This is Buxtehude's largest and possibly also his most grand cantus firmus-based composition. It couples many of Buxtehude's different compositional styles into one large entity. It sets the Te deum chant from the Gregorian repertoire. The chant is fairly long, and Buxtehude marks periodically in the score what portion of the chant he is working with. The work begins with a free toccata passage, followed by a fugue which breaks down into free toccata material just like one finds in his Präludia for organ. The chant cantus firmus does not appear until measure 44. At this point Buxtehude starts with a bicinium (two voice) setting of the Te deum laudamus portion of the chant, tossing the chant melody back and forth between the tenor and soprano. After 20 measures he places the chant melody in the bass and expands the texture to three voices. Starting in measure 74 he adds a fourth voice and at measure 80 expands yet further to five voices and double pedal texture. The bicinium and tricinium method of setting a chorale melody was old-fashioned by the time Buxtehude was working as a mature composer; however, the free voice in this setting appears incredibly original and could hardly be seen as something old fashioned. The pleni sunt coeli portion of the chant Buxtehude sets as a chorale fantasy, similar to what one sees in the second verses of Scheidemann's Magnificat settings. Typical of the North German chorale fantasy Buxtehude employs plenty of echo effects between the rückpositive and the haupt werk keyboards on the organ. The Te Martyrum portion of the chant Buxtehude sets the cantus firmus in the tenor in the pedals against two free contrapuntal voices in the manuals. The last portion of the chant, Tu devicto, appears with four voice imitative counterpoint creating a quadruple fugue which employs bits and pieces of the chant. The strict fugue breaks down at the end returning to the free toccata texture the work began with for a wild ending typical not all too dissimilar from the endings of his free Präludia.

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