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The name references Soft Machine while "Heap" comes from the first letters of the band's founders: Hugh Hopper (bass), Elton Dean (saxophone), Alan Gowen (keyboards) and Pip Pyle (drums). Hopper and Dean had worked together in Soft Machine, while Gowen and Pyle had worked together in National Health.
Soft Heap went on tour in 1978, but with Pyle busy with National Health, Dave Sheen replaced him and the name was changed to Soft Head.
Rogue Element, a live album from the Soft Head tour, was released in 1978, but the original Soft Heap line-up reconvened in October 1978 to record Soft Heap (released in 1979). John Greaves (also from National Health) replaced Hugh Hopper in 1979-80, while 1981 saw a new line-up of John Greaves, Elton Dean, Pip Pyle and Mark Hewins on guitar following Alan Gowen's death that year. 
Released only in 1996, A Veritable Centaur is a live album largely taken from a 1982 French show, with one track from a 1983 BBC Radio 3 performance while Al Dente is a 2008 archival release of a 1978 show.
The three other founding members (Hopper, Dean and Pyle) all died in the 2000s.
|1978||Soft Head||Rogue Element|
|1978||Soft Heap||Al Dente (released in 2008)|
|1979||Soft Heap||Soft Heap|
|1982||Soft Heap||A Veritable Centaur (released in 1996)|