The letters <p> and <f>, again

[Jorge Stolfi <stolfi@xxxxxxxxxxxxx>]

Hi folks,

You may recall my observation, several months ago, that there seemed
to be two variants of the EVA letters <p> and <f>, distinguished by
the presence or absence of a "hook" at the end of the horizontal arm.

The main argument for making that distinction is the "pronunciation
table" on f66r, where the two variants of <f> are listed next to each
other in the middle column, and then "exemplified" with two successive
words on the left column (and also on the right-hand text).

[Fancy versions?]

On the other hand, we all know that <p> and <f> are almost (but not
exclusively) found on paragraph-initial lines, where <k> and <t> seem to
be comparatively rare; and that the four letters tend to occur in
similar contexts (e.g. as parts of "platform gallows").

These facts, besides their shapes, strongly suggest that <p> and <f>
are basically ornate variants of <t> and <k>. But then the
hooked/straight distinction would have no parallel in <k> and <t>.

[Statistical differences]

Now, while reviewing the statistics of the "crust/mantle/core" word
paradigm, I just noticed another detail which may be relevant to that
question: namely, the EVA letter <e> essentially *never* --- with 1
exception in the whole book --- follows <p> and <f>, whereas it is
pretty common after <k> and <t>. (I believe Currier already had
noticed that.)

Here you can find a tabulation of the "mantle suffixes" --- essentially,
the <e>/<ch>/<sh>/ combinations that can follow each of the four gallows
letters:
http://www.dcc.unicamp.br/~stolfi/voynich/Notes/057/ktpf-cmp.txt 

[Platform gallows don't matter]

That table shows that the distributions of mantle suffixes after the
*platformed* gallows <ckh>, <cth>, <cph>, and <cfh> are are extremely
similar, even for the <e> suffix. 

We can explain this fact by assuming that the gallows conceptually
lies "inside" the platform, and is effectively shielded by it; hence
all four combinations are equivalent to <ch> as far as the following
letter is concerned.  So let's leave platformed gallows aside for now.

[Naked gallows are peculiar]

The suffix distributions after "naked" gallows, however, are quite
different between the "normal" and "fancy" versions. Below is a
condensed version of the table, restricted to the few significant
suffixes. (The rest, I believe, are mostly accidents created by
omission of word spaces.) The fractions, as in the big table, are
relative to total for each gallows:

     mantle suffix
     ----------------------------------------------------------
     -     e     ech   ch    sh    ee    che   she   eee   chee
     ----  ----  ----  ----  ----  ----  ----  ----  ----  ----
  t  .446  .168  .003  .112  .016  .128  .052  .012  .008  .004
  k  .443  .167  .005  .070  .010  .206  .032  .008  .017  .002  
  p  .290  ....  ....  .232  .019  ....  .269  .028  ....  .026
  f  .386  ....  ....  .234  .024  ....  .193  .017  .006  .027


[About <ee> and <ch>]

Note first the anomalously high counts for <ch> (but not <sh>) after
<p> and <f>, and the total absence of <ee> --- which is quite common
after <k> and <t>.

However, note that the combined frequencies of <ch>+<ee> after <k> and
<t> are quite close to the frequencies of <ch> only after <p> and <f>.
A possible explanantion for these numbers is that <ee> is actually
<ch> with the ligature omitted. (Or, possibly, <ch> is actually <ee>
with a ligature added to resolve ambiguities.) If that is the case,
then it seems plausible that, in those contexts where <k> and <t> are
replaced by fancier versions <f> and <p>, the scribe would also be
more careful about "crossing his <ee>s" with a ligature.

However this explanation fails to account for the <che>, <she>, and
<eee> suffixes. True, we see a relative absence of <eee> after <p> and
<f>, and an increase in the frequency of <che>; but the latter is way
too large to be explained as a "transmutation" of <eee> into <che>.
Perhaps some of the <k> and <t> mutated into <pche> and <fche>? Or is
there a more complex dance going on?

[About <e> and <ech>]

The point of this message is actually note the absence of suffixes <e>
and <ech> after <p> and <f>, contrasting with their extreme popularity
after <k> and <t>.

Given my theory that an isolated <e> is always a modifier for the
preceding letter, I think that these two columns are at least
consistent with each other: we can summarize both by saying the
letters <p> and <e> do not accept the <e> modifier (unlike <k> and
<t>).

[Hooked arm is an extra <e>?]

It remains to explain this difference between fancy gallows and regular
gallows? Well, perhaps the difference doesn't
actually exist. An intriguing possibility is that the hooked-arm
<p> and <f> are actually fancy versions of <pe> and <fe>.

Note that even though the hook comes physically before the <p>/<f>
body, it comes *after* it temporally: hence it is not unreasonable to
read <pe>/<fe>, as opposed to <ep>/<ef>. I believe that there are
plenty of examples of such "non-linear fancifications" in medieval
manuscripts.

[Hooked arms on platformed gallows]

A complication of this theory is that the hooked arms often occur on
platformed gallows. For example. On page f1r, line 13, we read

  shoy.ckhey.kodaiin.cphy.cphodaiils.cthey.she.oldain.d

The first <p> has a hooked arm, the second one is straight.

So we need readings for those combinations too. My current guess is
that hooked-<cph> should be read as <cphe>. Note that if we apply this
guess to the above example, we get an intriguing "alliteration":

  ckhey ... cphey ... cthey

If the "fancy variant" theory is true, that should be read as

  ckhey ... cthey ... cthey

For whatever it is worth.

I will try to get a larger sample of alternative "hook = <e>" 
readings.  From a few examples I have seen, however, it seems 
that the new reading is sometimes a plausible word, sometimes
not quite.  So, again, the truth may be more complicated.

Any comments?
  
All the best,

--stolfi