untangle and disentangle

So, there I was, enjoying a nice evening of nothing while on (AmE) vacation/(BrE) holiday, when Dave Summers of Ohio tweeted me to ask:
Heard "disentangle" the other day. Is that perhaps BrE for "untangle"?
To which I replied, "No, it's AmE too". But then I wondered whether the rates of their use were different and I found that they were. VoilĂ ! A Difference of the Day for my Twitter feed (which has been very sporadically updated while I've been on holiday/vacation as it gets hard to tell where one day starts and another ends). So, I tweeted:
AmE and BrE have both 'disentangle' and 'untangle'. But disentangle:untangle ratio = 2:3 in AmE and 3:1 in BrE.  (Source = COCA and BNC at Mark Davies' Corpora site.)
And I was all ready to call it a night when Gordon Hemsley of Georgia tweeted to say:
I actually think those words mean different things to me. Disentangle implies more than one thing; untangle can be 1.
...and while I thought he was probably right, I also know that it's very often the case that the stories we tell ourselves about how the differences between synonyms are often very different from how we actually use them. So, here I am researching this little thing at 1 in the morning instead of any of the other two things I have to do before bed or the opportunity to sleep that I really should take before restarting the academic term. Sigh-di-sigh-sigh-sigh.

Dictionaries don't tell us of any dialectal differences between these words, nor do they really mark Gordon's division of labo(u)r for the two words. The dictionaries I've looked at give two meanings for disentangle (or if not two meanings, then examples of both of these meanings): (1) to free something from its entanglement with something else, (2) to bring out of a tangled state, unravel.

I've started my investigation by looking at cases where the word from occurs within five words after the base forms of the verbs (untangle, disentangle). If you're removing the tangle in one thing, you probably wouldn't have a from--we don't untangle a knot from itself, we just untangle a knot.  So the from examples can be assumed to involve removing a tangle of two things (the first sense of the word, above). An example from COCA:

He managed to disentangle himself from his kayak before it was pulled into the hole.

In both dialects, there is a strong preference for using disentangle with from. So, more than 1/3 of  disentangles are closely followed by a from, and far fewer untangles have a from after them.

disentangle ... from36% [76/210]37% [28/103]
untangle... from11% [35/319]15% [4/26]

So far AmE and BrE aren't looking very different. The next question is how they act when only one thing is involved, and a tangle is removed from it. To look at that, I've looked at all the forms of each verb (i.e. untangle, untangled, untangling, etc.) followed by a/an/the and then a singular noun.
per 100 million wordsCOCA (AmE)BNC (BrE)
disentangl* a(n)/the sg-N 820
untangl* a(n)/the sg-N2612

This is far from a thorough investigation of these two words, but what the numbers here seem to be saying is that AmE has a strong preference for untangle with singulars and that this isn't shared by BrE. This is to say that Gordon's hunch was right in terms of how these words work in AmE and that the BrE use that Dave heard probably struck him as strange because it wasn't obeying the untangle-goes-with-singulars preference. Note that these differences are about preferences and probabilities of the uses of two senses of the words, not about one word (or even one sense of a word) being 'British' or 'American'. But they're still differences.

You know, this was an awful lot like work! I've only got three more days off.* Enough of this!**

* Vacation/holiday is, of course, irrelevant, since the blog isn't part of the job that I'm taking a break from. As my hobby, the blog is, I suppose, what I should be doing on my holiday/vacation. You know, instead of getting sleep or spending time with my family. Priorities, eh?

** Except to tell you that the 'fight with' sense of tangle is originally AmE. Just because I can't stop telling you things.

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AmE = American English
BrE = British English
OED = Oxford English Dictionary (online)