After two albums of ’80s-style synth-pop, Sara, left, and Tegan Quin are going acoustic to celebrate their heartbreak-heavy 2007 LP “The Con.” (Pamela Littky)

There are four things people say when they meet indie pop duo Tegan and Sara. “One, they thought we’d be taller,” Tegan Quin says. “The second thing is that they love ‘The Con.’ Like, seriously, it’s everyone’s favorite record. The third thing people say is that they miss the talking and banter [at live shows], and the fourth is, ‘We miss when you guys were acoustic.’ ” Except for the height part, that’s the genesis behind “The Con X,” a 10-year anniversary tour that delivers a stripped-down retelling of the identical twins’ 14-track, heartbreak-heavy album — a contrast to the synth-pop of 2013’s “Heartthrob” and last year’s “Love You to Death.” “It’s been amazing. It’s kind of checking all the boxes so far,” Quin, 37, says of the tour, which lands at The Wharf this weekend. “We’ve been in rock-pop-band mode for 10 years, so to be onstage as a four-piece, playing acoustically and telling stories, is so refreshing.”

The Anthem, 901 Wharf St. SW; Sat., 8 p.m., $50.50-$76.

You’ve released eight studio albums. Why do an anniversary tour for “The Con”?
“So Jealous,” the record before that, is arguably the bigger record. But there’s something about “The Con” — fans really attach to it. It’s hard to say it was this  kind of record or that kind of record. It was sort of undefinable. And I think it’s just such a raw, anxious record, and it was like our response to a popular record, it was like we were defiant. We went in and made a really strange record, but it was raw and real, and we recorded it the way we wanted. It’s quintessential Tegan and Sara. And it felt worthy of a tour. I don’t know that there’s another record I would feel quite so intensely passionate about.

How does the decision to go acoustic change the tour?
It’s wonderful. It feels really different from what we’ve been doing. When you’re doing a big pop show and there are thousands of people, they don’t really want to see you talking. They think they might, but then they talk and yell and they’re drunk, and it just doesn’t work. So we’re like, OK, we can make this acoustic and go into theaters, strip it down and try some new arrangements.

What was life like for you in 2007 when “The Con” was released?
We were both in really significant, five-year relationships, and both of us were about to shift out of them, so there were pretty significant changes happening to us. And I was really noticing a shift in our audience: Shows were getting bigger and the response was getting more passionate, and we were finally making money. So even though the record is very anxious and sad and depressing, I really recall it as being a good time. But Sara was miserable. She hated playing her own songs, and she seemed to dislike being on the road. It was a tough time for her.

Let’s talk about being a queer artist then vs. now.
A lot of our press, although somewhat positive, felt coded. The language still felt sexist; Pitchfork called us “tampon rock.” It’s weird to look back on because it’s become such an important record, but at the time, we still felt like we were out to sea. We didn’t have a scene; the queer movement hadn’t really gotten into full stride yet. And the indie rock world, they embraced us, but it was also predominately white straight dudes. It could be very alienating.

It’s improved in some areas, but I still think you and I could sit here for quite a long time and wouldn’t be able to come up with an openly lesbian artist who’s been on the charts. We’ve got a lot of white queer guys who are able to cut through, but you’re still kind of pushing a boulder up the hill. Although there are incredibly powerful women in the industry, the reality is that for a lot of women, in order to get to that level, it requires dancing and tight clothes and sexuality, and we aren’t going to do any of those things. But I do feel the narrative is changing. We’re an indie rock female-fronted queer band, and we’ve managed to build the career we have.

The pros and ‘The Con’

“The Con X” tour coincides with the release of “The Con X: Covers,” a track-for-track reimagining of Tegan and Sara’s 2007 album by other artists. The Canadian duo hand-picked a mix of emerging talent and heavyweights — including Hayley Williams, Chvrches, MUNA, Ryan Adams and Sara Bareilles — to put a new spin on each song. “Everyone needed to be either LGBTQ or an ally — and not, like, secretly. Publicly,” Tegan Quin says. Artists were free to reinvent each song however they liked, with no guidelines, and tracks could be as low-budget as an in-home demo. “We did a lot of chasing and cold-calling, and it was hard. But I couldn’t be happier. It’s very difficult to explain what it’s like to have Cyndi Lauper cover your song — it doesn’t feel real. In some cases, it just infused new life into these songs.”