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Elgar was once thought to have been born in 1885, but later interviews confirmed 1879 as his year of birth. Elgar played violin as a child, and played in Chicago from 1903 with the Bloom Theater Philharmonic Orchestra, returning to New Orleans late in the decade of the 1900s until about 1913. He put together a group in Chicago comprising in part musicians he had promised work in New Orleans, including Manuel Perez. His band played at the Dreamland Ballroom in Chicago from 1917 to 1922, both as a quintet and as a full 15-member ensemble. This band toured in the revue Plantation Days and traveled to London, though Elgar did not accompany it on this trip. However, he did play with Will Marion Cook's Southern Syncopated Orchestra in Europe. He led later bands in Milwaukee, 1925–28, and again in Chicago, 1926-30.
Aside from the above mentioned, his sidemen included Lorenzo Tio, Louis Cottrell, Jr., Barney Bigard, Ben Thigpen, Darnell Howard, and Omer Simeon. He recorded only four times in 1926 with the Creole Orchestra for Vocalion Records. He became a teacher in the 1930s and also worked as a union official later in his life.