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Page 43
IX
THE SYSTEMS OF HUCBALD AND GUIDO D'AREZZO--THE BEGINNING
OF COUNTERPOINT
We have seen that by order of Charlemagne, Ambrosian chant was
superseded by that of Gregory, and from any history of music
we may learn how he caused the Gregorian chant to be taught
to the exclusion of all other music. Although Notker, in the
monastery of St. Gall, in Switzerland, and others developed the
Gregorian chant, until the time of Hucbald this music remained
mere wandering melody, without harmonic support of any kind.
Hucbald (840-930) was a monk of the monastery of St. Armand in
Flanders. As we know from our studies in notation, he was the
first to improve the notation by introducing a system of lines
and spaces, of which, however, the spaces only were utilized
for indicating the notes, viz.:
[Illustration]
His attempt to reconstruct the musical scale was afterwards
overshadowed by the system invented by Guido d'Arezzo, and it
is therefore unnecessary to describe it in detail. His great
contribution to progress was the discovery that more than one
sound could be played or sung simultaneously, thus creating a
composite sound, the effect which we call a chord. However,
in deciding which sounds should be allowed to be played or
sung together, he was influenced partly by the mysticism of
his age, and partly by a blind adherence to the remnants of
musical theory which had been handed down from the Greeks. As
Franco of Cologne, later (1200), in systematizing rhythm into
measure, was influenced by the idea of the Trinity in making
his [3/8] or [9/8] time _tempus perfectum_, and adopting for
its symbol the Pythagorean circle [O.] or [O], so Hucbald,
in choosing his series of concords or sounds that harmonize
well together, took the first three notes of the overtones of
every sonorous fundamental, or, to express it differently, of
the series of natural harmonics, that is to say, he admitted
the octave and fifth: [F: g, d g]. But from the fifth to the
octave gives the interval of the fourth, therefore he permitted
this combination also.
From the works of Boethius (_circa_ 400) and others, he had
derived and accepted the Pythagorean division of the scale,
making thirds and sixths dissonant intervals; and so his perfect
chord (from which our later triad gets its name of _perfect_)
was composed of a root, fifth or fourth, and octave.
Hucbald, as I have already explained, changed the Greek tone
system somewhat by arranging it in four regular disjunct
tetrachords, namely:
[F: (g, a, b-, c) (d e f g) G: (a b c' d') (e' f+' g' a')]
This system permitted the addition of a fifth to each note
indiscriminately, and the fifths would always be _perfect_; but
in regard to the octaves it was faulty, for obvious reasons. As
his system of notation consisted of merely writing T for tone
and S for semitone between the lines of his staff, it was only
necessary to change the order of these letters for the octave
at the beginning of each line. With the fourth, however,
this device was impossible, and therefore he laid down the
rule that when the voices proceeded in fourths, and a discord
(or augmented fourth) was unavoidable, the lower voice was to
remain on the same note until it could jump to another fourth
forming a perfect interval:
[F: {g b} {g b} {g a} {g b} {d a} {d g} {c f} {c e} {a, d} {g, c}]
This at least brought into the harmony an occasional third,
which gradually became a recognized factor in music.
We probably know that the year 1000 was generally accepted
as the time when the world was to come to an end. In the
_Biblioth�que Nationale_ in Paris there is a manuscript
containing the prophecy which had been handed down for many
centuries; also the signs for the notes to which it was to be
sung, viz.:
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