The piece hasn’t been revised, but the three of them are very different from the three of us. I played my character in a way that was very related to my personality. I was in grad school, and then freshly out of grad school, and trying to figure out, “O.K., this is the kind of music I write in New York, and this is the kind of music I wrote as a kid; this is what I’m thinking about, but this is what my friends might think is cool” — all these intellectual and social concerns and cultural ideas. I ended up playing it kind of grouchy and ornery, like this grouchy professor thing. And Victoria [Benson], she’s more playful and gentle with it, which is cool. Neither way is better.

How did “Sirens” help you pull together all those different strands in your writing?

When I was a kid, I couldn’t write lyrics, so I would just put books of poetry on the piano and sing through them. So I have dozens of, like, Robert Frost settings. Then the first gig I had — I was 18 — I had written all these songs. It was an open-mic night in the basement of a dorm, and I raced through them five times faster than I was supposed to, and I didn’t look at the audience, but I loved it.

But I eventually started feeling a lot of panic and writer’s block about “I really want to be a composer, but what if I can’t do it.” I didn’t want to write songwriter-sounding music. I wanted to write like Xenakis or Berio. I would also write very confessional, personal lyrics, and I was getting a little older and more mature and wanting to value my privacy a little more. I feel like I outgrew it.

At Columbia [graduate school] I was interested in a cleaner, harder sound, so I was writing a lot of complex chamber music and stuff. I was loving it and being really invigorated by it, but I didn’t want to feel like I was prohibited from doing other stuff because it made me less of an intellectual. I think I was worried about how to reconcile my intellectual side with my singer-songwriter side. And “Sirens” was a good opportunity to write everything, because with the sirens you could say they have to sing in every style. There’s a setting of an Edna St. Vincent Millay poem that I did when I was 14 in there; I didn’t change a note. “Sirens” is a collage of my style, my influences.