When Sax first produced the saxophone, his strange but weirdly powerful hybrid of the woodwind and brass families was seized upon by adventurous composers and musical culture in his adopted Paris. Berlioz championed it, but only wrote for it once, in a now lost score; Bizet used it, and it became a staple of military and wind bands the world over. But it was, of course, in jazz and pop music in the 20th century that the saxophone achieved its greatest success; you might think that the story of the sax in orchestral culture is a mere sideshow to the main jazz event. This was the instrument that Edward Elgar declared was bound to have a future among the wind section of the regular orchestra – but it never quite happened. Not for the want of trying, as our saxophonic starter for 10 proves.

Bizet: L’Arlésienne suites: An early adopter in the early 1870s, Bizet uses the saxophone soloistically yet subtly in these two suites of incidental music for Alphonse Daudet’s play.

But the most famous moment of saxophony from a French composer is surely this, from Ravel’s Boléro; a solo that seems to define the saxophone’s distinctive voice in the orchestra as one of sultry, exotic otherness.

But it didn’t have to be like that: Rachmaninov, in his Symphonic Dances – his last composition, from 1940, makes the saxophone’s solo in the first movement a distillation of melancholy and nostalgia – and it’s essential to the music’s structure too, an integration of saxophonic-colour and quasi-symphonic architecture.

In the UK, there were concerted attempts to fulfil Elgar’s sax-prophecy: Vaughan Williams uses the instrument’s seductive sensuality to connote the oily hypocrisy of Job’s Comforters in the sixth scene of his Job, A Masque For Dancing.

The young Benjamin Britten does something different: in his Sinfonia da Requiem, the sax is an indivisible part of the symphonic texture: it’s one of the boldest and best realisations of how the saxophone could – and possibly should – have become a regular orchestral voice.

Yet the sax still says “solo” instead of “team player” for many composers, so why not go the whole hog, and write a concerto for it? Richard Rodney Bennett did in his Concerto for Stan Getz (Getz’s illness and death, the same year the concerto was finished, meant he never played it): it’s a dazzling fusion of modernism and jazz harmonies – and it works thrillingly.

But there’s also this, one of the most notoriously riotous and riotously notorious pieces in the Proms’s history: Harrison Birtwistle’s Panic, for saxophone, jazz drummer, woodwind, brass, and percussion. It’s music that releases all of the noisesome possibilities of the saxophone in sounds that are animal, primal, and irresistible. Birtwistle has made the saxophone an essential part of his instrumentarium; it’s in pieces from 1972’s The Triumph of Time, to his 2008 opera, The Minotaur.

In terms of fusing the worlds of jazz and classical, Mark-Anthony Turnage has done as much as any composer; with his favourite saxophonist collaborator Martin Robertson, he has created such pieces as Blood on the Floor and Your Rockaby, indelible parts of the contemporary saxophone repertoire. And there’s this, a concerto for soprano sax and chamber orchestra, Hidden Love Song.

But if you want full-on saxophonic integration in the soundworld of a piece, then you need Nixon in China in your life. John Adams’s 1987 score for his opera puts a quartet of saxes at the centre of the ensemble, and it’s their undiluted energy that propels the whole piece...

...Just as they do even more violently, blaringly, and brilliantly in Louis Andriessen’s De Stijl, one of my all-time favourite pieces from the 1980s – or from any other time. It has taken leaps of imagination for composers to understand what the saxophone sounds like, what it can do expressively, what it means, and how to use it. Classical and contemporary music would be a much less interesting place without it.