Thanks for the very helpful collection of chime tunes on your website.
I'm a longtime church organist who can probably help clarify your question about the Oxford/Magdalen/Parsifal chime tunes. I came across your website in the course of studying a concert piece called "Carillon of Westminster," whose composer based it on the familiar chime tune that Westminster borrowed from Cambridge University to go with Big Ben. You're probably familiar with this concert piece yourself, since you're a clock guy and your wife is an organist! (composer Louis Vierne, 1927)
Anyway, your "Oxford" tune weblink indeed represents the Magdalen melody. The graphic to which you link indeed represents the Parsifal melody, which Wagner's opera borrowed from a German abbey. Magdalen and Parsifal are entirely separate tunes you'll find recordings and graphics for both of them as Exhibits in a very detailed online article by Daniel Harrison, who was the carillonneur and music department chairman at University of Rochester.
The tune displayed in your graphic "Oxford-ParsifalChimes" was originally published in 2000 as Exhibit 1 in Prof. Harrison's article above.
I suspect that "Oxford chimes" isn't the official name for *any* clock tune. In fact, some people use "Oxford chimes" as the name of a musical instrument!
Magdalen College is one of several institutions located in Oxford, so this may be how the confusion arose. Merton College is another Oxford school with its own chime tune. In your webpages, it's probably safest to avoid calling anything "Oxford,"and just always use "Magdalen" and "Parsifal" explicitly.
Thanks again for your terrific website -- hope this info helps a bit.
New York City