Sara Quin spends a good portion of the Straight’s all-too-brief interview with her gushing about Taylor Swift, and it’s hard to blame her. Just a couple of nights before, on August 20, Quin and her twin sister and musical partner, Tegan, were on-stage with Swift at the Staples Centre in Los Angeles, performing their own hit single “Closer” with the superstar singer in front of 15,000 screaming fans.

The whole thing can be seen on YouTube, of course, and that includes Swift’s introduction, during which she says of Tegan and Sara’s Heartthrob, “I think that this album is one of my favourites of all time.”

This wasn’t the Canadian siblings’ only big concert cameo of the summer. Earlier in August, they joined Macklemore and Ryan Lewis on-stage at the Osheaga Festival in Montreal to sing the hook to the hip-hop act’s marriage-rights anthem “Same Love”.

Singing with Swift was special for several reasons, though, as Quin explains. “The cool thing about it is that often you get asked to come out on-stage, like we did with Macklemore, and sing something on one of their songs,” she says, reached in Denver, where Tegan and Sara are playing a pair of shows at the Red Rocks amphitheatre with coheadlining tourmates fun. “And what I think is so incredibly generous about Taylor Swift, truly, is that she is bringing artists out to sing their songs. She’s a fan of music and of other people, and there’s a real positive energy around her.”

If Tegan and Sara’s Staples Centre moment is a testament to Swift’s generosity, it also speaks to the post-everything nature of pop culture circa now. When you consider that Ke$ha has recorded an album with perennial weirdo outsiders the Flaming Lips, or that Daft Punk’s latest features contributions from everyone from Paul Williams to Panda Bear, just about anything seems possible.

“One of the most interesting tweets after the performance was from Grimes, actually,” Quin recalls. “She tweeted Taylor and us and just said, ‘I wish I was there to see that,’ or something. And I just thought, ‘How funny is it that there’s so much cross-pollination between all of these different genres, all of these different artists?’ We all share very different aesthetics and different music, and yet we’re able to compliment each other without the threat of losing a gain or something. It just feels really nice.”

It no doubt also feels nice that, 14 years after debuting with the self-released Under Feet Like Ours, Tegan and Sara have unambiguously stormed the mainstream. Released last September, “Closer” was a Top-40 hit in both Canada and the U.S., hitting the number one spot on the Billboard Hot Dance Club Songs chart. And no wonder: a cowrite by the sisters and hitmaker Greg Kurstin (Kelly Clarkson, Pink), it’s a driving-with-the-top-down synth-pop banger with the type of yearning verses and fireworks-detonating choruses that the likes of Katy Perry have built careers on. The rest of Heartthrob follows suit, with Tegan and Sara pushing further into pure-pop territory than they ever have before.

Quin admits that the duo had been guilty of “coasting” through its career in recent years, and that they saw Heartthrob as an opportunity to break out of a self-imposed rut. “I think that for both of us, the idea of doing something completely new, fresh, exciting, for both ourselves and for the audience, was a must from before we’d even written one song for this record,” she says. “We realized that after The Con and Sainthood there was no point in making another record where we would sort of be hitting the same targets.”

Quin looks back to 2004’s So Jealous as “a real moment of pushing forward”. Songs from that LP ended up on TV shows like Grey’s Anatomy, and one of them, “Walking With a Ghost”, was covered by the White Stripes, who released their version on an EP bearing the same title. Heady times for the Calgary-born twins, but in retrospect, it probably seems like mere foreshadowing.

“I think right now, with this record, we’re experiencing that real rush forward again, where it’s the right sonic record for what’s happening in pop radio, but we have enough integrity, or I guess we have enough respect in some of the other circles that we run in, that there’s praise or there’s investment from a lot of different kinds of groups,” remarks Quin, who has a unique ability to say an awful lot without taking a breath, “and all of a sudden the song is making sense on radio and there’s opportunities to do things like the Taylor Swift performance. There’s just, like, a real momentum because of a lot of different things.”

In many respects, the stars have finally aligned for Tegan and Sara, but there’s a lot more than sheer luck at play. “This is not an accident,” Quin says. “We are not sitting around in beach chairs drinking mimosas, being like, ‘Holy shit! This is crazy!’ We’re working our asses off. We started work on this record a year-and-a-half ago—I mean, longer than that, actually—and we started rehearsing and touring it in August [of 2012], months before it even came out. We’ve been on the road. I think the longest break I’ve had has been two weeks.”

You don’t keep that kind of schedule without being in top fighting form, and Quin acknowledges that being a pop star takes a lot of discipline. “This record has been incredibly challenging for us,” she says. “I started running a year ago to get my lung capacity up. I do vocal warm-ups for 45 minutes every day before we go on-stage. I feel like it’s making me a better musician and a better performer.”

That’s what you need to do if you want to share a stage with the Taylor Swifts of the world—even if it’s only for three-and-a-half glorious minutes.