Peck was the only one of the nine brothers who showed much interest in the family's upright piano. He received his first instruction on the instrument from the teenaged daughter of a neighbor but soon quit because she kept rapping his knuckles with a pencil when he made a mistake. His interest in the piano continued, however, and by 1919 he was reportedly playing with Jack Sharpe in the red-light district south of Buffalo Bayou. In the fall of 1921 he organized his own band, Peck's Bad Boys, which at various times during the decade included such notable musicians as Jack Teagarden, Pee Wee Russell, Wingy Manone, Snoozer Quinn, Johnny Wiggs, Leon Prima (the brother of Louis), and Leon Roppolo. The band played dances and fraternity parties around the Houston-Galveston area and also performed at the Washington Hotel in Shreveport in 1926. In addition, Kelley played occasional solo engagements around Houston and provided accompaniment for silent films at several local theaters.
He studied harmony and musical theory with Aldrich Kidd in Houston in the mid-1920s. He also studied classical piano with his friend Patricio Gutierrez and, possibly, with Albino Torres. Kelley idolized Vladimir Horowitz, though jazz immortal Art Tatum was the pianist to whom his peers most often compared him; many of his fellow musicians considered Kelley "the finest white jazz pianist of all time." In late 1925 Kelley journeyed briefly to St. Louis, where he played with Frankie Trumbauer's orchestra, which also included former Bad Boy Russell and Bix Beiderbecke. Beginning in 1929 Kelley played with several local bands that performed at the Gunter Hotel in San Antonio, the Adolphus Hotel in Dallas, and the Hollywood Club in Galveston, and briefly in New Orleans. In 1931 he also had a regular gig at the cafeteria of the Rice Hotel in Houston.
As alumni of his bands moved on to other organizations and spread word of his talents, Kelley became a legend in jazz circles, but he stubbornly resisted the stardom that seemed his due. "I never liked to play for a living," he once said, "but I liked to play on the piano." He refused to leave Houston, turning down offers from Paul Whiteman, Tommy Dorsey, Jimmy Dorsey, Benny Goodman, Artie Shaw, and Rudy Vallee, among others. "If I was working with a top band," he reasoned, "it would be rehearse, record, broadcast, play, rush, hurry, with no time to myself." He also declined recording contracts from Decca and OKeh. One measure of his growing reputation came in July 1939, when an admiring article by John Hammond, Peck Kelley Is No Myth, appeared in Down Beat. Kelley attracted more attention in February 1940, when Collier's ran an article titled Kelley Won't Budge. Kelley began an engagement in 1938 at the Southern Dinner Club, where he played off and on until late 1950. He joined the United States Army in 1942 and was stationed in San Antonio. There he organized a band, but eye problems led to his discharge in March 1943, whereupon he found work in a Houston shipyard for the duration of World War II.
Plagued by deteriorating vision from cataracts and glaucoma, Kelley retired from the music business in 1950, although he reportedly spent hours practicing at home on a stringless, silent piano so as not to disturb his neighbors. He had begun to show the symptoms of Parkinson's disease. He finally recorded informally, at the urging of friends, in 1951, 1953, and 1957. The 1957 session, recorded at the studios of radio station KPRC, was released as a double album in 1983. At a Houston gig in 1960 his old friend Teagarden invited Kelley to sit in, but Kelley, nearly blind, refused to play in public.
Kelley married in 1920, but he and his wife were divorced amicably two years later, reportedly over her refusal to attend a Christmas party at a movie theater where he had been working. In later years he lived with his nephew and his nephew's wife. Despite his lack of formal education he was a dedicated reader of philosophy and was especially fond of the essays of Ralph Waldo Emerson. "He was extremely modest," remembered his old friend Johnny Wiggs. "He just wanted to stay on in Houston and live a quiet life." Kelley died in Houston on December 26, 1980.
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