chord, sort = TRUE)\n",
    "\n",
    "# Displaying the top 20 chords\n",
    "head(bb_count, n = 20)"
   ]
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   "source": [
    "## 3. Visualizing the most common chords\n",
    "<p>Of course, it's easier to get a feel for just how common some of these chords are if we graph them and show the percentage of the total chord count represented by each chord.\n",
    "Musicians may notice right away that the most common chords in this corpus are chords that are easy to play on both the guitar and the piano: C, G, A, and D major — and to an extent, F and E major. (They also belong to keys, or scales, that are easy to play on most instruments, so they fit well with melodies and solos, as well.) After that, there is a steep drop off in the frequency with which individual chords appear. </p>\n",
    "<p>To illustrate this, here is a short video demonstrating the relative ease (and difficulty) of some of the most common (and not-so-common) chords in the McGill Billboard dataset.\n",
    "<br><br>\n",
    "<a href=\"https://player.vimeo.com/video/251381886\" target=\"blank_\"><img style=\"max-width: 500px;\" src=\"https://assets.datacamp.com/production/project_78/img/smaller_video_screenshot.jpeg\"></a></p>"
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PTFqyZIkMHjz44x0XeZfo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\nKMuXL5f7779fsrKyzDOKnN546ocAA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AgAcEdAUcEgII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\nJH/1J61BAAEEEEAAAQQQQACBSgj8H2cHrzm1GJ8+AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a bar plot from bb_count\n",
    "bb_count %>%\n",
    "  slice(1:20) %>%\n",
    "  mutate(share = n / sum(n) * 100,\n",
    "         chord = reorder(chord, share)) %>%\n",
    "  ggplot(aes(x = chord, y = share, fill = chord)) +\n",
    "  geom_col() +\n",
    "  coord_flip() +\n",
    "  xlab(\"Chord\") +\n",
    "  ylab(\"Percentage Share\") +\n",
    "  theme(legend.position='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "dc": {
     "key": "26"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "tags": [
     "context"
    ]
   },
   "source": [
    "## 4. Chord \"bigrams\"\n",
    "<p>Just as some chords are more common and more idiomatic than others, not all chord <em>progressions</em> are created equal. To look for common patterns in the structuring of chord progressions, we can use many of the same modes of analysis used in text-mining to analyze phrases. A chord change is simply a <em>bigram</em> — a two-\"word\" phrase — composed of a starting chord and a following chord. Here are the most common two-chord \"phrases\" in the McGill Billboard dataset.\n",
    "To help you get your ear around some of these common progressions, here's a short audio clip containing some of the most common chord bigrams.\n",
    "<br><br></p>\n",
    "<audio controls src=\"http://assets.datacamp.com/production/project_79/img/bigrams.mp3\">\n",
    "  Your browser does not support the audio tag.\n",
    "</audio>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "dc": {
     "key": "26"
    },
    "tags": [
     "sample_code"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 20 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>bigram</th><th scope=col>n</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>G:maj D:maj </td><td>241</td></tr>\n",
       "\t<tr><td>C:maj F:maj </td><td>234</td></tr>\n",
       "\t<tr><td>C:maj G:maj </td><td>217</td></tr>\n",
       "\t<tr><td>B:maj E:maj </td><td>202</td></tr>\n",
       "\t<tr><td>F:maj C:maj </td><td>195</td></tr>\n",
       "\t<tr><td>A:maj E:maj </td><td>190</td></tr>\n",
       "\t<tr><td>A:maj D:maj </td><td>189</td></tr>\n",
       "\t<tr><td>D:maj G:maj </td><td>185</td></tr>\n",
