Tanging actually was a method of claiming ownership of the swarm while it was in flight.

From “The Feminine Monarchie: or The Historie of Bees" Butler (1623), in Chapter 5, "tinging" (not tanging,  but close enuf) the swarm is discussed.
Rewording into more modern English, and summarizing:

"If you see [a bee swarm] fly aloft, cast dust among them to [try in vain] to [get] them down. If they cannot be stayed (they won't!), the ancient laws of Christendom (Actually *Roman* Law for the nitpickers) permits you to pursue [the swarm], to recover your own [property].  Sometimes [the bees] will [fly] away, and [fly] too far, [and then] you must leave them to the lucky finder [and "finders keepers" then applies]. When you have lost sight and hearing of them, you have lost all right [to them] and property [interest] in them."

So, if you can keep up, the swarm is still yours.  Lace up those sneakers!

Willam Harrod-Hempsall in the 2-volume "Bee-Keeping, New and Old", (1937) credited John Keys with detailed instructions for tanging, but pointed out the obvious - “the only valid reason for tanging is as a means of **claiming** the swarm.”

The tanging was simply a way to announce to a general public, many who had bees of their own, that you were in pursuit of YOUR swarm, and that you were asserting ownership, just as one would pursue a cow that had gotten out of the pasture, and was wandering across the countryside.  Bees were wisely classified as inherently wild creatures under Roman Law, so unlike a cow, if a swarm appeared on my tree, I was allowed to hive it and call it "my property", as long as no one was actively chasing it, banging away on an old pot.

It would have also been an excellent way of advertising that one was not a poacher or thief when crossing the property of strangers.  Yet again, once identified as a beekeeper, one is immediately classified as "harmless".

I once tried a pair of hand-held 12-inch diameter cymbals (borrowed from a neighbor who was in the school marching band) on a high-branch swarm, to no effect at all.  So, I used a child's toy bow and arrow to shoot a string over the branch (success after multiple attempts), and pulled up a pair of long ropes attached to each end of a cable saw.  Pull back and forth on the ropes, and the branch was soon cut, and down came the swarm onto a tarp for easy installation into a cardboard nuc box.  In general, the combination of height, stinging insects, and chainsaws does not seem safe, as adrenaline, bee venom, 2-stroke gas, and testosterone are a mix that can only end in tears and worse yet, a posthumous humorous YouTube video.

And yet again, we see another dangerous intersection of beekeeping and kitchen utensils.  I am lucky enough to be married to a kindred spirit who keeps her own hives, but you are not so lucky, so do NOT grab a pan and a large serving spoon from the kitchen to go chase a swarm.  Never, ever use anything from the kitchen in beekeeping, but if you succumb to temptation and make the error of doing so, DON'T PUT IT BACK - buy a new one for the kitchen, and keep the one you took as "beekeeping equipment", as it is now covered with propolis, beeswax, honey whatever, and you won't ever get it clean enough, and you will be in very big trouble with She Who Must Be Obeyed.  There, I just saved your marriage.

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