Serialist composers would constrain their music such that it would go through every one of the twelve tones before coming back to the first one. The sequence of twelve tones is called a "tone row". This was intended to prevent it from being in any particular key. For example you couldn't say it's in the key of C, because C is only ever played within a tone row with other equally important notes. But oddly, this constraint often isn't sufficient to defeat tonality. Even when you have a random sequence of twelve notes, our minds tend to pick out some pattern, and fit it into a key.
Mathemusician Vi Hart has a great video about serialism, which includes a few serialist compositions that are intentionally tonal:
Vi Hart talks a bit about The Owl and the Pussycat, a song by Igor Stravinsky. But she doesn't play it because it's copyrighted. But there are other people are willing to violate copyright, so here it is:
But before I move on, I have to talk about these silly lyrics. I was disappointed to learn that Stravinsky didn't write them himself. Instead, they come from a poem by Edward Lear:
The rest of the poem describes how the owl and pussycat buy a ring from a pig and get married by a turkey. Mysteries in the poem abound: How can they spend a year and a day searching for a ring right after the pussycat delivers the line, "too long we have tarried"? Why do they only get one ring: which of the two will wear it? What is a runcible spoon? I thought the incongruities were just too absurd, until I remembered that "rockabye baby" is a lullaby about a baby falling to its death.The Owl and the Pussy-cat went to seaIn a beautiful pea-green boat,They took some honey, and plenty of money,Wrapped up in a five-pound note.The Owl looked up to the stars above,And sang to a small guitar,"O lovely Pussy! O Pussy, my love,What a beautiful Pussy you are,You are,You are!What a beautiful Pussy you are!"
As for Stravinsky's music, it sounds like all the notes are wrong. But I may have an unusual opinion: I think it is catchy. As in, I literally caught the singer's melody in my head. I had a serialist earworm.
This raises the question of whether my earworm accurately reflects the song. Is it truly an atonal earworm? Or is my mind interpreting the music as being in a particular key?
This can be tested with an experiment! A couple days after listening to the song, I transcribed it from memory. Then I transcribed the original song, almost finishing the first stanza before giving up. Here are the results:
Each line represents one of Stravinsky's tone rows. In blue is Stravinsky's tone row (I ignore repeated notes for simplicity). The other colors show the corresponding notes that were in my earworm.
Perhaps unsurprisingly, my earworm is full of inaccuracies. Besides getting a bunch of notes just wrong, there are also a few sections that were shifted up or down by an interval. There are also some missing parts. I hadn't at all remembered the line, "And sang to a small guitar." And lastly, my earworm gets completely derailed in the last line ("What a beautiful pussy...").
The last line is different from the others, because it's not really a tone row. The note F is repeated three times! D# and F# are also repeated. Perhaps Stravinsky didn't follow tone rows strictly. Or I transcribed the notes wrong (transcription is hard). Or the singer sung the wrong notes (who would know?). In any case, there's one part of the line that stands out as having conventional tonality: the sequence C#, A#, B ("-ssy you are!"). This is called an "authentic cadence", and it tends to establish a key of B.
The authentic cadence is such a strong structure that it appeared in my earworm, albeit shifted to the key of D. And then it seems like the entire line got derailed into a key of D major.
No wonder my earworm is so inaccurate in this spot.
This leads me to conclude that while some parts of my earworm roughly represent the original, there's also a tendency for my mind to substitute the atonal melody with a tonal one. This is more likely to occur as we get further into the song, since I tend to have a poorer memory of those parts.
I wonder if there is any research on how well earworms tend to reflect the songs that they come from. I daresay that I would have a much easier time transcribing Lady Gaga from memory.