So much movie music sounds like just that: movie music. It’s rare these days to come across a score with character that really makes you sit up and listen.

One musician who consistently manages to pull that off is punk drummer-turned-composer Cliff Martinez, whose work can be heard in two places this month: trippy supermodel horror film “The Neon Demon” and Season two of Cinemax’s turn-of-the-century hospital drama “The Knick.” These are just about the coolest electronic music scores to grace the screen since Tangerine Dream and Vangelis were active in the 1980s, and the recent synthwave trend — see “Stranger Things” and “Mr. Robot” — seems to be playing catch-up.

Martinez first caught my attention with his hauntingly beautiful score for Steven Soderbergh’s 2002 sci-fi film “Solaris.” I’m not alone; although his collaborations with Soderbergh date back to the director’s very first film in 1989, “Sex, Lies, and Videotape,” check out online comments and you’ll find that “Solaris” is the soundtrack people rave about in “music I want to hear when I die and go to heaven” terms.

“I wish I could roll out of bed and write music like that every day,” says Martinez laughing, in a Skype interview with The Japan Times. “Solaris” is in many ways classic Martinez, influenced by minimalist and ambient music, yet also displaying the percussive sensibility of a former drummer who’s played with outre artists such as no-wave icon Lydia Lunch, The Weirdos and The Red Hot Chili Peppers.

“A lot of people thought it was electronic,” says Martinez of the “Solaris” soundtrack, “but a lot of it was the orchestra, it just sounded atypical.”

The ethereal, chiming soundtrack was performed by Martinez primarily on steel drums and mallet instruments including tubular bells and xylophones, but with a 90-piece orchestra adding dense, sul tasto textural swells. That is actually a rarity for Martinez, as he himself admits: “I’m not the first name that pops up if people want an orchestral score.”

Instead, what he’s known for is rhythmic experimentation, whether it’s echoing electric guitar on “Traffic” (2000), hammered cimbalom on “Kafka” (1991) or sequenced synths in “Drive” (2011). This eclectic approach is a residual effect of his time in the ’80s playing in Captain Beefheart’s legendary Magic Band — music so mad and complex that it still defines the outer reaches today.

“That was a peak musical experience for me … and there’s nowhere to go after that. Where do you take that skill?,” notes Martinez. “So I’ve tried to have Beefheart in my music. Basically, the spirit of Beefheart lives on through this idea of primitivism, of expressing yourself on instruments you have no technical proficiency on, and also the idea of taking random and spontaneous stuff and later sculpting and editing it to make something that’s coherent.

“Gary Lucas, who played guitar on the Beefheart album that I’m on (‘Ice Cream for Crow’), described it as throwing a deck of cards up in the air, taking a picture of it and then handing one of the musicians the picture and saying ‘re-create this’ (Laughs.) That’s what I aim for.”

Part of the reason Martinez’s music stands out so much is that he often works with filmmakers who are comfortable doing extended visual sequences with little to no dialogue: The spellbinding runway sequence in Nicolas Winding Refn’s “The Neon Demon” is nearly six minutes long, while barely seconds into episode one of Soderbergh’s “The Knick,” we’re treated to a long, mood-setting ride through the Bowery.

“Both those guys are unique or courageous in giving the score such a fat and juicy role, letting the music tell the story,” says Martinez. “I don’t see that very often. It only comes from those two, because they’re repeat customers, and they can kind of anticipate what I’m going to do. But that’s why they’re so much fun to work with.”

For the hallucinatory catwalk scene in “The Neon Demon,” where Elle Fanning seems to split into three and makes out with herself, Martinez notes that “sometimes the music does a better job of explaining abstract things,” but adds that the director had a clear vision for the scene: “She begins to fall in love with herself, become an extreme narcissist … the music is part of showing that transformation.”

And what about the mysterious neon triangle that entrances her, a point that leaves many viewers scratching their heads? Martinez chuckles and says that he did a lot of press conferences with Winding Refn, but “I never heard Nic give a straight answer on the meaning of the triangle. I’m not sure whether he knows. I think he likes to set things up that will engage the audience’s imagination. Soderbergh is that way too, he doesn’t want to talk down to the audience and spell things out all the time. Both directors approach the music that way, they never want it to be terribly obvious, or repeat what’s in the dialogue or imagery. It’s more fun to watch a movie when you’re in doubt (about) what it means to you.”

“The Knick” also embraces cognitive dissonance, placing an electronic music score over a horse-and-buggy period piece. Somehow it makes sense. The music recalls ’60s artists like Isao Tomita and Wendy Carlos, and a time when musicians were struggling to figure out the new technology of analog synthesis, just as the doctors in “The Knick” grapple with advances such as X-rays and electricity. But was Martinez ever afraid the approach wouldn’t work?

“Well, my first thought was that the language, the look of everything was so authentically New York 1900 that I was afraid I might mess up that balance and take people out of the period,” says Martinez. “It felt like a high-risk idea, but Steven was pretty confident; he had already started editing to (temp) music from ‘Drive,’ and in his mind it was already working. But once I started to get my hands dirty, it made perfect sense to me.

“I mean, there’s no soundtrack in real life! When someone’s having a surgical procedure there is no music playing. Music is one of the abstract elements anyhow, so it’s my belief that as long as you get the needs of the film right, you have a lot of latitude when it comes to instrumentation.”

Spontaneity plays a big role for Martinez: “I feel like my best work is the stuff where I get it the first time, the more times I have to go back and do it over, the worse things get,” he says, describing the soundtracks to “The Knick” and “Drive” as primarily “first take, first impulse music.”

Another hallmark is how stripped-down these soundtracks are — often just one or two, maybe three, elements in play. This minimalism is integral to scoring for film. Martinez notes how music is often “the third level of perception, below the dialogue and the visuals, so you really can’t have too much going on.” But as for the “less-is-more aesthetic,” he says he developed that early on from Soderbergh, when he worked on “Sex, Lies, and Videotape.”

“He’d come by my place and say, ‘Yeah, that sounds good, let’s just take off the top.’ ‘Umm, that’s the melody, Steven.’ ‘And that thing on the bottom.’ ‘That’s the bass.’ ‘Yeah, get rid of that.’ He would strip away all the stuff,” Martinez explains. “But I realized that with the remaining parts of the music, if you put a lot of expression into that, one instrument is all you need.”