Daman is thought to have been born in Liège (modern-day Belgium) around 1540 and came to England as a servant of Thomas Sackville, 1st Earl of Dorset on his return from Rome in 1566.
From 1576 until his death he was in the royal household of Elizabeth I, where he was one of six musicians in a recorder consort that played dance music.
His work appeared first in 1579, printed by John Day, with a preface by Edward Hake, who relates how these compositions were secretly "gathered together from the fertile soyle of his honest frend, Guilielmo Daman", by one "John Bull, citezen and goldsmith of London", and how Bull "hasted forthwith of himself … to commit the same to the presse".
The work appeared in four oblong quarto part-books, and is now of great rarity, the edition probably being bought up by the composer or his friends.
In the preface to this work Swayne says that the former publication "not answering the expectation that many had of the auctor's skill, gave him occasion to take uppon him a new labour to recover the wrong his friend did in publishing that that was so done".