Again, we begin by searching for common bonds between the two systems we wish to link together. The obvious first choice is that the Runic futhark is divided into 3 aettir, each of which represents a separate journey from the mundane world to joy and salvation. The Tree of Life also depicts a journey between these states. Usually we see energy descending from Kether to Malkuth, but there is also a way to climb up from Malkuth to Kether; from the mundane to the divine.
In fact, since there are three pillars on the Tree, there are three distinct ways to go from Malkuth to Kether. Three ways, three aettir; each of the three aettir must be assigned to a pillar on the Tree. The first aett belongs to Freyja, the second to Heimdall, and the third to Tyr. Based on the natures of these three gods it makes sense to place Freyja's aett on the leftmost pillar, Heimdall on the right pillar, and Tyr up the middle.
Unfortunately, the paths on the Tree are not evenly distributed. The middle sephirah, Tiphareth, has a disproportionately high number of paths emerging from it. If the system is going to work, all three of the aettir are going to have to pass through Tiphareth, and this seems to disrupt the "one aett per pillar" idea. The number of Runes, 24, also indicates that some Runes will have to share a path. Perhaps a true correspondence is not possible?
Once more a common bond comes to the rescue. What do the three aettir have in common? Despite the fact that they all start out differently, they finish in similar ways. Wunjo, Sowilo and Dagaz are all Runes of joy and enlightenment, often of a spiritual nature. One could easily see the three as different perspectives of the same thing. Therefore all three of these Runes must be assigned to the same path. That will leave 21 Runes and 21 paths: a one-to-one correspondence.
Which path are Wunjo, Sowilo and Dagaz assigned to? It is obvious if you look at the structure of the Tree, and the aettir. Each aett's eighth rune is a rune of salvation. But the seventh rune is nothing like that at all. Gebo is a rune of gifts, Algiz is for protection and Othila is for property; all very mundane concepts. So the final path must be a path from the mundane world (below the Abyss) to the spiritual (above the Abyss). There is just such a path running right up the middle of the Tree - from Tiphareth to Kether.
Once this fact is discovered, the final arrangement of the Runes is easy to determine. Freyja's aett (yellow on the diagram) follows the left pillar of the Tree up to Binah, then it falls back down to Tiphareth and loops around Hod and Netzach, before returning to Tiphareth and proceeding to Kether. Heimdall's aett (red) follows a nearly identical path up the right side, though it encircles Geburah and Chesed before reaching Kether. Tyr's aett (blue) fills in the remaining paths. This gives two distinct groupings to fit with that aett's two parts.
If you attempt to correspond this attribution to most of the existing
Tarot attributions, particularly the Golden Dawn system, you will find
that most of it does not make sense. There will be some interesting
correspondences, but nothing that would not be achieved by chance.
Are the attributions of the Runes incorrect? Maybe, but it is equally
likely that the Runes are positioned correctly while the Tarot cards
are not. We must re-examine the system of Tarot correspondences to
see if it can be united with the Runes.