Notes on the Voynich Manuscript - Part 16 [1992 February 4]
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The Gallows Letters
For me, the strangest letters in the Voynich script are the eight
"gallows letters". The more I look at them, the stranger they seem.
First, let's look at the frequencies. This is in the whole Currier
transcription, including all symbols. If we exclude spaces, line
breaks, and miscellaneous, the frequencies all increase by about
1/4, but who cares?
F lp 4.9%
P qp 2.8%
B q; 0.6%
V l; 0.1%
X clpt 0.5%
Q cqpt 0.7%
W cq;t 0.1%
Y cl;t negligible
Together, the eight account for 9.7% of the text (~12% of letters only).
By contrast, O is 12.5% of text, 9 is 9.8%, and even the infamous 4 is
3.0%.
That's my first problem. Why devise contractions or combined forms
that occur so very infrequently? The cXXt forms together are less than
2% of the letter count; it makes no sense to have them. For example,
English printers badly needed a letter for "th", because that letter
pair occurs very, very often. Latin contractions, again, go for the
hot spots: -us, -an, qu-, con-, ...
Secondly, are the cXXt forms related to the XX forms? The above
frequencies support the idea - approximately, 15% of the total
occurrences for each pair are of the cXXt form, which is what one
would expect if the distribution of adjacent letters was largely
independent of WHICH gallows letter it was. That also suggests that
the letters are phonologically related, as T/D or P/B. I presume
this reasoning explains the Currier assignment.
But that doesn't explain the anomalous frequencies at the start of
lines and paragraphs. Both Currier's and Mr Guy's reasoning I think
refute the idea that cXXt is a contraction of XX followed by ?? -
that contraction would not be less likely at the beginning of a line.
So my first hypothesis, that this was a consonant cluster with the
second consonant L or R (P/PL, F/FR) is probably wrong. If it's the
other way, is this a fusion of a prior sibilant? (P/SP, F/SF). If so,
Mr Guy's tables should show one letter - the sibilant?? - that never
precedes the XX letters, because it fuses to give cXXt.
Well, it turned out to be easier to recompute, because I could then
filter the information by machine. Here's the table, in Currier, of
the letters that precede any of PFBV:
count percent expected Guy form
O: 4177 58.5% 12.5% o
sp: 823 11.5 16.6
9: 698 9.7 9.8
nl: 413 5.7 2.9
E: 394 5.5 5.2 x
C: 356 4.9 8.6 c
S: 144 2.0 6.0 ct
Z: 32 0.4 2.7 c't
A: 21 0.3 6.1 a
8: 19 0.2 7.2
2: 12 0.1 1.2 z
3: 12 0.1 0 iiiv
4: 9 0.1 3.0
I: 6 0 i
R: 4 0 3.2 2
U: 4 0
6: 1 0
D: 1 0
G: 1 0
J: 1 0 0.4
L: 1 0
Q: 1 0
W: 1 0
Well, that 'o' is amazingly frequent - I still can't imagine it as
anything but the definite article. Moreover, it distorts the statistics,
since all the other letters have to fight for the left over 41.5%. So
we should perhaps correct for this by doubling the "found" frequency
of everything else.
Just for the record, here's the table if we strip all spaces:
count percent
O: 4237 59.3%
9: 1223 17.1
E: 537 7.5
nl: 414 5.8
C: 361 5.0
S: 144 2.0
R: 39 0.5
Z: 33 0.4
8: 24 0.3
A: 23 0.3
M: 21 0.3
2: 17 0.2
3: 14 0.2
4: 13 0.1
I: 6 0
N: 6 0
J: 4 0
U: 4 0
D: 2 0
6: 1 0
G: 1 0
K: 1 0
L: 1 0
Q: 1 0
T: 1 0
W: 1 0
Notice first that is much more common than expected. This is
what we already knew - those consonants occur especially at the beginning
of a line or paragraph. Note also the change in the value for '9', which
we again know likes to be followed by a space. And if we add the stats
for 'a' and '9', we find further evidence that they are the same letter.
There's also some confirmation (at last) of my "medial-9" conjecture.
If the gallows letters do usually start words, and important ones, then
we would expect a preceding 'a' to be written as a '9' by a scribe who
was following the words as well as the sounds.
But the point of the experiment is to find the missing letter. What
letter occurs far less than expected? There are two candidates visible
in the table - 8 and R (Mr Guy's '8' and '2'). But R, again, seems very
much a final form - look at the difference if we strip spaces - and 8 is
stable at 0.2 - 0.3% found, against 7.2% expected.
Now, the crucial test: if cXXt is a fusion of 8XX, we would expect the
frequency of the cXXt forms to be close to the product of the frequencies
of the two components. Let's do the sums. There are 7143 occurrences
of XX, and 1221 of cXXt, and 6001 of 8. So, ex hypothese, there are
actually 7222 cases of 8 and 8364 of a gallows letter, for frequencies
of 10.4% and 12.0% respectively, if we ignore spaces. The combined
frequency is therefore 1.25%, for about 860 fusions.
Hence: computed: ~860; found: 1221. Low by about 30%, which is not
wholly convincing, but the method was pretty rough.
So, if cXXt is the result of fusion with a prior letter, that letter
is '8', which we have already conjectured is a sibilant. Additional
wild conjecture: that 'R' is the final form of '8'. That gives us
9908 occurrences of the sibilant, and an expected value for the cXXt
of ~1180. Wow!
Now for the down side. Scribes don't always write contractions, so
we should sometimes find "8qp" instead of "cqpt". Let's look through
the whole online MS for all occurrences of 8qp and 8lp (Currier 8P
and 8F), and see whether a similar contracted form also occurs. The
answer is desperately ambiguous.
These forms occur in hypothesised expanded form, and many times in
hypothesised contracted form:
8lp9
8lpcox
8lpc89 (twice)
8lpcc9 (twice)
8qpc9
These, however, occur once as shown, and never (!) as contractions:
8lpct9
8lpcco2
8lpct2a2
8lpc'tc9
8qpc'tcc9
8qpctav
What is going on here?
Robert
[Note: a question I did not address in 1992, but might have
occurred to the reader, is this: if indeed these cXXt forms
represent S + consonant, and if they often occur at the
beginning of a word, what known language does that suggest?
The answer, of course (major chord, sforzando, please) is Italian.
And if so, the frequencies suggest the consonant clusters are,
in descending order, "sp", "st", "sf" and a fourth that I can't
convince myself is "sth".]