Canine Heart Sounds play The Pinhook in Durham Friday, May 8, at 9 p.m. Tickets are $7. Schooner and Hammer No More the Fingers join the bill.

Decades of committed activism by progressive rock bands have had results, it seems. Following the go-go indie ’90s, rhythmic hanky-panky and sci-fi wistfulness have grown in acceptance. Via nerds as disparate (or similar) as Phish, Tortoise, Primus and others mixing post-rock and math-rock with jam and jazz tendencies, the world has become safe for playfulness and prog.

But on their second LP, the decade-old Durham-via-Duluth quartet Canine Heart Sounds begin the inevitable process of dialing it down a notch. Across these 40 minutes, multi-instrumentalists Zach Hegg, Matt McElroy, Dan “Yan” Westerlund and Matt Peterson trade curling Zappa thrashers for music that is no less dizzying but graced by a few more niceties. Still, they remain stranger than most. (After spending a touring season accompanying the fluorescent Grandma Sparrow, the brother of Canine drummer Westerlund, it would be hard not to be.) Live on the Moon doesn’t quite nail the balance between digestible and dense, but Canine Heart Sounds do start to refine their voice.

Seemingly influenced by Anticon non-rapper Why?, album standout “Buffaloes” finds an appealing middle ground with an off-kilter, half-spoken delivery. Other parts of Live on the Moon go for polished and detailed space-pop, topped by a not-quite-Thom-Yorke falsetto, an asset that saves them from chops-choked units like Umphrey’s McGee.

For any person, band or album in this digital age, joking come-ons like “Come on, let’s build a robot,” which begins Live on the Moon, are as plausible as any. The ultra-serious Floyd vibes of “Canyon Song,” however, have a harder time getting off the ground.

Still, the Canines’ most intriguing work arrives when they leave pop behind, locate their freak flag and wave it high. The instrumental “Saturday Morning Cartoons” is a through-composed lunar chase that could make The Flaming Lips envious. It’s the only one of its kind here, but the approach surfaces elsewhere. When the band threads instrumental interludes between verses, for instance, those pieces present the set’s highest musical drama. Appropriately, the closing “Worship Team” seems to integrate the two approaches best, pointing the way toward a harmonious futureor at least a third Canine Heart Sounds album.

Label: Self-released