THE ETUDE, which described itself as "A monthly journal for the musician, the music student, and all music lovers," was one of the magazines about music, and musical performance, and the singers and players and musicians who fill our lives with joy, sorrow, and entertainment. It was heavily oriented toward classical music, and the study of and instruction in performance and technique.

The Library of Congress says that it was published as "THE ETUDE AND MUSICAL WORLD" in 1896-1897, and they have Vol. 14, no. 1 (Jan. 1896)-v. 15, no. 11 (Nov. 1897). Height, 31 cm; publisher T. Presser, Philadelphia, PA. (Presser is listed as publisher for all subsequent title changes as well.) Call number is ML1 .E8 for all title variations. Title became THE ETUDE for 1897-1922 (36 cm), ETUDE MUSIC MAGAZINE 1922-1948, and simply ETUDE 1948-57 (30 cm). Last issue in LC was 1957-05+06.

Scarecrow published in 2004 An Index to Music Published in The Etude Magazine, 1883-1957. If this is too rich or too detailed for your blood, consider Piano Lessons in the Grand Style: From the Golden Age of The Etude Music Magazine (1913-1940).
Not so surprisingly, you can buy old issues of ETUDE on Amazon's Marketplace or on eBay.

The entire run of this magazine has been scanned, and can be searched or browsed.