       "\t<tr><td>G:maj C:maj </td><td>185</td></tr>\n",
       "\t<tr><td>D:maj A:maj </td><td>179</td></tr>\n",
       "\t<tr><td>E:maj A:maj </td><td>175</td></tr>\n",
       "\t<tr><td>F:maj Bb:maj</td><td>143</td></tr>\n",
       "\t<tr><td>Bb:maj F:maj</td><td>134</td></tr>\n",
       "\t<tr><td>E:maj B:maj </td><td>134</td></tr>\n",
       "\t<tr><td>Bb:maj C:maj</td><td>133</td></tr>\n",
       "\t<tr><td>G:maj A:maj </td><td>133</td></tr>\n",
       "\t<tr><td>A:maj B:maj </td><td>112</td></tr>\n",
       "\t<tr><td>A:maj G:maj </td><td>105</td></tr>\n",
       "\t<tr><td>F:maj G:maj </td><td> 99</td></tr>\n",
       "\t<tr><td>D:maj C:maj </td><td> 93</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 20 × 2\n",
       "\\begin{tabular}{ll}\n",
       " bigram & n\\\\\n",
       " <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t G:maj D:maj  & 241\\\\\n",
       "\t C:maj F:maj  & 234\\\\\n",
       "\t C:maj G:maj  & 217\\\\\n",
       "\t B:maj E:maj  & 202\\\\\n",
       "\t F:maj C:maj  & 195\\\\\n",
       "\t A:maj E:maj  & 190\\\\\n",
       "\t A:maj D:maj  & 189\\\\\n",
       "\t D:maj G:maj  & 185\\\\\n",
       "\t G:maj C:maj  & 185\\\\\n",
       "\t D:maj A:maj  & 179\\\\\n",
       "\t E:maj A:maj  & 175\\\\\n",
       "\t F:maj Bb:maj & 143\\\\\n",
       "\t Bb:maj F:maj & 134\\\\\n",
       "\t E:maj B:maj  & 134\\\\\n",
       "\t Bb:maj C:maj & 133\\\\\n",
       "\t G:maj A:maj  & 133\\\\\n",
       "\t A:maj B:maj  & 112\\\\\n",
       "\t A:maj G:maj  & 105\\\\\n",
       "\t F:maj G:maj  &  99\\\\\n",
       "\t D:maj C:maj  &  93\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 20 × 2\n",
       "\n",
       "| bigram &lt;chr&gt; | n &lt;int&gt; |\n",
       "|---|---|\n",
       "| G:maj D:maj  | 241 |\n",
       "| C:maj F:maj  | 234 |\n",
       "| C:maj G:maj  | 217 |\n",
       "| B:maj E:maj  | 202 |\n",
       "| F:maj C:maj  | 195 |\n",
       "| A:maj E:maj  | 190 |\n",
       "| A:maj D:maj  | 189 |\n",
       "| D:maj G:maj  | 185 |\n",
       "| G:maj C:maj  | 185 |\n",
       "| D:maj A:maj  | 179 |\n",
       "| E:maj A:maj  | 175 |\n",
       "| F:maj Bb:maj | 143 |\n",
       "| Bb:maj F:maj | 134 |\n",
       "| E:maj B:maj  | 134 |\n",
       "| Bb:maj C:maj | 133 |\n",
       "| G:maj A:maj  | 133 |\n",
       "| A:maj B:maj  | 112 |\n",
       "| A:maj G:maj  | 105 |\n",
       "| F:maj G:maj  |  99 |\n",
       "| D:maj C:maj  |  93 |\n",
       "\n"
      ],
      "text/plain": [
       "   bigram       n  \n",
       "1  G:maj D:maj  241\n",
       "2  C:maj F:maj  234\n",
       "3  C:maj G:maj  217\n",
       "4  B:maj E:maj  202\n",
       "5  F:maj C:maj  195\n",
       "6  A:maj E:maj  190\n",
       "7  A:maj D:maj  189\n",
       "8  D:maj G:maj  185\n",
       "9  G:maj C:maj  185\n",
       "10 D:maj A:maj  179\n",
       "11 E:maj A:maj  175\n",
       "12 F:maj Bb:maj 143\n",
       "13 Bb:maj F:maj 134\n",
       "14 E:maj B:maj  134\n",
       "15 Bb:maj C:maj 133\n",
       "16 G:maj A:maj  133\n",
       "17 A:maj B:maj  112\n",
       "18 A:maj G:maj  105\n",
       "19 F:maj G:maj   99\n",
       "20 D:maj C:maj   93"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Wrangling and counting bigrams\n",
    "bb_bigram_count <- bb %>%\n",
    "    mutate(next_chord = lead(chord), next_title = lead(title)) %>%\n",
    "    mutate(bigram = paste(chord, next_chord)) %>%\n",
    "    filter(title == next_title) %>%\n",
    "    count(bigram, sort = TRUE)\n",
    "\n",
    "# Displaying the first 20 rows of bb_bigram_count\n",
    "head(bb_bigram_count, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "dc": {
     "key": "33"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "tags": [
     "context"
    ]
   },
   "source": [
    "## 5. Visualizing the most common chord progressions\n",
