He is mainly known by a few small piano pieces (especially a Sonatina in C Major and the Fanfare or Fanfare Minuet) that are still reprinted in pedagogical collections. They are probably excerpts of the Progressive lessons for the harpsichord and piano forte, published in 1778 (or 1785).
Duncombe is frequently confused with the writer William Duncombe (1690 – 1769).
- First Book of Progressive Lessons for the Harpsichord and Piano Forte — London : J. Bland, n.d. 
- Second Book of Twelve Progressive Lessons for the Harpsichord or Piano Forte — London : J. Bland, n.d. 
- The Favorite Air, of God save the King, with variations for two performers on one piano forte, or harpsichord — London, 
- What tho' the sun withdraws his ray — London, n.d. [1760?]
- Sources : LoC, MusicSack
- There is a record of a concert he gave there in 1793.
- For example: Fanfare: , , ; Sonatina: , ; both: .
- See WorldCat.
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