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<big>Dear all,<br>
<br>
David Clampitt wrote :</big>
<blockquote
cite="mid:287dcdd50904170854h6258b785v83db17aa2fdf6f51@mail.gmail.com"
type="cite">
<pre wrap=""><big>But in the conception I set forth, which follows the
later Hermannus's rule: "Take any tetrachord you wish, add a tone at
both ends, you then have the limits of the tonal patterns which form
the basis for the modes [sedes troporum]." Ellinwood's translation.
</big></pre>
</blockquote>
<big>This I take to be a mistaken translation, as explained in the
paper of which I gave the reference
(<a class="moz-txt-link-freetext" href="http://www.plm.paris-sorbonne.fr/Modi_vocum.pdf">http://www.plm.paris-sorbonne.fr/Modi_vocum.pdf</a>). What Hermannus says
is "Take any tetrachord you wish, add a tone at both ends, then you
have the limits of the note qualities (<i>modi</i>) that form the seats
of the tropes" (<i>Accipe tetrachordum quodcumque volueris</i> [...]<i>,
addito utrinque tono, habes terminos modorum qui fiunt sedes troporum</i>).
Hermannus says <i>tropus </i>for what we call "mode" today; and what
he calls <i>modus</i> (Guido's <i>modus uocum</i>, "modes of the
notes")<i> </i>is a quality of individual degrees of the diatonic
system.<br>
What this means is that the quality of the notes is to be measured
within a (common) pattern of a sixth (a hexachord, "Hermann's major
sixth" as Crocker describes it). The four individual notes so qualified
(the 2d, 3d, 4th and 5th notes, respectively, of the common pattern)
then serve as seats for the four pairs of modes. For instance, the
modes of the protus seat on the first notes of the tetrachords, A, D, a
and d; the unique quality of these notes is that they all have a tone
below, a tone, a semitone and two tones above – i.e. that they are all
the second note in the hexachord, the first note in the tetrachord.<br>
My arguments for this are given at length in my paper. Very
shortly: adding a tone at both ends of the tetrachord produces a single
major sixth of the type TTSTT, which cannot form the "basis" for four
or eight different modes. The hexachord merely forms the common basis
on which to judge the four different seats of the modes (these seats
being the four notes of the tetrachord).<br>
</big>
<blockquote
cite="mid:287dcdd50904170854h6258b785v83db17aa2fdf6f51@mail.gmail.com"
type="cite">
<pre wrap=""><big>So, I mostly agree with your statement: "then we have a modal
hierarchy where modes on D-G are a subset of modes on C-A. Modes on
C-A are conceptually prior, in exactly the same way that the final is
conceptually prior to its neighbors." It is clear that B cannot be
principalis, in Hucbald's terms, because it can't form the authentic
form.
</big></pre>
</blockquote>
<big>Even although the <u>quality</u> of the four finals is to be
measured in the overall interval of a major sixth, there is no need to
extend the <u>number</u> of finals to six, because the C in one
hexachord is the same thing as the F in the other, and the A in the one
is the same as the D in the other. (There are only two diatonic
hexachords, C–A and G–E.)<br>
One may question the logic of this and present it otherwise today,
saying that there should be a set of six (pairs of) modes, instead of
four (as Glarean said). I am perfectly prepared to follow this
reasoning, which makes full sense today. I maintain however that it
does not represent Hermannus's view (nor that of Hucbald or Guido
before him), for whom the two degrees added at the ends of the
tetrachord to form the hexachord are redundant. <br>
Allow me to add this: I believe that my paper refered to above
proposes a novel reading of these doctrines; it is hard to swim against
the tide in such matters, especially against such respected scholars as
Ellingwood, Crocker, Pesce, Powers and so many others. Please do read
the paper carefully. I am prepared to hear objections – and to provide
any additional explanation, in English, if necessary...<br>
<br>
Yours,<br>
<br>
Nicolas Meeùs<br>
<br>
</big>
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