    "<p>We can get a better sense of just how popular some of these chord progressions are if we plot them on a bar graph. Note how the most common chord change, G major to D major, occurs more than twice as often than even some of the other top 20 chord bigrams.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "dc": {
     "key": "33"
    },
    "tags": [
     "sample_code"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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X3p0qVWqVIla9++fb7X/PLLL+2zzz6z7du3W7Vq1VxbO3bsaGXKlMn3vHDuDLat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\nyqghh4Ce46afrKysHNt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IIIAAAggggAACCCDgVyCoNUi6A7fuxJ21fPPNN7Zq1aqsm3mOAAIIIIAAAggggAAC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73XLr30Ups5c6ZdeeWVrnVJgUHbtm1d683q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\nSCG4CBQBAQQQQAABBBBAAAEEwiHw/0heHaOIi73kAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a column plot from bb_bigram_count\n",
    "bb_bigram_count %>%\n",
    "  slice(1:20) %>%\n",
    "  mutate(share = n / sum(n) * 100) %>%\n",
    "  arrange(share) %>%\n",
    "  mutate(bigram = factor(bigram, levels = bigram)) %>%\n",
    "  ggplot(aes(x = bigram, y = share, fill = bigram)) +\n",
    "  geom_col() +\n",
    "  coord_flip() +\n",
    "  xlab(\"Chord Change\") +\n",
    "  ylab(\"Percentage Share\") +\n",
    "  theme(legend.position = 'none')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "dc": {
     "key": "40"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "tags": [
     "context"
    ]
   },
   "source": [
    "## 6. Finding the most common artists\n",
    "<p>As noted above, the most common chords (and chord bigrams) are those that are easy to play on both the guitar and the piano. If the degree to which these chords are idiomatic on guitar or piano (or both) <em>determine</em> how common they are, we would expect to find the more idiomatic guitar chords (C, G, D, A, and E major) to be more common in guitar-driven songs, but we would expect the more idiomatic piano chords (C, F, G, D, and B-flat major) to be more common in piano-driven songs. (Note that there is some overlap between these two instruments.)</p>\n",
    "<p>The McGill Billboard dataset does not come with songs tagged as \"piano-driven\" or \"guitar-driven,\" so to test this hypothesis, we'll have to do that manually. Rather than make this determination for every song in the corpus, let's focus on just a few to see if the hypothesis has some validity. If so, then we can think about tagging more artists in the corpus and testing the hypothesis more exhaustively.</p>\n",
    "<p>Here are the 30 artists with the most songs in the corpus. From this list, we'll extract a few artists who are obviously heavy on guitar or piano to compare.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "dc": {
     "key": "40"
    },
    "tags": [
     "sample_code"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[90m# A tibble: 378 × 2\u001b[39m\n",
      "   artist                 n\n",
      "   \u001b[3m\u001b[90m<chr>\u001b[39m\u001b[23m              \u001b[3m\u001b[90m<int>\u001b[39m\u001b[23m\n",
      "\u001b[90m 1\u001b[39m Elvis Presley         13\n",
      "\u001b[90m 2\u001b[39m Brenda Lee             9\n",
      "\u001b[90m 3\u001b[39m Dion                   8\n",
      "\u001b[90m 4\u001b[39m Bob Seger              7\n",
      "\u001b[90m 5\u001b[39m James Brown            7\n",
      "\u001b[90m 6\u001b[39m Kenny Rogers           7\n",
      "\u001b[90m 7\u001b[39m The Beatles            7\n",
      "\u001b[90m 8\u001b[39m Chicago                6\n",
      "\u001b[90m 9\u001b[39m Dr. Hook               6\n",
      "\u001b[90m10\u001b[39m Eric Clapton           6\n",
      "\u001b[90m11\u001b[39m John Denver            6\n",
      "\u001b[90m12\u001b[39m Johnny Tillotson       6\n",
