[Smt-talk] rationalizing the octenary system

David Clampitt david.clampitt51 at gmail.com
Fri Apr 17 16:04:43 PDT 2009

Hello Eytan, hello Nicholas,

 Yes, Hucbald is clear that there are alternative finals for each tone,
alternatively *lichanos hypaton* [D] or *mese *[a], *hypate meson *[E] or *
paramese* [hard-b], *parhypate meson* [F] or *trite diezeugmenon* [c],
and *lichanos
meson* [G] to *paranete diezeugmenon* [d].

Then, in the passage I cited earlier, Hucbald insists that the lower notes
are suitable for placing the beginnings, not endings, of chants:

Hucbald’s text (p. 202 of Chartier’s edition):

Cum inferioribus quoque quartis et in quibusdam quintis, parem quodamodo
obtinent [hae quattuor finales] habitudinem, quamuis non fini sed initiis
deputentur: usque ad has enim metam inchoandi declinant. Hae sunt.
Proslambanomenos: ad lichanos hypaton…

What follows is what I cited earlier: A is associated with D, B with E
(rarely), C with F, D with G.

The crucial phrase is qamuis non fini sed initiis depetuentur: these [lower
notes] should be assigned not to the end but to beginnings.

So, I think that literally B (the lower element) cannot be a finalis, but
the higher hard-b, can so serve. I agree with Nicolas that our 21st-century
notions blind us to some of these distinctions, above all octave

Nicolas, I see your latest post has arrived before I have finished this one.
I will say that yes, the four maneriae suffice to include the higher notes
in the system, a and c, and hard-b, via socialitas, so in medieval terms
there was no need for six, agreed. As to the meaning of the Hermannus
Contractus phrase, I’ll have to digest your article. I notice you discuss
Crocker, which is where I derive my understanding of that treatise, and that
may be outmoded, so to speak. But, since Eytan asked about post-Hucbald
developments, I note that you begin with this from Guido (which I don’t take
exception to): “Puisqu’il n’y a que sept notes, car les autres, comme nous
l’avons dit, sont les mêmes, il suffit d’en expliquer sept, qui diffère par
le mode et par le qualité.” Your article goes deeply into issues of mode and
quality. But already there is more recognition of seven note names of a
diatonic system (Guido also quotes Vergil: septem discrimina vocum). This
would seem to be getting closer to Eytan’s query.


David Clampitt

School of Music

The Ohio State University
*<david.clampitt51 at gmail.com>*

2009/4/17 Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr>

>  Dear Eytan,
> I really do believe that your interpretation is not in line with what
> Hucbald means. You understand that a melody may end a fifth above its own
> final or, in other words, that the final is not necessarily the last note of
> the melody but rather some abstract reference note. Such a view rests, in my
> opinion, on presuppositions about modality/tonality, or about the link
> between the melodies and the underlying diatonic system, that cannot fit the
> situation in the late 9th century.
> My own view is largely inspired by a paper by R. Weakland, "Hucbald as
> Musician and Theorist", *MQ* 42/1 (1956), to which you might refer.
>     Hucbald's readers were familiar with the chant repertory, but they had
> no idea of the diatonic system, nor of ways of comparing the melodies
> between themselves from an intervallic point of view; they did not even have
> note names, nor any clear notion of the modal final. Hucbald's purpose,
> therefore, cannot have been to discuss which degrees of the system could
> serve as finals, as none of these notions was available. What he tried to
> show is that, if the melodies were considered in terms of their inner
> intervals (to the description of which he devotes a lot of space), it is
> possible to align them all along one single general scale (the diatonic
> system) – the alignment, as we today can realize, really is a matter of
> adjusting the pitches to a single standard; but they had no notion of that.
>     Hucbald further says that if the alignment is done correctly, one
> discovers that all the melodies in the repertory can be adjusted so as to
> have their final note on D, E, F or G. Why he chooses that particular
> tetrachord is unclear, but may result from the fact that the modes already
> were numbered and that these finals fitted their numerical order. He
> immediately adds that the same melodies could also be adjusted to end on
> other degrees of the underlying system: so doing, he is trying to describe
> aspects of the structure of the diatonic scale, but he is not discussing
> differences in the structure of the melodies. When he states that *many* (
> *plera*) melodies may end a fifth above D E F G, he does not mean that
> these cannot end on D E F G, but well that they can *also* end on A B C D.
>     The reason to think so is that this remains a constant doctrine for
> centuries after Hucbald. The theory of the *affinitas* (or *socialitas*)
> is a theory of the structure of the diatonic scale, which states that notes
> a fifth (or a fourth) apart are surrounded by the same intervals. Guido's
> hexachordal theory is a theory of the extent to which *affinitas* is true.
> In solmization terminology, the four modal finals are *re*, *mi*, *fa* and
> *sol*. Until late in the middle ages, some theorists state that the
> melodies of the protus end on *re* – that is, any *re*, be it D, G or A –,
> those of the deuterus on (any) *mi*, of the tritus on *fa*, of the
> tetrardus on *sol*.
>     I wrote a paper on Jacques of Liège and the practice of partial
> transposition (*Revue belge de musicologie*, 1995), in which I discuss
> Jacques's statement that, in some churches of Liège, when the melody
> lingered too long in the high, singers mistakenly end it a fifth too high:
> it is not that they end on the "fifth above the final" in the way you seem
> to imply, but rather that they end, say, on the wrong *re*, on A*re*instead of Dre – not realizing, in other words, that they had shifted their
> pitch standard.
> The number of melodies notated with A or C as final was higher in the
> middle ages than today: it is because the 19th-century normalization of the
> chant reduced all these melodies to their theoretical final whenever
> possible. The very fact that this was possible shows that the question of
> the *affinals *in many cases merely is a matter of notational convenience,
> not of a structural difference in the melodies. Note also that changing from
> the regular finals to the *affinals* a fifth above merely involves
> replacing the F-clef by the C-clef on the same line.
> A and C were not rejected as possible finals, they merely were not deemed
> necessary in Hucbald's highly pedagogical description because modes on D and
> F respectively could be written with a B flat. As a matter of fact, melodies
> ending on F almost always have a B flat, so that strictly speaking it are
> the modes on F that do not exist, not those on C. It would theoretically
> have been possible to write melodies on E with B flat (corresponding to
> modes on B), but these merely do not exist. As to melodies on G with B flat,
> they can as easily be written on D without.
> Glarean cannot be considered the "inventor" of the modes on A or C: they
> existed from the start. What he did is normalize the notation, considering
> that modes written with a B flat were transpositions. This, by the way,
> happened not so long after another, more important invention, that of pitch
> standards (Arnolt Schlick, 1511).
> Yours,
> Nicolas
> Eytan Agmon a écrit :
>  Nicolas,
> Thanks for your thoughtful message. I look forward to reading your paper
> (hopefully my French is up to it!). In the meantime, here is a comment and a
> question.
> Hucbald most certainly does *not* say A, B, and C *can* serve as finals.
> Even though a melody may end on the upper fifth, there is a clear
> distinction between the upper fifth and the final. On the other hand,
> Hucbald refers to “the four finals” D, E, F, and G so many times, that the
> exclusion of A, B, and C (for whatever reason), can hardly be missed.
> In terms of your “emic” theory, why does Hucbald choose D-G as finals,
> rather than (say) E to a? The lower fourth that he supposedly needs will
> exist, and he will even be using a true tetrachord of the Greater Perfect
> System, rather than an arbitrary one.
> Glarean, by the way, rejects a B-mode, due to the diminished fifth above
> the final.
> Yours,
> Eytan
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