A good pop song works like a pocket watch. To find out what makes a watch tick, a jeweler will take it apart and lay its pieces side by side, going over each one until they make sense. That’s the strategy that composer Terry Riley used in 1968 when a Philadelphia discotheque asked him to record a theme song for it. Inspired by his nickname “Poppy Nogood,” Riley took the Harvey Averne Dozen’s little-known three-minute soul single “You’re No Good,” disassembled it, and layered and rearranged the components every way they fit. The 20-minute piece that resulted was finally released a few months ago on Riley’s You’re No Good (Cortical Foundation), and it’s very much in the ’60s avant-garde tradition, but also totally pop. Riley lets the song roll as written for a couple of minutes, then starts looping it in and out of synch with itself: extending phrases by a beat, making the chorus do a call-and-response routine with itself, obsessing over the hook, rewriting the Latin-soul vibraphone parts a line at a time, doubling and tripling the background singers voices.

New York guitarist Alan Licht has played both pop songs (with Run On and Love Child) and extreme noise, and he’s curious about the ways in which they can be brought together. He also knows avant-garde history inside and out, and it seems likely that his new “The Old Victrola,” on Plays Well (Crank Automotive), is inspired by Riley’s cut-up. It starts with Licht playing Captain Beefheart’s recording “Well” and accompanying it with a little two-chord guitar riff. Then he abruptly cuts to a four-bar disco loop. A woman’s voice ululates endlessly. There’s a loud, flickery buzz over the top, Licht controlling his feedback like a laser-eye-surgery beam. When he’s finished with one passage, he moves to another and works it over thoroughly. Sixteen minutes into the piece, he finally releases his guitar, unlatches the loop, allows the song to roll forward, takes off our blindfold, and lets us see us where we are: in the middle of Donna Summer’s “Dim All the Lights.” Which proceeds, unimpeded and unaltered, for another five minutes before the feedback shows up again and takes over.

Nobukazu Takemura (who’s also recorded under the name Child’s View) has some similar ideas, but his clockwork’s entirely digital. Takemura doesn’t use existing recordings or even the busy polyphonies of pop songs; on his new Hoshi No Koe (Thrill Jockey), he separates tone sequences and simple chords into chunks of what seem like only a few bytes and turns them over and over until every note has been heard from all angles. Sometimes this sounds like what happens when you press the scan-forward button for a CD of test tones. Mostly, though, it forces you to examine Takemura’s timbres with care. “Honey Comb” sounds like a cross-section of a song; “Sign” flickers randomly through a set of tones until it finds a particularly nice stutter-skip sequence, then turns that happy accident into the hook for a long, exquisite piece of techno-funk.

To extend the watchmaker metaphor maybe a little too far, Takemura also pays lots of attention to the etched-gold-and-glass casing: the glitchworks on Hoshi No Koe are accompanied by sustained tones from keyboards and other instruments (is that a xylophone? an oboe? or just a good synth?); and the single version of “Sign” (on Thrill Jockey) is accompanied by a 35-minute collaboration with a few members of Tortoise, who maintain a rippling groove alongside his digital wow and flutter. What’s more, his habit of considering glitch music’s context as well as its content is starting to become an influence on younger laptop musicians: the new Start Breaking My Heart (Leaf/Bubblecore), by Manitoba, is practically a homage to Takemura.

There are plenty of other musicians mining the digital fragmentation territory right now, from the mini-genre’s granddaddy, Oval (whose forthcoming Kommers, on Thrill Jockey, is what he calls his “rock record,” meaning not that it has a particular sense of beat but that it uses rough, sloppy timbres for its source material), to most of the artists who populate the two Clicks and Cuts compilations on Mille Plateaux. But Takemura sets himself apart from them by concentrating on playful, pastoral sounds. Even at its techiest, there’s something sweetly relaxed about Hoshi No Koe, as if he were reproducing the secret songs computers make up to entertain themselves while they’re idling, or the melodies the watch whistles to the watchmaker.