      "\u001b[90m13\u001b[39m The Beach Boys         6\n",
      "\u001b[90m14\u001b[39m Abba                   5\n",
      "\u001b[90m15\u001b[39m Billy Idol             5\n",
      "\u001b[90m16\u001b[39m Cliff Richard          5\n",
      "\u001b[90m17\u001b[39m Glen Campbell          5\n",
      "\u001b[90m18\u001b[39m The Rolling Stones     5\n",
      "\u001b[90m19\u001b[39m Billy Joel             4\n",
      "\u001b[90m20\u001b[39m Cheap Trick            4\n",
      "\u001b[90m21\u001b[39m Cyndi Lauper           4\n",
      "\u001b[90m22\u001b[39m David Bowie            4\n",
      "\u001b[90m23\u001b[39m Elton John             4\n",
      "\u001b[90m24\u001b[39m Genesis                4\n",
      "\u001b[90m25\u001b[39m Heart                  4\n",
      "\u001b[90m26\u001b[39m Jackson Browne         4\n",
      "\u001b[90m27\u001b[39m Little River Band      4\n",
      "\u001b[90m28\u001b[39m Michael Jackson        4\n",
      "\u001b[90m29\u001b[39m Pat Benatar            4\n",
      "\u001b[90m30\u001b[39m Stevie Wonder          4\n",
      "\u001b[90m# ℹ 348 more rows\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# Finding 30 artists with the most songs in the corpus\n",
    "bb_30_artists <- bb %>%\n",
    "    select(artist, title) %>%         \n",
    "    unique() %>%\n",
    "    count(artist, sort = TRUE)     \n",
    "\n",
    "# Displaying 30 artists with the most songs in the corpus\n",
    "print(bb_30_artists, n = 30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "dc": {
     "key": "47"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "tags": [
     "context"
    ]
   },
   "source": [
    "## 7. Tagging the corpus\n",
    "<p>There are relatively few artists in this list whose music is demonstrably \"piano-driven,\" but we can identify a few that generally emphasize keyboards over guitar: Abba, Billy Joel, Elton John, and Stevie Wonder — totaling 17 songs in the corpus. There are many guitar-centered artists in this list, so for our test, we'll focus on three well known, guitar-heavy artists with a similar number of songs in the corpus: The Rolling Stones, The Beatles, and Eric Clapton (18 songs).</p>\n",
    "<p>Once we've subset the corpus to only songs by these seven artists and applied the \"piano\" and \"guitar\" tags, we can compare the chord content of piano-driven and guitar-driven songs.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "dc": {
     "key": "47"
    },
    "tags": [
     "sample_code"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[90m# A tibble: 1,101 × 10\u001b[39m\n",
      "    year chord  root_integer root_roman quality title_compressed\n",
      "   \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<chr>\u001b[39m\u001b[23m  \u001b[3m\u001b[90m<chr>\u001b[39m\u001b[23m        \u001b[3m\u001b[90m<chr>\u001b[39m\u001b[23m      \u001b[3m\u001b[90m<chr>\u001b[39m\u001b[23m   \u001b[3m\u001b[90m<chr>\u001b[39m\u001b[23m           \n",
      "\u001b[90m 1\u001b[39m  \u001b[4m1\u001b[24m984 C:maj  0            I          maj     aninnocentman   \n",
      "\u001b[90m 2\u001b[39m  \u001b[4m1\u001b[24m984 D:min  2            II         min     aninnocentman   \n",
      "\u001b[90m 3\u001b[39m  \u001b[4m1\u001b[24m984 F:maj  5            IV         maj     aninnocentman   \n",
      "\u001b[90m 4\u001b[39m  \u001b[4m1\u001b[24m984 G:maj  7            V          maj     aninnocentman   \n",
      "\u001b[90m 5\u001b[39m  \u001b[4m1\u001b[24m984 C:maj  0            I          maj     aninnocentman   \n",
      "\u001b[90m 6\u001b[39m  \u001b[4m1\u001b[24m984 D:min  2            II         min     aninnocentman   \n",
      "\u001b[90m 7\u001b[39m  \u001b[4m1\u001b[24m984 F:maj  5            IV         maj     aninnocentman   \n",
      "\u001b[90m 8\u001b[39m  \u001b[4m1\u001b[24m984 G:maj  7            V          maj     aninnocentman   \n",
