When Steve Reich heard Jonny Greenwood perform his 1987 classic Electric Counterpoint at a Polish festival, he was swamped. By his own admission, he was floundering beneath a massive, unmanageable multiple-orchestra commission for the London Sinfonietta, and watching Greenwood's bracing, devoted rendition, originally written for Pat Metheny, he felt something settle in with a "click." It occurred to him that, despite friends' repeated urgings, he had yet to "check out" Radiohead, so he finally did. Radio Rewrite, a five-movement piece built on themes from Radiohead songs, was the result.

The songs he focused his piece around were "Everything in Its Right Place", from Kid A, and In Rainbows' "Jigsaw Falling Into Place". In an interview last year, he called the opening series of chords on "Everything in Its Right Place" "one of the classics in Western music," elaborating: "'Everything' is a very rich song. It's very simple and very complex at the same time. What does it mean? Maybe it's about a relationship, maybe I should ask Thom Yorke."

The piece itself doesn't quote Radiohead's songs, exactly, as cock a quizzical eyebrow towards them. You can hear the jagged heave of "Jigsaw"'s rising action in the first movement, and the tabula rasa drone of "Everything" in the second, but by the third movement, the lines of transmission grow spotty, by design: "The piece is a mixture of moments where you will hear Radiohead, but most moments where you won't," Reich remarked in an interview with his publisher Boosey & Hawkes. The harmonic language starts to complicate itself, stirring up clouds and creating something that feels more like a series of dreams the songs themselves are having than a straightforward tribute.

When Reich's music quietly departs from its source material, the piece achieves lift off, as the form fades and the piece settles into a seething, anxious rhythm of its own. The piece follows the by-now familiar Reich structure—pairs of movements, titled "Fast " and "Slow", alternating between thrumming low-level unease and calm—and the familiarity has a bittersweet tinge to it. When the piece directly references Radiohead, the piece feels troublingly like a printout, with new material going in one end and the churning minimalist music emerging reliably on the other. His final two movements, with their scrambled rhythmic pulses and sumptuous string writing, help mitigate this feeling.

Jonny Greenwood's recording of Electric Counterpoint, meanwhile, feels genuinely different. His version, which he's honed live over years and is included on Radio Rewrite, has a nagging, insistent edge, with more space in between the guitars than in the famous Pat Metheny version, as if the tracks are echoing from opposite corners of a massive, empty room. Greenwood's phrasing is choppier; you can hear almost every pick strike, making it sometimes feel like you need to swat away a locust cloud. In Greenwood's hands, Electric Counterpoint suddenly becomes body music.

Greenwood's taken the unusual step of pre-recording 1o of the 11 guitar tracks that comprise the piece. His guitar tone is unmistakable, especially on the second movement, which directly channels "Let Down". Oddly, it feels more like more of a meeting of the minds between Reich and Radiohead than Radio Rewrite itself. There is another piece on the album, a reworking of Reich's Piano Counterpoint, played here by Vicky Chow, who surfs atop the pre-recorded tracks with fierce aplomb. Watch her do it in real-time here, with a half-smile on her face, to get a sense of her calm ease and total control, and then listen to this recording; you can almost hear the same half-smile. It's ironic, and maybe fitting, that the younger musicians on this album find more easeful communion with the hardy, contrarian spirit of Reich's works than Reich does.