The ambiguous end of Beethoven's Diabelli Variations raises many interesting issues with regard to the closure of the work. The issue of closure is investigated with respect to theories of closure in music and in other literary fields. In examining the role of the coda in the Diabelli Variations, one finds that the coda answers some of the questions raised by the ambiguous end, and explains how the 'surprising final sonority' fulfils some of the expectations set up earlier. Closures of the variations are examined with respect to five parameters, namely melody, rhythm, register, texture, and dynamics. Theoretical writings of 18th _ century theorists (Kirnberger, Koch, and Reicha) and modem theorists (Schenker, Hopkins, Narmour, Oster, Sheer) are investigated to uncover the factors affecting the degree of closure in each parameter. The set of 50 Variations by 50 Viennese composers based on the same theme is used as a comparison to Beethoven's set. Comparison of the two sets finds more weak closures in Beethoven's set, with a large proportion of weak closures occurring in the second half of the set. A kind of 'system' is at work in Beethoven's set, whereby closures are weakened in the latter part of the set to create a more fluid structure. Such planning is absent in the 50 Variations, where the distribution of weak closures is more or less random. There are also more linked variations in Beethoven's set, and where obvious links are absent, subtle links are present through the connections of particular tones or the use of register and dynamics to link one variation to the next. Such subtleties are absent in the 50 Variations. Where existing sketches show alternative endings to the variations, these are used as comparisons to the final versions. The study of sketches often reveals alterations to the final bars of the variations. This shows that Beethoven was very conscious of the way one variation leads into the next, and he put considerable effort in writing these final bars. The fact that these changes occur at a relatively late phase of composition further proves that the closure of the variations is intimately linked to the structure of the work, which is why it was only at this late phase of composition, when the entire structure of the set was in sight, that Beethoven made these alterations. The five parameters of melody, rhythm, register, texture and dynamics are then considered together to see how they interact and a method of measuring the closural strength of each variation is suggested. The structure of the Diabelli Variations is re-evaluated by considering the closural strength of the individual variations. A three-division structure with closural points at Var. 10 and Var. 20 is proposed. Comparison of seven recordings by different artists finds the proposed grouping agrees with what performers have instinctively felt.