I recently (link) wrote about William E. Caplin's Cadence: A Study of Closure in Tonal Music (2024), which is in two parts, each at over 300 pages: the first concerns the familiar Viennese trio of composers, about whose music Caplin without doubt has the most detailed and most comprehensive knowledge of anyone alive; but the second part looks at cadences in the earlier 18th and later 19th centuries.
The final section of chapter 8 (of the book's 9) is a survey of all the Chopin Preludes. Of course, the one of interest here is no. 9 in E major. I repeat a paragraph from an earlier post: link.
[Quote from notes in my 1987 JMT article]: "Pieces that appear to use a rising line from ^5 but in fact do not include Chopin, Prelude in E Major, op. 28, no. 9 (three-part Ursatz with line from ^3 above ^2 implied in the cadence)." ---- I have already written about this at length: link to the first post; link to the follow-up post. The "short version": Until recently I was comfortable with the comment above, despite the work needed to imagine ^2; Carl Schachter repeated the analysis without giving me credit for precedent (and his editor Joseph Straus failed to catch it); but recently Emily Ahrens Yates revisited the piece and produced a thoroughly convincing analysis that shows the piece does have an ascending Urlinie.
Caplin doesn't dispute the ascending line in the cadence, but he interprets the cadence in a decidedly qualified way:
[Bars 9-12] see the melody again rise stepwise from ^5 in the context of a general ascending-step model-sequence technique. This time, however, the various modal inflections of the harmony yield chromatically flattened ^6 and ^7 degrees; only the final V-I leading into measure 12 resolves the leading tone to tonic in the melody. In itself, of course, this final progression qualifies as cadential, yet because it seems to emerge as the last link in a broader ascending-stepwise sequence, its cadential effect seems rather forced. Combined with the rhetorically powerful dynamic, it is as though Chopin were insisting hard that we take the final progression as cadential, even if it seems to be a part of the broader sequential process.

