Santa Maria was a Dominican monk and an accomplished organist and composer. He spent sixteen years perfecting his Arte de tañir fantasia; it was finished in 1557, but due to a shortage of paper at that time was not printed until 1565. The work is an introduction to the art of playing fantasies on keyboard instruments, on the vihuela (the precursor of the Spanish guitar) and on every instrument on which it is possible to play in three or four parts or more; it is divided into two parts, the first dealing with the technique of playing, the second with composition.

His own skill as a composer is shown in the second part where the short pieces used as examples are all that remain to us of his own work.