The Lover's Wheel of Oswald Wirth, and four alternatives

In a previous post (qv) I have mentioned Oswald Wirth's schema in which the 22 Major Arcana of the Tarot are arranged at regular intervals around the circumference of a wheel, and each card is considered to have a special relationship with those horizontally and vertically opposite it on the wheel.

Since the oppositions being considered are rectilinear rather than diametric, which cards are opposite which depends entirely on which card is placed at 12 o'clock. Wirth puts the 6th trump, called the Lover, in that position, so I have found it convenient to dub his schema the Lover's Wheel. When the 6th trump is at 12 o'clock, the 17th (the Star) is at 6 o'clock. Obviously, rotating everything 180 degrees, so that the Star was at 12 o'clock, would yield the same set of oppositions, so putting the (n + 11)th trump at 12 o'clock is equivalent to putting the nth trump there. That means there are 11 distinct ways of arranging the trumps around the wheel, of which Wirth's Lover's Wheel is just one possibility.

In practice, though, most of those possible arrangements are too arbitrary to be worth considering. We might naturally expect the first (or perhaps the last) trump to be located at 12 o'clock (or at 6 o'clock, which is functionally equivalent). Nine o'clock (or 3 o'clock) would also be a natural place to put the first or last trump -- but because 22 is not divisible by 4, a wheel that has a trump at 12 o'clock will not have one at exactly 9 o'clock; instead, one is at (to make our clock-face terminology a bit more precise than is customary) 8:27, and another is at 9:33. All in all, I think there are three tolerably natural arrangements:

1. first trump at 12 o'clock
2. last trump at 12 o'clock
3. first and last trumps at 9:33 and 8:27

Of course, any of these three arrangements can be rotated 90, 180, or 270 degrees, or mirrored, without affecting the card-to-card relationships.

Things are further complicated by uncertainty as to which trump should count as the first. Because the Fool is traditionally unnumbered (often numbered 0 in modern decks, generally treated by Wirth as if numbered 22), it can be considered either the first trump (in which case the World is the last) or the last trump (in which case the Magician is first).

Taking all this into consideration, the bottom line is that there are only five plausible candidates for the 12 o'clock position: the Lover (Wirth's choice), the Fool (my own hunch after seeing Wirth's version), the Magician, the Pope (seen in a "coʀʀecᴛed veʀsioɴ" of Wirth modified by an unknown hand), and the World. (Again, I am only saying "12 o'clock" for the sake of simplicity; 3, 6, or 9 o'clock would be functionally equivalent.)

The way to evaluate the relative merits of these five schemata is to look at the card-to-card relationships each creates and decide which seem the most meaningful. That means looking at 105 different links (21 for each wheel, with no overlap). My original plan was to discuss all 105 of these in this post, but it was starting to turn into one of those dissertation-length mega-posts that I'm not supposed to be writing anymore, so I'll stop this post here and discuss the individual wheels in detail in future posts.