# The Most Repetitive Songs

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In 1977, the great computer scientist Donald Knuth published a paper called The Complexity of Songs, which is basically one long joke about the repetitive lyrics of newfangled music (example quote: “the advent of modern drugs has led to demands for still less memory, and the ultimate improvement of Theorem 1 has consequently just been announced”).

I’m going to try to test this hypothesis with data. I’ll be analyzing the repetitiveness of a dataset of 15,000 songs that charted on the Billboard Hot 100 between 1958 and 2017.

## Measuring repetitiveness?

I know a repetitive song when I hear one, but translating that intuition into a number isn’t easy. One thing we might try is looking at the number of unique words in a song, as a fraction of the total number of words. But this metric would call the following lyric excerpts equally repetitive:

baby I don’t need dollar bills to have fun tonight
I love cheap thrills
baby I don’t need dollar bills to have fun tonight
I love cheap thrills
I don’t need no money
as long as I can feel the beat
I don’t need no money
as long as I keep dancing

~ Sia, Cheap Thrills

tonight I need dollar bills
I don’t keep fun
cheap thrills long to feel money
the bills don’t need the dancing baby
fun dollar dancing thrills the baby I need
don’t have fun
no no don’t have dancing fun tonight
beat the can as I don’t feel thrills
love the dancing money

~ Colin Morris, Original composition

These are both 52 words long and use the same 23 word vocabulary, but the first one is clearly more repetitive, because it arranges words in a predictable, repetitive order.

## Repetitiveness ≈ compressibility?

You may not have heard of the Lempel-Ziv algorithm, but you probably use it every day. It’s a lossless compression algorithm that powers gifs, pngs, and most archive formats (zip, gzip, rar…).

What does this have to do with pop music? The Lempel-Ziv algorithm works by exploiting repeated sequences. How efficiently LZ can compress a text is directly related to the number and length of the repeated sections in that text.

You can explore some examples of the algorithm applied to full songs here. It turns out, for example, that the entire lyrics of Cheap Thrills reduce in size 76% when compressed.

Continue at: https://pudding.cool/2017/05/song-repetition/index.html

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