Ian Carr (born 21st April 1933, died 25th Febuary 2009) was a Scottish jazz musician, composer, writer, and educator.

Carr was born in Dumfries, United Kingdom, the younger brother of Mike Carr. From 1952 to 1956 he went to King's College, now Newcastle University, where he read English Literature, followed by a diploma in education.

At the age of seventeen Carr started to teach himself trumpet. After university he joined his brother in the Newcastle band EmCee Five from 1960 to 1962, before moving to London, where he became co-leader with Don Rendell of the Rendell–Carr quintet (1963–1969). In its six years, the group (including pianist Michael Garrick, bassist Dave Green, and drummer Trevor Tomkins) made five albums for EMI – all of which have been re-issued – and performed internationally.

After leaving the quintet, Carr went on to form the ground-breaking jazz-rock band Nucleus. This led to the release of twelve albums (some under the band's name, some under Carr's), and a successful international career. In their first year they won first prize at the Montreux Jazz Festival, released their first album (Elastic Rock), and performed at both the Newport Jazz Festival and the Village Gate jazz club. He has also played with the United Jazz and Rock Ensemble since 1975.

Carr has worked as a session musician in non-jazz contexts, with Nico, No-Man, Faultline, and others.

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