Chicago-based soul singer Willis Earl Beal once told an interviewer he wanted to be an underground cult legend, which isn’t a thing people usually set out to become on purpose.

Beal, 28, recently issued his official debut, “Acousmatic Sorcery,” a roughly hewn, bewitching, cult-stardom-baiting collection of anti-folk and blues songs. It positions Beal as the heir to outsider artists such as Daniel Johnston and Wesley Willis, with a back story to match: Formerly homeless, Beal used to write songs, record them to burnable CDs and leave them in public places to be found. Or he’d put up fliers with his picture sketched on them: “Call me and I will sing you a song.” Or, “I like oatmeal, train stations, night-time and chamomile tea. Call me RIGHT NOW.”

Beal made a few friends, attracted a few cranks, upset his grandmother (he had left her number on some of the fliers) and eventually drew the attention of XL Records, home to Adele, which released “Acousmatic Sorcery” this month. Rapturously reviewed, it has drawn the requisite comparisons to Johnston and Willis and made Beal a curiosity piece, the sort of artist hipsters praise for being “authentic” when what they really mean is quaint — and possibly mentally ill.

Beal seems both genuinely strange and, unlike Willis or Johnston, profoundly aware of the effects of his strangeness. Able to calibrate it, even. On the phone from the road, on his first-ever tour (he opens for Wu Lyf at the Rock & Roll Hotel on Monday), Beal talked about life on the streets, life on the road, and how everything is working out according to plan.

How’s the tour going?

Sometimes it’s rough opening for somebody else. People who show up don’t expect me or even want me. That’s a difficult thing, especially for my first tour ever.

When you were first writing the songs on “Acousmatic Sorcery,” did you ever imagine that it would lead to being on a big label, to actually being a musician on the road?

I can’t say that I didn’t preconceive it, because I did, but I didn’t think it was gonna happen in real life. I just imagined it happening. There’d be many times where I’d interview myself. I would fantasize and pretend like I was something much greater than I was, because that was my way of passing the time. So I did imagine going on tour and imagine a lot of the things that are actually manifesting themselves right now.

Some of the songs were recorded five years ago, isn’t that right? What do you make of them now?

The songs are about arrested development, about the merging of dreams and reality. I still feel that way a lot of the time. One thing I’ve noticed is that I’ve started to come down a bit, to write more conventional songs, with a verse and a chorus. I want to get back in my own head space and stop thinking about who’s listening, and record deals and all that kind of s---, instead of doing it because I’m some kind of songwriter or performer or something. The songs are much more honest than the new songs I’m writing.

It must play with your head, to know that now people might be listening to what you have to say, and to try to anticipate what they want.

Yeah. I really don’t care what people want. I thought I did, but . . . this is just an outside thing that’s happening. The environment has changed, but I haven’t changed very much. I never did anything because someone else wanted me to, and that’s been to my detriment from time to time, but it’s all adding up now. I’m starting to see the fruition of my hardheadedness.

Were you surprised to see your interview tape [from “The X Factor,” where Beal once made it to the Boot Camp round] out there?

None of it’s weird. None of it surprises me at all, because, like I’ve said, I’ve already imagined it. Everything seems to be an extension of my imagination. . . . It feels like I’m walking in a dream or something. My own dream, and everyone’ s just an extension of my personality, and it’s not really that I have so much talent, it’s just that nobody else is real except me, so why wouldn’t I be successful? It’s my dream.

Do you worry that if you got better at stuff like playing the guitar that it would ruin things?

The stuff that people hear on “Acousmatic Sorcery” is not a true representation of my true musical abilities. It’s just like walking in on somebody in the bathroom. I never intended for those songs to be heard in that way by a whole lot of people. They kind of insisted that I release them that way, but I’m kind of embarrassed that that CD is out.

You used to record your music on CDs and leave them for people to find.

I was doing that not because I wanted to be famous. It was like regurgitation. I was alone and I didn’t know what else to do. It was something I had to let go of, unless I wanted to become some kind of serial killer.

When you do live on the streets for a while, does that always stay with you? Is it necessarily something [scarring]?

It does stick in my mind, but the only thing I can think of is good times, because I met a lot of strange people. It was new for me, because I’d been sheltered my whole life. Somehow I felt like I wasn’t gonna be homeless for a long time, anyway. I felt like I was touring, or on vacation. I did sleep outside, I did dumpster dive. I did do day-labor jobs. I had stuff stolen from me at the homeless shelter, I stole things from other people at the homeless shelter, but it never seemed harsh to me. Maybe it was the good weather.

Willis Earl Beal

opens for Wu Lyf on Monday at Rock & Roll Hotel, 1353 H St. NE, 202-388-7625.