Some Observations on Bench Gallows (2)

Further to my last post, I wanted to add more observations about bench gallows and they way they work. I also have an embryonic hypothesis to share at the end.

Although the position and function of bench gallows within word is very similar to other gallows, the relative proportions are often very different. So while a string such as [qoke] is common, occurring nearly 1,400 times, the string [qockh] occurs 70 times, or only one twentieth. Given that [k] is about ten times more common that [ckh], then [qockh] is half as common as we might expect.

We should thus not expect that what is true for gallows is always true for bench gallows. Investigation into the differences could be insightful, and the ‘neighbourhood’ characters of bench gallows will be the theme of this post.

What Comes Before

I used to make some basic stats for the bench gallows [ckh, cth] and their gallows counterparts [k, t]. In each case different environments were put before the gallows and the counts converted into percentages for the total occurrences of these characters.

[k] [t] [ckh] [cth]
Word Start 13 17 22 53
Start [oG] 28 42 4 5
Start [qoG] 35 19 8 3
Start [yG] 7 9 1 0
Start [WG] 15 12 57 31

(In the above table, G stands for any kind of gallows, and W for a weak string.)

Some differences are obvious, others less so. We can see straight away that most words with a bench gallows either begin with that character or with a weak string. For both bench gallows about 80% of all occurrences are from these two environments, which account for just under 30% of [k, t]. However, [ckh] and [cth] themselves act differently in these two positions, which suggests something deeper is occurring.

The bench gallows are both less common after a word–initial [o] or [qo], though with enough occurrences to show that such a string is valid. There’s also a difference between [ckh] and [cth] which might be mirroring in that between [k] and [t].

Most interestingly is the almost complete lack of bench gallows after a word–initial [y]. The actual counts for both are in single figures. We might have expected somewhere between 50 and 100 for each were they as common as for [k, t].

What Comes After

Here is the same table, with percentages, for different environments occurring after the gallows.

[k] [t] [ckh] [cth]
Before [o] 9 14 11 24
Before [y] 8 8 50 39
Before [a] 30 27 4 8
Before [ch, sh] 13 20 0 0
Before [e] 38 30 27 21

Again, there are some stark differences. Firstly, as is well known, benches simply don’t come after bench gallows. The percentages are zero, and the actual counts are three each.

More interesting is the crossover between [y] to [a]. Gallows are followed by a moderate amount of [y] but plenty of [a], whereas bench gallows are followed by lots of [y] and only a moderate to low amount of [a]. The cause must be due to a lack of words ending [l, r, m, n]. Though I need to do more research on this point, it would seem that the string [iin] is very uncommon in bench gallows words.

Gallows before [o] is ambiguous with no clear pattern. It seems as though [k, ckh] and [t, cth] is a more natural split, so something else is happening and may be unrelated to the nature of bench gallows. The same may be true for gallows before [e], though splitting the figures down for [e] and [ee] shows an interesting pattern I’ll save for another post.


There is good preliminary evidence that bench gallows don’t have the same environments as plain gallows. There are several environments which are so utterly different in frequency.

The question is whether such environments are caused by bench gallows or are the cause of bench gallows. It is not easy to answer, though I think the latter is more likely.

Further investigation into the more interesting environmental differences may yield further clues concerning bench gallows. Certainly looking at weak strings before bench gallows, and the lack of [a] after them, seem the best bets.

I think there’s a potential hypothesis which could explain much of what we’re seeing, though it’s not without its flaws. It could be that a bench gallows is where a plain gallows has ‘captured’ adjacent characters in some way.

If the [h] of [ckh] were a ‘captured’ [e], that would explain 1) the lack of [ch, sh] following as [kech, kesh] are relatively rare, and 2) the lack of [a] as [eai] is also rare.

Quite why this might happen is a whole other question.


3 thoughts on “Some Observations on Bench Gallows (2)

  1. I think that this is very probably one of those places where you would need to separate out A pages from B pages before trying to draw inferences. Not only do bench gallows happen more frequently on A pages, there’s also the issue of qoke-‘s strange distribution to contend with.


    • I did the figures for A and B this evening. While there are some interesting patterns which emerge as a result, the overall impression still stands. The environments of [k, t] and [ckh, cth] are unalike in both languages. The frequencies for various characters before and after are very different.

      The key observations of there being no [ch, sh] and fewer [a] are still true, although the difference between [ka] and [ckha] is much starker in language B. It is 17 to 4 percent in A yet 36 to 4 percent in B.


  2. You might also consider the question of whether you should normalize your A results to folios that have any bench gallows at all. Doing the stats for this without misleading yourself is quite a tricky challenge. :-/


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