Belding wasn't one of the big time composers of the ragtime era. He was born in Jefferson Iowa to a mother who taught music and from whom he probably received some musical instruction. Some time around 1889, Harry's father began selling pianos and organs (of the musical sort, not the kind used in giblet gravy), so it's fair to say he came from a musical family. By 1910 Harry had moved to the ragtime hotbed of St. Louis, MO where he managed a vaudeville theater and the exposure led to his taking on a partner and going on tour during 1912 and 1913 under the moniker Alexander and Belding. This was the act that introduced Good Gravy Rag in 1913. The following season Belding teamed up with a singer named Myrtle Sounders and in late 1913, Belding released his only other known piece, Apple Sass Rag.
Belding virtually disappears after 1914, he either left show business or didn't find a receptive audience. In 1918 he shows up with his wife Minnie and daughter Dorothy in Los Angeles where his draft records show his occupation as farmer employed by his father. Eventually he would remarry, move to San Diego, and become a successful real estate agent and part-time performer. He died in 1931 at the age of 49 after falling down a flight of stairs.