Variations on the "Transverse Exchange"

I've been playing with a particular class of string figures a lot lately. However, I've not been able to find any existing published nomenclature for many of the maneuvers that I've been playing with, so I wanted to describe them here and see if anyone else knows what they may be called. (This is not to say that I've invented the maneuvers! Far from it. It is only that the maneuvers have no specific name, as far as I am aware.) For now, I'm calling this class of figure a "transverse exchange".

The reason for the name is that the figures all begin with an exchange of the transverse string on 1n with the transverse string on 5f. There are many ways this exchange can happen; thus the name is a general term that describes a family of similar maneuvers.

For example, the Navaho "Many Stars" figure begins with a transverse exchange, after Opening A:

1. 1 moves over 2 loop and picks up 5n.
2. 3 picks up 1f. Release 1.
3. 1 moves through 2 loop from above, under 3 and 5 loops, and returns with 5f. Release 5.
4. 5 removes 3 loop from above.
5. ...then perform the rest of Many Stars!

If you analyze the movements and the final string configuration, you'll see that the result of the above steps is to move the near transverse thumb string to the far side of the little finger, and to move the far transverse little finger string to the near side of the thumb. It's a transverse exchange.

Another form of the transverse exchange occurs in the Tikopian maneuver called "Tao-sokotosi, Ta-sokotosi" (which means "hold one, manipulate one"). Beginning with any configuration where 1, 2, and 5 have a loop on them (e.g. Opening A):

1. 1 moves over 2n and holds it down to the palm.
2. 2 and 3 move under 2f, pinch 1n, and by rotating 2 away and up, place 1n on 2, releasing 1.
3. 1 moves through lower 2 loop from above, under 5 loop, and returns with 5f. Release 5.
4. 5 removes upper 2 loop from above.

A third published form of the transverse exchange is in the Nauruan "Eongatubabo". (This has been described in some places as the Banaban ending, I believe, though I could be wrong about that!) Again, assuming an initial configuration like Opening A:

1. 1 moves over 2n and holds it down to the palm.
2. 2 enters the 5 loop from above, hooks back 5n and 2f, and hooks up 1n (releasing 5n and 2f).
3. 1 moves though the 2 loop from below, picks up 5f and returns.
4. Release 5.
5. 5 removes upper 2 loop from above.

In all three of these examples, the final result is to have the former TV 1n at 5f, and the former TV 5f at 1n. In fact, there are a great number of ways to do a transverse exchange, but they all consist of 4 distinct phases, and each of those phases have some very distinctive characteristics.

Structure of the Transverse Exchange

In "Phase A", there are loops on (at least) 1 and 5, and 1n and 5f are both transverse. There must also exist 1f and 5n (so First Position alone is not sufficient). Note that there is no requirement that loops exist on any other fingers, although it is most common to see a transverse exchange from an "opening A" configuration.

In "Phase B", the 1 loop is held "in storage", so to speak, making room for the 5 loop to come to roost on 1 during Phase C. Generally speaking, Phase B involves using the thumb to pull some string (or strings) toward you, exposing 1f. Then, either 2 or 3 (or, conceivably, 4, though I've not seen it done anywhere) pick up that exposed 1f, and the thumb is released from all loops. In some cases, though (as in Eongatubabo, or "Tao-sokotosi, Ta-sokotosi"), the 1 loop is removed via 1n, instead of 1f. Regardless, though, the original 1 loop is kept "aside", on finger 2 or 3 (or 4), until Phase D where it will eventually land on 5.

In "Phase C", the 5 loop rotated a half turn and transferred to the now-empty 1 finger. This is done by weaving the thumb through the existing loops and returning it with 5f, releasing 5 in the process. The final result of this phase is to have the former transverse 5f string on the thumb, as 1n.

Lastly, in "Phase D" we complete the exchange. The former 1 loop, held in "storage" on 2, 3, or 4, is given a half turn rotation and transferred to 5, such that the transverse string becomes 5f.

"Transverse Exchange" Variations

Note, though, that in none of these phases is there a strict guide for how the strings need to be moved. The transverse exchange is not a description of a specific maneuver! This means there is a great deal of possibility for exploration with this class of figure.

For example, in phase A, you can start with Opening A, Nauru Opening 1, 2 or 3, or any other opening that gives you transverse 1n and 5f strings. Given the requirements of TV 1n and 5f, and the existence of 1f and 5n, the simplest configuration that you can apply a transverse exchange to would be the "X Open" (opening A, release 1, and transfer 2 to 1), but there is no "upper bound" on the complexity of your opening.

For phase B, there are even more possibilities. Consider just a few of the ways in which you might expose 1f to the 2, 3 or 4 finger:

• 1 picks up 2n
• 1 moves over (or under) 2n and returns with 2f
• 1 moves over (or under) 2 and returns with 5n
• 1 moves over (or under) 2, over (or under) 5n, and returns with 5f
• 1 moves under 2 and returns with both 2f and 2n
• 1 moves under (or over) 2 and under 5 returns with both 5f and 5n
• 1 moves through 2 from above (or below) and returns with 5n
• 1 moves through 2 from above (or below), over (or under) 5n, and returns with 5f
• 1 moves through 2 from above (or below), under 5, and returns with both 5f and 5n
• etc, etc, etc.

Using an opening configuration in which there are loops on more fingers (like Nauru Opening 1 or 2) gives you even more possibilities.

Then, consider phase C. The thumb is typically moved through the (lower) 2 loop from above, and returns with the 5f string, but there is no reason it must be that way. The Navaho "Two Coyotes" figure, for instance, moves the thumb through the lower 2 loop from below. You might try returning with 5f by moving entirely over all the strings, or entirely under. Or you might try some more complex weaving of the thumb, especially if there are loops on more of the fingers.

Lastly, even phase D offers opportunities for variation. There's no reason the little finger needs to directly remove the "storage" loop. Try moving that loop to 5 by bringing it entirely around the near side of the figure, or by weaving it through other loops (if there are any available). For example, if the storage loop is the upper 2 loop, you might try inserting 5 from below into the lower 2 loop and hooking down the upper 2f, pulling it through the lower loop and removing it from 2. Then, rotate 5 down and away from you to bring the loop to rest on 5, with a transverse 5f string. As long you end up with a transverse 5f, it's all fair!

And, interestingly, note that the final configuration is exactly what is needed for the transverse exchange in the first place; this means you can chain transverse exchanges together, one onto another, for even more variation!

Next?

In the end, though, a transverse exchange is only really interesting insofar as it is results in an interesting presentation. I'll cover possible ways to present a transverse exchange figure in my next post.

In the meantime, experiment! See what kinds of interesting exchanges you can find. I'm not exaggerating when I say that this family of figures has kept me occupied for many, many hours. There is a lot of room for variation.