Theatre's attempts to be relevant and contemporary often major on experimental formats and clunking references to issues. Vivian's Music, 1969 is unashamedly old school, telling a story from the recent past through the simplest structure – two actors, a poetic and moving script with an attention to detail – and a resonance for Black Lives Matter that does not need to be signposted.

Monica Bauer's script is astonishing: whether relating the tragic death that motivates the almost optimistic finale – resilience and hope maintain a shaky hold on the jazz drummer-turned-social entrepreneur – or describing the magic of a band jamming together, it doesn't need anything more than the fluid performances of Russell Jordan and Kailah S King to impress. By turns naturalistic and allusive, Bauer's words evoke the late 1960s in a torrent of personal ambitions, dramatic scenes and a compassionate depiction of multiple lives caught in the racial conflicts after the deaths of Malcolm X and Martin Luther King.

Stressing the importance of community history and wisdom, and weaving personal redemption into a political narrative, Vivian is emotive, provocative and elegant. Jordan's drummer is a complex yet sympathetic man, while Vivian is a charming protagonist, all youthful enthusiasm and joy and delight. Yet its tragic structure lends a soft-spoken authority to a reflection on how the individual is always part of wider community and historical currents.

Sweet Grassmarket, until 25 Aug (not 14, 20, 21, 26), £7 (£5).