Joseph plays a large variety of repertoire, covering a range of styles. Here is a list of some of the pieces he has played:

Concertos (bb = brass band, wb = wind band, orch = orchestra)
Sparke, Tuba Concerto (bb)
Gregson, Tuba Concerto (bb, wb, orch)
Vaughan-Williams, Tuba Concerto (orch, bb)
Horovitz, Tuba Concerto (orch, bb)
Ellerby, Tuba Concerto (bb, wb)
Steptoe, Tuba Concerto (orch)
Williams, Tuba Concerto (orch)

Solo pieces with brass band:
Baadsvik, Fnugg
Newton, Capriccio
Brand, Tuba Tapestry
Monti (arr. Sykes), Czardas
Rossini (arr. Roberts), Largo al factotum
Hubay, Hejri Kati
Abreu (arr. Catheral), Tico-tico

Solos with Piano:
Glass, Sonatina for Tuba and Piano
Plog, Three Miniatures
Koetsier, Concertino for Tuba
Koetsier, Sonatina for Tuba
Salzedo. Sonata
Hindemith, Sonata
Gordon, McPlethian the Hardy

Unaccompanied solos:
Penderecki, Capriccio
Wiggins, Soliloquy X
Gregson, Alarum
Glass, Prelude, Waltz and Finale
Baasdvik, Fnugg

Kraft, Encounters II