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The Black Mirror episode "Loch Henry" features a song by Melanie called "People in the Front Row."
In the last verse, she sings:
These chords that I'm using are usually sad
I had to use them, they're the best chords that I have
Oh yeah, this progression is usually sad
But it felt my sorrow and I wanted it to feel me glad
This grabbed my ear immediately. I'm always interested in a song that describes its own musical content. But are these chords usually sad? In the context of the Black Mirror episode (it's about the making of a true crime documentary), the song is incongruously cheerful. But let's take Melanie at her word. What's going on here?
The chord progression is an endless loop of G, Bb, F, and C. There is no single key or mode that fits these chords. The tonic is G, simply by virtue of its metrical placement and emphasis. The F and C chords belong to G Mixolydian, that's a standard rock/pop/folk sound, and not a particularly sad one. The Bb chord suggests parallel G minor, and that is certainly a stereotypically sad sound. This combination of chords could sound bluesy, but they don't in the Melanie song. So maybe the sadness she's talking about comes from the cycling back and forth between Mixolydian and minor?
Another more likely source of sadness is the voice leading. Here's a simplified chart. I colored some notes blue to show the B in the G chord leading down to the B-flat in the Bb chord, which leads down to the A in the F chord, which leads down to the G in the C chord. The green notes show the root of the F chord leading down to the E in the C chord. Finally, the purple notes show the root of the C chord leading down to the B in the G chord, which starts the blue cycle over.
The most iconic music-theoretically self-referential song is "Hallelujah" by Leonard Cohen: "It goes like this, the fourth, the fifth, the minor fall and the major lift."
There's another classic example in "Every Time We Say Goodbye" by Cole Porter: "How strange the change from major to minor" (though jazz musicians tend to play it as "how strange the change from IVmaj7 to bVII7".)
Less seriously, there's this Family Guy bit.
Here's some more music theory comedy.
Twitter has some more examples. Also, I tried making a bunch of songs that explain their own music-theoretic content.
Anyway, thank you Melanie for giving me a nice hook for my upcoming music theory class!