President and Mrs. Carter summoned up lovely shades of nostalgia Thursday night for the music following their state dinner for British Prime Minister James Callaghan.

Mezzo-soprano Jan De Gaetani sang six songs by Stephen Foster, a composer she treats with rare beauty. Tenor Robert White sang a half-dozen ballads and popular songs of past generations, songs he has brought to new fame through recent recordings, and which he sings with the perfect touch of belief and longing.

The President introduced the two singers, saying that they would take their listeners back either to the time when the radio brought us most of our home entertainment, or to a period even earlier when the piano in the living room was the place members of families gathered to sing these songs.

Gilbert Kalish, playing for De Gaetani, and Samuel Sanders for White, played on a beautiful square rosewood Chickering piano from the Smithsonian collection. It was brought to the White House to make the idea accompanment for the songs. Among White's ballads were "Sylvia," "Little Boy Blue," and "A Perfect Day." At the close of the evening, in response to a request from the President in honor of his Welsh guest, White sang "All Through the Night." first in Welsh, then in English. The Prime Minister complimented him on his Welsh.