Do you like your music rare? That’s fine. Before we knew how to record it, all music was rare. It was an invisible wiggle in the air that materialized and vanished.

Then we learned how to encode our songs onto discs and tapes, and rareness became an issue of scarcity, with little supply-and-demand cults forming around various musical geniuses that time forgot. But today, with so many streaming services bringing so much forgotten music back to the digital surface, a “rare record” can really only be a recording that feels precious and inimitable — something like the 1984 debut from Admas, a quartet of Ethiopian expatriates who emerged from extraordinary circumstances to make extraordinary music.

The album was called “Sons of Ethiopia,” it’s recently been reissued on Frederiksberg Records, and it still sounds like nothing else. Summoning traditional Ethiopian melodies from the newest instruments within reach (synthesizers, drum machines, electric guitars), Admas specialized in paradox, generating exquisite new grooves that felt high-tech and low-budget, worldly and local, futuristic and nostalgic, funky and delicate.

But ultimately, “Sons of Ethiopia” feels like an expression of exploration and loss. In the liner notes of the reissue, author and researcher Francis Gooding provides social context, describing the album as “a music of exile made by players who performed week in and week out for crowds of their fellow Ethiopians who had lost family and friends to the Derg” — the military junta that deposed Emperor Haile Selassie in 1974 “and had often fled to the US in fear for their lives.”

That explains the latent melodic ache in this effortlessly propulsive music. Listen hard enough and you can hear the players pushing into the future while longing for a past they were forced to leave behind.

The members of Admas were born too late to contribute to the “golden age” of Ethiopian song. Selassie was overthrown by the Derg in ’74, marking the end of an era in which jazz-minded musicians — including the legendary vocalists Mahmoud Ahmed and Alemayehu Eshete — helped Addis Ababa earn the nickname “Swinging Addis.” But according to Gooding’s liner notes, the brutality of the new regime didn’t silence the music altogether. The Derg “were not against music,” says Admas keyboardist Tewodros Aklilu. “They were against Western music.”

In fact, the new government encouraged youth bands to form in urban neighborhoods with the express purpose of performing propaganda songs that celebrated Ethiopia’s national heritage. The members of Admas considered it an education. As adolescents learning to play their instruments in state-sponsored groups, they were plunged into a deep well of traditional and tribal songs.

Then, in 1977, the Derg initiated the Red Terror, a campaign of violence against civilian groups competing for control of the country, and in the years that followed the members of Admas fled to Washington. The musicians, some of whom were friends from childhood, reassembled in D.C. in the early ’80s under the name Gasha, and took up residency at the Red Sea, a lively Ethiopian restaurant in Adams Morgan. (“An evening at the Red Sea is something like having a picnic in a busy airport,” Washington Post food critic Phyllis C. Richman wrote in 1985.)

The members of Gasha played Ethiopian songs for Ethiopian crowds, but their ears stretched across the city. They heard go-go in neighboring nightclubs. They heard funk and electro on the radio. They soaked up jazz at Blues Alley and the Saloon in Georgetown. It was a second education.

Having fully immersed themselves in the sounds of their new home, the foursome — keyboardist Aklilu, multi-instrumentalist Abegasu Shiota, bassist-guitarist Henock Temesgen and drummer Yousef Tesfaye — started scrambling genres under a new name. As Admas, they captured their experiments with a four-track cassette recorder, and their music began to move in disparate directions at different speeds.

Remember, this was the ’80s, so some of the band’s synthesizer tones might sound tart to 21st-century ears, but keep listening and it wears off: “Anchi Bale Gane” feels like a midnight stroll through another world, with little fireworks of guitar and keyboard fizzing in the atmosphere overhead. “Tez Alegn Yetintu” (“I Remember,” in Amharic, roughly) floats off into a zero-gravity jazz-funk reverie. “Kalatashew Waga,” the album’s centerpiece and masterpiece, drives a drum machine over rumble strips of synth-bass into landscapes unknown.

After eight months of tinkering, Admas brought the “Sons of Ethiopia” tapes to Ambient Studios in College Park for a final mix, then mailed the masters off to a plant in Nashville that pressed 1,000 copies. The band delivered one LP to the Library of Congress, sold 200 or so more, and gave the rest away free.

If you found a copy of “Sons of Ethiopia” for a few dollars at, say, a flea market on New York Avenue NW umpteen years ago, you may have felt a trivial thrill (original vinyl copies have sold for as much as $400 online) followed by a lasting enchantment (these songs make “rareness” feel like a musical quality).

The album’s reissue doesn’t reveal too much about what happened to Admas after “Sons of Ethiopia.” A short, incomplete version: The Derg was abolished in 1987 (although Ethiopia remained under authoritarian rule into the early ’90s); most of the band’s members eventually repatriated, continuing their respective musical careers in Addis Ababa; some reunited around 2000 to record a second Admas album that might be reissued next year. But the liner notes do help to explain how and why this music sounds so singular.

The first how-and-why has to do with technology. Shiota, the band’s primary synth player and de facto producer, had to be resourceful while “bouncing tracks” on the band’s four-track machine, a recording technique that involves funneling three tracks into one. On “Sons of Ethiopia,” those bounced tracks swirl the sound, putting the elegance of the band’s arrangements to the test. Gracefully performed and meticulously recorded, this is why the music’s softly smeared timbres feel smoothed and congealed rather than smudged or dimmed.

The album’s other big how-and-why has to do with humanity. These were bright, young men bending melancholic, old melodies into fresh, new shapes — and the album’s closing cut, “Astawesalehu,” quietly pushes all of those contrasts to the fore. Delivered as a nostalgic call-and-response between guest vocalist Simeon Beyene and the band, Beyene sings what roughly translates to, “I remember.” The band replies in Amharic, “I will never forget.”

But even without an approximate translation of those lyrics, the recording communicates its cosmic yearning by submerging the vocal tracks in a gently disorienting echo effect. Five voices sing to each other inside a dream, across oceans, across time.