Sitting on a Rainbow

I got this letter recently:

“Standing on the deck. The cacophony from the frogs sounds good. A welcoming reminder of spring. Where have these apparently full grown frogs been hanging out all winter?  Is it suspended animation like Austin Powers or have they miraculously grown overnight? And why are there so many songs about rainbows?”

Kermit, too, wondered why there are so many songs about rainbows. I’m not certain he’s right.

I downloaded a list of song titles (with artist name and year recorded) from the Million Song Dataset. This file contains 515,576 tracks – mostly from the 1980s through 2011 – and 466,801 after I de-duped it.

So, as far as rainbow songs go, the set has Johnny Mathis’ version of Rainbow Connection, and Me First and the Gimme Gimmes and the The Carpenter’s cover, but not Jim Henson’s original. (Likewise, it has World of Twist’s really good cover version of She’s a Rainbow, but not the Rolling Stones’ original.)

I counted the number of times each word appears, filtering out so-called ‘stop words’ (so “so“, like “like” and “and”. “Too”, too). I also filtered out words that appear in song names that aren’t really part of the name, like ‘remix’ and ‘remastered’ and ‘featuring’). I then sorted those words from the one that appears the most (“love”), second-most (“don’t”), and so forth, stopping at number 100,000 (“jawbone”).

Here’s the result:

popularity-of-rainbow-in-song-titles(click image to enlarge)

Written text often follows the Zipf-Mandelbrot distribution (named after George Zipf (pronounced ‘ziff’) and Benoit Mandelbrot, the mathematician who studied fractals (where fractals are iterated (that is, nested or (some might say) repeated) structures that exhibit ‘self-similarity’)) and song title words seem to be no exception. You can see that “rainbow” is relatively popular (#645), appearing in Elvis Presley’s Pocketful of Rainbows and the more-contemporary Angus and Julia Stone’s Living on a Rainbow. Certainly not out-of-line with thousands of other popular words. (The file only contains song titles, not lyrics, so these counts don’t include songs like John Prine’s excellent In Spite of Ourselves, which mentions ‘rainbow’ in the lyrics but not the title.)

“Rainbows” is on the graph too, though down at position 3330.

But the first 40 or so words on the list are seen more-frequently than George’s calculations would suggest. Here are those outlier words, written in order of popularity, though as if they are song titles. Effectively, they are the Most-Overused Words in Song Titles:

1-3.    Love, Don’t Live
4-7.    Time One-Up Song
8-11.   Man Down & Out Blues
12-13.  I’m Life
14-15.  Night World
16-18.  Day-Go Heart
19-21.  Back Little Way
22-27.  Come, It’s Good Baby Girl
28.      New
29-31.  Never Know Home
32-33.  Away Take
34-36.  Black Can’t Blue
37-38.  Over Last
39-41.  Want More Now

As for where the frogs go, I’m certain you already know the answer to that question.

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