Notes on the Voynich Manuscript - Part 16 [1992 February 4] ----------------------------------------- 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".]