Harry C. Thompson was born in Grandview, Louisa County, Iowa, to Iowa native farmer and American Civil War veteran William Beard Thompson and his second wife, British immigrant Maria "Mae" Bennett, daughter of another Civil War veteran who fought in an Iowa regiment in spite of his British heritage. Harry was somewhere around the middle of six siblings, including Carrie J. (1859), Frank John (1861) and Libbie (1873) from William's first marriage, and, Ralph U. (10/1878) and Herbert Garfield (12/1880) from his second. Around 1889 the family moved to Muscatine, Iowa, the county seat in the southeast corner of the state.

Little could be found on Harry's upbringing in Muscatine. However, he was known to have been part of "Iowa's biggest little drum corps" which marched in local parades and performed at political events. He was also versed in playing piano and brass instruments. At a young age he reportedly fought in the Spanish-American War, later honored as a veteran by and as a commander of the local post of the United Spanish-American War Veterans. By 1900 Harry had left the nest, and was likely still in college working on a music degree, or traveling as an itinerant musician around the United States, as no definitive census record was located for him. The parents and their two younger sons were still in Muscatine in 1900. Ralph and Herbert would open the law firm of Thompson and Thompson around 1903, and both became active in local politics. In that capacity, Ralph was believed to be responsible for bringing municipal power and water to Muscatine before 1910.

Harry, of course, went into the field of music as a career. His first pieces were published in Chicago, and some arrangements he worked up as well. There were also some early rags published in New York by Leo Feist and William C. Polla, but they could have easily been submitted by mail, or a trip to New York as a performer, or even through a branch office in Chicago. Why some earlier pieces didn't go to one of the Rossiter brothers, Victor Kremer, McKinley or some other Chicago publisher is unclear, but it may have been based on travel and/or opportunity more than anything else. There is no indication that Thompson spent any substantial period of time in New York as a lodger, but was found in Chicago directories in 1906 and 1908, making a permanent New York City residency less likely.

In August, 1901, Harry reportedly married Ettna M. King in Chicago. This is challenged by later records that indicate he had been married around 1899 to Jessie Ramey of Des Moines, Iowa. In the 1910 census taken in Chicago he was listed as a musician writing and playing, but no profession for Jessie, further calling in the question of the record showing Etta King as they were shown as having been married for eleven years. In terms of his career, what he had been up to during the prior decade was summed up in this 1911 History of Muscatine County published in Iowa, published in reference to his locally famous brother Ralph, who had now become a politician at the state level, and their father. "The eldest son is prominent in musical circles, being a composer and arranger of music. He has played with the Innis, Kryl, Thauvius and Brooks bands, which have world-wide reputation and has also been connected with St. Paul's Symphony and the International Grand Opera Company orchestras." Certainly some of these positions required travel, which could further explain the New York publications of a Chicago musician.

Harry's earlier works included three racially skewed rags, Le' Go Thar, A Black Bawl and The Watermelon Trust. They are all fine works, and responsibility for both the titles and covers might well have been at the discretion or lack thereof of the publisher more so than the composer, a frequent practice of the time. In 1911 he released two more pieces, including the two step Tete a Tete and the bouncy Wig Wag Rag, which has remained one of his more popular pieces for over a century. In September 1912, Jessie died of pneumonia, leaving Harry a widower. In 1914 some of his compositions were played and recorded on Edison discs by the bands of Arthur Pryor and John Philip Sousa. Thompson had played at one point with Pryor's Band, but there was difficulty in finding specific dates during which he was a member. By the mid-1910s Harry had arranged several other ragtime works for both piano and concert band, including some of his own. Three band arrangements of his pieces released in the mid 1910s, although not fully confirmed to be arranged by Harry, include From Hand to Hand, The Great Mid-West and The American Boy, in addition to his last known rag, Dimpley Smiles, which was recorded by several groups and to piano roll as well.

From the mid 1910s on Harry was pretty much a union musician playing short and long term gigs in Chicago and around the Midwest. By 1918, Harry was listed on his September 12, 1918, last call draft card as a music writer, with a note that correspondence and a "statement of time" should be addressed to the Chicago Federation of Musicians, given how much he traveled. Fon the 1920 census Harry was still in Chicago, listed as a music arranger both there and in a city directory. On November 19, 1920, he married again, this time to Mrs. Clara D. Weipplehauser Smith, acquiring a stepson in the process.

Given that Harry was both a working musician and arranger, but not so much a soloist, very little appears on him much of anywhere except in official records, and he does not appear to have made enough of a splash to appear in local papers like the Chicago Tribune, Sun and Economist, so except for notices on the groups he was working with there is nothing of note on his musical life there. Later articles in Muscatine mention him as a fine percussionist and well-known tympani player. Among those that he trained on marimba, drums, tympani and bells was Muscatine music teacher Elmer Ziegler, who proudly touted his association with Harry in his advertisements for his school of music.

By the time of the 1930 census Harry and Clara were living in a rooming house in Chicago, and he was employed - well in advance it appears - as a musician for the upcoming Century of Progress World's Fair to be held there in 1933. Whether this was in the capacity as a musical director, arranger or contract musician is unknown at this time. One interesting sideline in his capacity as a music instructor was a book published in 1931 by Leedy Manufacturing in Elkhart, Indiana. It is the Elementary Instructor for Vibraphone and Vibra Celeste. This book was likely the first of its kind for these relatively new mallet instruments.

Meanwhile, back home in Muscatine, Ralph had been serving in the Iowa legislature as a state senator, and Herbert as a successful lawyer and business entrepreneur, as well as the town mayor. By 1932 Harry had moved back to live with his brother, Mayor Herbert Thompson, in Muscatine, working as a music teacher in the same building as the Thompson and Thompson law firm. He also took over leadership of the local drum and bugle corps of the American Legion It is unclear if Clara moved back with him, but she is not mentioned in any Muscatine articles.

By the late 1930s Harry, along with former Ringling Brothers Circus bandmaster John J. Richards, helped to form an adult municipal band in conjunction with the high school music program. He headed up percussion for the organization, including marimba duties. Harry also frequently accompanied other artists visiting Muscatine, and played bugle at many funerals. Herbert G. Thompson died in 1942, followed by Senator Ralph U. Thompson in 1946, and finally Harry C. Thompson in 1947. In fact, he died in a bandstand just after having heard his composition Hand to Hand, dedicated to another director, Armind Hand, played by the Tipton Concert Band. Having been in poor health for several months, when he stood in recognition of the applause, Harry suffered a massive heart attack and was dead within minutes. He is buried with his brothers at Greenwood Cemetery overlooking the Mississippi River in Muscatine.