A whole is divided into two parts, nearly equal in size. While sharing a fundamental character, they diverge just as fundamentally. A section that could be described as recalling the color blue — even if it’s the midnight variety — is connected by a tiny, fragile bridge to an evocation of dark, churning red.

Esa-Pekka Salonen doesn’t mention Democrats and Republicans — or Leavers and Remainers, or other bitter bicameral oppositions of our time — in the program notes for his new orchestral work, “Gemini.” But thoughts of politics, of face-offs between countrymen, were inescapable as the New York Philharmonic gave the local premiere of this two-headed piece on Wednesday at David Geffen Hall.

“Gemini” is the union of “Pollux” (2018) and “Castor” (2019), which can also be performed individually and are named for the half brothers of Greco-Roman myth: both sons of Leda, but Castor mortal and Pollux divine.

Conducting the Philharmonic in these performances, Mr. Salonen has nestled the twins amid works written by Hindemith and Schoenberg in the 1920s and ’30s. Those German composers looked toward the past for inspiration and consolation at a time of national and international unease; with his classical subject matter and our similar moment, Mr. Salonen has placed himself in their company.