The Prelude to the third act of Parsifal is one of Wagner's most advanced essays in expanded tonality. One author has described it as "set[ting] foot in atonal territory as it re-explores the melancholy, disjointed polytonal idiom of the introduction to the third act of Tristan, " and a noted analyst has suggested that it is motion around the diminished-seventh chord including Bb rather than the tonic triad of Bb minor that defines the background structure of the Prelude. This music also raises issues of form and expressive meaning that have yet to be thoroughly addressed. A valuable means of approaching the Prelude is through Wagner's surviving compositional documents, particularly the individual sketches for the Prelude that preceded the writing-out of his first continuous draft for the third act (the Kompositionsskizze [Composition Draft]). These manuscripts are held in the Wagner-Archiv at Bayreuth. When these sketches are transcribed and compared with the detailed record contained in Cosima Wagner's diary entries, insight can be gained into the way that Wagner composed the Prelude, during late October 1878. This article shows in detail how the Prelude was composed on the basis of sketch sources that are virtually complete. It is supported by several facsimiles of Wagner's sketches, transcriptions, analytical graphs, and music examples. The study indicates that the "melancholy, disjointed polytonal" idiom of the Prelude is coordinated with a framework of associated tonalities reaching across vast stretches of musical time. These include not only the Bb-minor idiom of Titurel's burial, but also the associated tonality of Parsifal's Prophecy motive. The structural background of the Prelude to act III of Parsifal is not simply a diminished-seventh prolongation, but a tensional framework of motivic combinations and rotational cycles that effectively convey the bleak wandering and promise of deliverance that lie at the core of the drama.