The composer ­Elliott Carter, who died last week at the age of 103, had, by virtue of longevity and industry, become the dean of American composers: honored, commissioned, and, especially in his extraordinarily productive final years, celebrated.

But just how “American” Carter’s music was had been often debated. Coming out of an era when composers like Charles Ives (an early mentor to Carter) and Aaron Copland (an often skeptical colleague) were held up as having created a truly American style, deliberately evocative of American landscapes and traditions, Carter instead wrote music that was modernist and unapologetically intellectual. Copland, for instance, worried that the music of his own generation, which had “fought hard to free American composition from the dominance of European models,” was being lost in the techniques and sounds of European modernism that Carter freely adopted. Carter, it was said, was an American composer who wrote European music.