Murrath has performed as a recitalist and soloist at venues around the world including Wigmore Hall, Royal Festival Hall in London; Suntory and Kioi Hall in Tokyo; and Théâtre de la Ville in Paris.

Murrath won first prize at the Primrose International Viola Competition and has received top prizes at the Tokyo International Viola Competition. He received a 2014 Avery Fisher Career Grant and in 2017 released his debut solo album, which features works by Henri Vieuxtemps, Rebecca Clarke, and Paul Hindemith. 

As a soloist, he has played with the Tokyo Symphony Orchestra, London Mozart Players, Orchestre National de Lille, Brussels Philharmonic, and Tokyo Metropolitan Orchestra,

An active chamber musician, Murrath has been a member of the Esmé Quartet since 2023 and was a member of the Boston Chamber Music Society from 2013 to 2023. He has collaborated with such esteemed musicians as Richard Goode, Gidon Kremer, Menahem Pressler, and Mitsuko Uchida, as well as members of the Cleveland, Mendelssohn, and Guarneri quartets. 

Murrath began his musical studies with Natalia Boyarsky at the Yehudi Menuhin School before earning a Bachelor of Music degree at the Guildhall School of Music and Drama in London, where he studied with David Takeno. He went on to earn an Artist Diploma from NEC, where he studied with Kim Kashkashian.