      "\u001b[90m 9\u001b[39m  \u001b[4m1\u001b[24m984 C:maj  0            I          maj     aninnocentman   \n",
      "\u001b[90m10\u001b[39m  \u001b[4m1\u001b[24m984 G:min7 7            V          min7    aninnocentman   \n",
      "\u001b[90m# ℹ 1,091 more rows\u001b[39m\n",
      "\u001b[90m# ℹ 4 more variables: artist_compressed <chr>, title <chr>, artist <chr>,\u001b[39m\n",
      "\u001b[90m#   instrument <chr>\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "tags <- tibble(\n",
    "  artist = c('Abba', 'Billy Joel', 'Elton John', 'Stevie Wonder', 'The Rolling Stones', 'The Beatles', 'Eric Clapton'),\n",
    "  instrument = c('piano', 'piano', 'piano', 'piano', 'guitar', 'guitar', 'guitar'))\n",
    "\n",
    "# Creating a new dataframe bb_tagged that includes a new column instrument from tags\n",
    "bb_tagged <- bb %>%\n",
    "    inner_join(tags, by = \"artist\")\n",
    "    \n",
    "# Displaying the new data frame\n",
    "print(bb_tagged)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "dc": {
     "key": "54"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "tags": [
     "context"
    ]
   },
   "source": [
    "## 8. Comparing chords in piano-driven and guitar-driven songs\n",
    "<p>Let's take a look at any difference in how common chords are in these two song groups. To clean things up, we'll just focus on the 20 chords most common in the McGill Billboard dataset overall.</p>\n",
    "<p>While we want to be careful about drawing any conclusions from such a small set of songs, we can see that the chords easiest to play on the guitar <em>do</em> dominate the guitar-driven songs, especially G, D, E, and C major, as well as A major and minor. Similarly, \"flat\" chords (B-flat, E-flat, A-flat major) occur frequently in piano-driven songs, though they are nearly absent from the guitar-driven songs. In fact, the first and fourth most frequent piano chords are \"flat\" chords that occur rarely, if at all, in the guitar songs.</p>\n",
    "<p>So with all the appropriate caveats, it seems like the instrument-based-harmony hypothesis does have some merit and is worth further examination.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "dc": {
     "key": "54"
    },
    "tags": [
     "sample_code"
    ]
   },
   "outputs": [
    {
     "data": {
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C9BmoKVOmiAZHEydOlCFD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4gCIoAAAggggAACCCCAQKoECJBSJc1yEEAAAQQQQAABBBBAIO0FCJDS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\nBHlaJtctyOvF77KXtV140/Tfe+5HOf1afnSdo5/7ZeDHcr1lJqP+gQiQli5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oevjhh12XOh0H1M1OA7fcdNNNkXqF6Tuhc6Hi34kzryu6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\nJPVAAAEEEEAAAQQQQACBKgv8f849MFEkw/qxAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The top 20 most common chords\n",
    "top_20 <- bb_count$chord[1:20]\n",
    "\n",
    "# Comparing the frequency of the 20 most common chords in piano- and guitar-driven songs\n",
    "bb_tagged %>%\n",
    "  filter(chord %in% top_20) %>%\n",
    "  count(chord, instrument, sort = TRUE) %>%\n",
    "  ggplot(aes(x = chord, y = n, fill = instrument)) +\n",
    "  geom_bar(stat = \"identity\", position = \"dodge\") +\n",
    "  facet_grid(~instrument, scales = \"free_x\", space = \"free_x\") +\n",
    "  coord_flip() +\n",
    "  xlab(\"Chord\") +\n",
    "  ylab(\"Frequency\") +\n",
    "  theme(legend.position='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "dc": {
     "key": "61"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "tags": [
     "context"
    ]
   },
   "source": [
    "## 9. Comparing chord bigrams in piano-driven and guitar-driven songs\n",
