Eric Francis Harrison Coates (27 August 1886 – 21 December 1957) was an English composer of light music and, early in his career, a leading violist.

Coates was born into a musical family, but, despite his wishes and obvious talent, his parents only reluctantly allowed him to pursue a musical career. He studied at the Royal Academy of Music under Frederick Corder (composition) and Lionel Tertis (viola), and played in string quartets and theatre pit bands, before joining symphony orchestras conducted by Thomas Beecham and Henry Wood. Coates's experience as a player added to the rigorous training he had received at the academy and contributed to his skill as a composer.

While still working as a violist, Coates composed songs and other light musical works. In 1919 he gave up the viola permanently and from then until his death he made his living as a composer and occasional conductor. His prolific output includes the London Suite (1932), of which the well-known "Knightsbridge March" is the concluding section; the waltz "By the Sleepy Lagoon" (1930); and "The Dam Busters March" (1954). His early compositions were influenced by the music of Arthur Sullivan and Edward German, but Coates's style evolved in step with changes in musical taste, and his later works incorporate elements derived from jazz and dance-band music. His output consists almost wholly of orchestral music and songs. With the exception of one unsuccessful short ballet, he never wrote for the theatre, and only occasionally for the cinema.

Coates was born in Hucknall Torkard, Nottinghamshire, the only son, and youngest of five children, of William Harrison Coates (1851–1935), a medical general practitioner, and his wife, Mary Jane Gwyn, née Blower (1850–1928). It was a musical household: Dr Coates was a capable amateur flautist and singer, and his wife was a fine pianist.

As a child, Coates did not go to school, but was educated with his sisters by a governess. His musicality became clear when he was very young, and asked to be taught to play the violin. His first lessons, from age six, were with a local violin teacher, and from thirteen he studied with George Ellenberger, who was once a pupil of Joseph Joachim. Coates also took lessons in harmony and counterpoint from Ralph Horner, lecturer in music at University College Nottingham, who had studied under Ignaz Moscheles and Ernst Richter and was a former conductor for the D'Oyly Carte Opera Company. At Ellenberger's request, Coates switched to the viola, supposedly for a single performance; he found the deeper sound of the instrument to his liking and changed permanently from violinist to violist. In that capacity he joined a local string orchestra, for which he wrote his first surviving music, the Ballad, op. 2, dedicated to Ellenberger. It was completed on 23 October 1904 and performed later that year at the Albert Hall, Nottingham, with Coates playing in the viola section.

Coates wanted to pursue a career as a professional musician; his parents were not in favour of it, but eventually agreed that he could seek admission to the Royal Academy of Music (RAM) in London. They insisted that by the end of his first year there he must have demonstrated that his abilities were equal to a professional career, failing which he was to return to Nottinghamshire and take up a safe and respectable post in a bank. In 1906, aged twenty, Coates auditioned for admission; he was interviewed by the principal, Sir Alexander Mackenzie, who was sufficiently impressed by the applicant's setting of Burns's "A Red, Red Rose" to suggest that Coates should take composition as his principal study, with the viola as subsidiary. Coates was adamant that his first concern was the viola. Mackenzie's enthusiasm did not extend to offering a scholarship, and Dr Coates had to pay the tuition fees for his son's first year, after which a scholarship was granted.

At the RAM Coates studied the viola with Lionel Tertis and composition with Frederick Corder. Coates made it clear to Corder that he was temperamentally drawn to writing music in a light vein rather than symphonies or oratorios. His songs featured in RAM concerts during his years as a student, and although his first press review called his two songs performed in December 1907 "rather obvious", his four Shakespeare settings were praised the following year for the "charm of a sincere melody". and his "Devon to Me" (also 1908) was credited by The Musical Times as "a robust and manly ditty, worthy of publication".

Coates was fortunate in his viola professor. The New York Times called Tertis the first great protagonist of the instrument, and Grove's Dictionary of Music and Musicians ranks him as the foremost player of the viola. He was also regarded as a great teacher, and under his tutelage Coates developed into a first-rate viola player. While still a student he earned money playing in theatre orchestras in the West End, including the Savoy, where he played for several weeks under François Cellier in a Gilbert and Sullivan season in 1907.