Every Wednesday, Douglas Wolk explores the people, places and coincidences that tie disparate musicians together.

Re-Mit -- the 30th or so studio album the Fall have released in their 36-year career -- came out in the U.K. this week. (The alternate version of its track "Sir William Wray" that was released a few weeks ago as a Record Store Day single is below.) The Manchester rock institution has now had the same lineup for four consecutive albums and nearly six years, which is longer than they've ever managed before.

The typical band-member tenure in the Fall has historically been brief, with a few exceptions (like bassist Steve Hanley, who played in the band from 1979 to 1998). The one permanent Fall member is their snarling, orating, one-of-a-kind frontman, Mark E. Smith; he won the British music newspaper NME's "Godlike Genius" award in 1998, and that's probably the best way to describe him.

Smith has occasionally dropped in on other artists' recordings over the years. His highest-profile guest appearance may be his 1994 guest shot with the Manchester garage rock band Inspiral Carpets. On their album Devil Hopping, "I Want You" was a straightforward, high-speed rocker. Then they let Smith loose on the single version, and it became something else altogether.

One of the first "featuring Mark E. Smith" credits appeared with one of his least likely collaborators: the cut-and-paste hip-hop production duo Coldcut. Smith provided vocals for "(I'm) In Deep" on their 1989 record What's That Noise? -- the same album that introduced Lisa Stansfield to the world, and featured Queen Latifah before she'd even released an album of her own.

The Fall have occasionally experimented with dance music -- Coldcut produced several tracks on the subsequent Fall album Extricate -- but they've more often been distinctly a rock band. Still, Smith's scrawl of a voice sounds amazing over hard electronic beats. In 1996, he worked with the electronic duo D.O.S.E. (Kier Stewart and Simon Spencer) on a single called "Plug Myself In," for which they made the video below; both members of D.O.S.E. ended up playing briefly with the Fall the next year.

After Smith appeared on the experimental electronic duo Mouse on Mars' 2004 single "Wipe That Sound," the three of them formed a new band, Von Südenfed. They played a few live shows together, and recorded a full album, Tromatic Reflexxions, released in 2007. Here's the video for its woozy, thumping single "Fledermaus Can't Get It," in which Smith is distinctly not one of the people lip-synching his vocals.

There even exists something approximating Smith disco: he contributed nearly unintelligible guest vocals to "Seventies Night," on Edwyn Collins' 1997 album I'm Not Following You.

The Fall have had a massive reputation in Iceland for decades: they recorded parts of their epochal 1982 album Hex Enduction Hour (which includes a song called "Iceland") there, and played in Reykjavik in 1981 and 1983, at a time when foreign bands scarcely set foot in the country. In 2005, Ghostigital -- the electronic project headed by former Sugarcubes member Einar Örn -- released the single "Not Clean," featuring seemingly improvised vocals by Mark E. Smith.

Speaking of tentative connections to Björk, years before Scottish novelist Luke Sutherland wrote Venus as a Boy, he sang and played violin in the marvelously weird rock band Long Fin Killie. Their 1995 single "The Heads of Dead Surfers" coasts along for a few minutes before Smith leaps in and delivers his own, much more overtly caustic take on the themes of Sutherland's lyrics.

Every time the World Cup comes around, British bands rush to record songs about the glory of England's footballers. In 2010, Smith, Jenny Shuttleworth (who also records as Girl Peculiar), and former Fall member Ed Blaney made the single "England's Heartbeat" under the name Shuttleworth. It's got the kind of chorus that tends to appear in World Cup anthems, although those don't usually also include somebody muttering lines like "Socks up at last/ Or Brazilian breakfast" through a megaphone.

Smith put in a brief appearance on Gorillaz' 2010 album track "Glitter Freeze" -- fewer than 20 words. When they performed it live at the Glastonbury festival that year, though, his role was greatly expanded.

The terrific '90s post-punk revivalists Elastica were enormous Fall fans (and their lineup included former Fall keyboardist Dave Bush for a few years). Their self-titled EP in 1999 included two tracks guest-starring Smith, including "How He Wrote Elastica Man."

That song was, in fact, named after a Fall original: their 1980 single "How I Wrote 'Elastic Man.'"

All of those guest appearances end up sounding rather Fall-like, it's true; Smith famously once noted that any group that included him could be the Fall, up to and including "me and your granny on bongos." We'll close this week with a song on which Smith doesn't appear -- a dead-on Fall parody by that name, courtesy of the garage-rock band Armitage Shanks.