    "<p>Since chord occurrence and chord bigram occurrence are naturally strongly tied to each other, it would not be a reach to expect that a difference in chord frequency would be reflected in a difference in chord bigram frequency. Indeed that is what we find.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "dc": {
     "key": "61"
    },
    "tags": [
     "sample_code"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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btEZ01+CCCAAAIIIIAAAgikrUAoWpD27t1rd999t/3yl7+0VatWWeXKlW3x4sXW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\n/qc//an7v6Bffsuq7dU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V4ewMgQQJ5PbY1kW7XvoR8G7KJNiEPNlc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\nHy2tzqoAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The top 20 most common bigrams\n",
    "top_20_bigram <- bb_bigram_count$bigram[1:20]\n",
    "\n",
    "# Creating a faceted plot comparing guitar- and piano-driven songs for bigram frequency\n",
    "bb_tagged %>%\n",
    "    mutate(next_chord = lead(chord), next_title = lead(title)) %>%\n",
    "    mutate(bigram = paste(chord, next_chord)) %>%\n",
    "    filter(title == next_title) %>%\n",
    "    filter(bigram %in% top_20_bigram) %>%\n",
    "    group_by(bigram, instrument) %>%\n",
    "    count(bigram, instrument, sort = TRUE) %>%\n",
    "    ggplot(aes(x = bigram, y = n, fill = instrument)) +\n",
    "    geom_bar(stat = \"identity\", position = \"dodge\") +\n",
    "    facet_grid(~instrument, scales = \"free_x\", space = \"free_x\") +\n",
    "    coord_flip() +\n",
    "    xlab(\"Bigram\") +\n",
    "    ylab(\"Frequency\") +\n",
    "    theme(legend.position='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "dc": {
     "key": "68"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "tags": [
     "context"
    ]
   },
   "source": [
    "## 10. Conclusion\n",
    "<p>We set out asking if the degree to which a chord is \"idiomatic\" on an instrument affects how frequently it is used by a songwriter. It seems that is indeed the case. In a large representative sample of pop/rock songs from the historical Billboard charts, the chords most often learned first by guitarists and pianists are the most common. In fact, chords commonly deemed <em>easy</em> or <em>beginner-friendly</em> on <strong>both</strong> piano and guitar are far and away the most common in the corpus.</p>\n",
    "<p>We also examined a subset of 35 songs from seven piano- and guitar-heavy artists and found that guitarists and pianists tend to use different sets of chords for their songs. This was an extremely small (and likely not representative) sample, so we can do nothing more than hypothesize that this trend might carry over throughout the larger dataset. But it seems from this exploration that it's worth a closer look.</p>\n",
    "<p>There are still more questions to explore with this dataset. What about band-driven genres like classic R&amp;B and funk, where artists like James Brown and Chicago build chords from a large number of instruments each playing a single note? What about \"progressive\" bands like Yes and Genesis, where \"easy\" and \"idiomatic\" may be less of a concern during the songwriting process? And what if we compared this dataset to a collection of chords from classical songs, jazz charts, folk songs, liturgical songs?</p>\n",
    "<p>There's only one way to find out!</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "dc": {
     "key": "68"
    },
    "tags": [
     "sample_code"
    ]
   },
   "outputs": [],
   "source": [
    "# Set to TRUE or FALSE to reflect your answer\n",
    "hypothesis_valid <- TRUE\n",
    "\n",
    "# Set to TRUE or FALSE to reflect your answer\n",
    "more_data_needed <- TRUE"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.2.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}