A decade ago, the cellist Anton Lukoszevieze was reading Gene Santoro’s magisterial biography of Charles Mingus, Myself When I Am Real, when a brief mention of a forgotten, maybe even lost composition captured his imagination. Mingus’s String Quartet No.1 was performed for the first and, during his lifetime, only time at the Whitney Museum in New York in 1972. It wasn’t recorded. Lukoszevieze got copies of the sheet music from the Mingus papers housed at the Library of Congress in Washington DC and discovered that, true to form, Mingus had rewritten the rulebook, including a part for voice and trading one of a conventional string quartet’s violins for a second cello.

Last month, as part of the Totally Thames Festival in London, Lukoszevieze’s ensemble Apartment House, with the singer Elaine Mitchener, put on a series of 14 concerts with the Mingus piece as a focal point. The performances took place in the Bascule Chamber beneath Tower Bridge, where mammoth counterweights had once winched the spans up and down. ‘Charles would never have got his bass down here,’ someone joked as we were led down the twisting, claustrophobic staircase – a long way from the Whitney, or the jazz clubs of New York where Mingus spent so much of his career, I thought, but it turned out to be not inappropriate for such peculiar and haunted music.

The concert at the Whitney was staged in memory of Frank O’Hara, who had died after a road accident in 1966. Virgil Thomson, Ned Rorem and Lukas Foss were among the other composers who wrote music in memoriam. For his String Quartet, Mingus set O’Hara’s poem ‘The Clown’ (nothing to do with his 1957 album of the same name).

Mingus’s usual way of doing things was to give the musicians he worked with – Eric Dolphy, Booker Ervin, John Handy and others – intricate, integrated compositional structures to improvise around, and there’s a clear link between his methods as an improviser and the way he composed. String Quartet No.1 coils together like cotton wool, densely compressed but also expansive, and always on the move. Mingus achieves this apparently contradictory effect through his mastery of counterpoint. Lines weave together into a satisfying whole as, at the same time, grinding harmonic tension throws up their differences. If you unwound all these overlays of line, laying them out in sequence, the piece might last an hour. But Mingus concentrates his material into a taut, lean and mean structure that doesn’t waste a note and runs for about ten minutes.

It reminded me of the string quartets of Bartók, Berg and Schoenberg, whose Second String Quartet, written in 1908, had incorporated a part for female voice. In the Schoenberg, the soprano voice levitates above the ensemble, but Mingus preferred to embed his vocal writing deep in the unfolding textures of the string instruments – which emphasises the sense of an already condensed music collapsing into itself.

As Mingus’s health began to fail later in the 1970s, and he could no longer play the bass, the String Quartet was one piece that his wife, Sue, sent around to encourage interest in him as a composer. Nobody took any notice then. Now, not only has Lukoszevieze recovered the piece, but Apartment House have created a new performance edition with the conventional two violins, viola, and cello instrumentation. Every Mingus fan will want to hear this piece. I trust it will be recorded soon.