Although it can be played on a piano, this piece is ideal on a sustaining instrument such as an organ or electronic keyboard. The music was written for the hymn (or psalm) as the 3rd of the 9 "Tunes for Archbishop Parker's Psalter" composed by Tallis in 1567 and sometimes called "Why fumeth in the Fight". The melody was also used and arranged by Vaughan Williams in his Fantasia on a theme by Thomas Tallis, which in turn was used most effectively on the soundtrack to the film "Master and Commander: The Far Side of the World". The video below shows this music being played, or scroll down to play the mp3 file and see the sheet music. Note that there is a difficult stretch of a 10th (two notes more than an octave). If you can't play the 2 notes together then "arpeggiate" them by playing the bottom note first and then the top note quickly afterwards. We also have an arrangement of this piece for four SATB recorders.
Here is a video of Tallis' Third Mode Melody for piano:
The image below is the first page of the sheet music, and here you can download the full sheet music for Tallis' Third Mode Melody for piano in PDF format.