podatus signifying a rising motion, or the clivis representing a descending
motion, could indicate an interval as small as a minor second or as large as a fourth or
fifth. The notation did not, moreover, permit the relationship between the last pitch of one
neume and the first note of the succeeding neume to be determined.
Some notations incorporated nuances indicating longer rhythmic values and specially
shaped “liquescent” neumes, reserved for combinations of consonants (gn, lm) or vowels
(au, ui) that require special care in pronunciation. In addition, expressive nuances could
be signified either by letters above the notation or by special neume symbols (quilisma,
oriscus). Their exact manner of interpretation is subject to speculation, particularly since
most of these special signs disappeared in many regions at an early date.
Certain regional notations began to dispose the notes on the page in a manner that
reflected the relative size of the intervals separating them. The next step in the
development of this “diastematic” notation saw the line that served as the point of
reference become etched more deeply into the parchment. A pitch value, usually F or C,
was assigned to it and indicated at the beginning of each line of music.
The better to distinguish the two lines, the lower (F) was drawn in red and the upper
(C) in yellow or green. Aquitanian manuscripts employ cleffing other than C or F, and
sometimes only a B-flat sign under a line is employed. One of the French regional
notations, Norman, developed into “square” notation. Placed on a four-line staff drawn in
either black or red, it became the standard chant notation of the Roman Catholic church
and has continued in use for printed chant books up to the present time. The same
notation was adapted for the earliest polyphonic music.
During this period originated the distinction between the new rhythmic polyphony,
cantus mensuratus, and plainchant (cantus planus), sung in relatively equal note values.
Chant was sometimes sung in proportional duration values and notated with symbols
derived from the mensural polyphonic notation of the 13th century.
One of the important contributions of Frankish monastic musicians was the
development of a music theory that sought to classify the new music that had replaced
Gallican chant. This process took some time, and it was not until the middle of the 9th
century that the first chant treatise, the Musica disciplina of Aurelian of Réôme, was
written. Frankish music theory combined Byzantine concepts (a system of eight modes)
and ancient Greek theory in an original synthesis. The result could hardly claim to be
more than an approximate explanation of a repertoire created without reference to an
explicit theoretical foundation.
At the beginning of the 11th century, there developed the concept of the hexachord, an
ascending pitch set from C to A that could be duplicated on G and F (in the latter case
with B-flat). By means of “mutation,” one could move from one hexachord to another
and remain within a familiar configuration of steps and half-steps. Guido d’Arezzo (ca.
990–1050) assigned syllables (ut, re, mi, fa, sol, la) to each of the steps of the hexachord
as an aid to learning new or unknown chants.
It had long been realized that although chants customarily cadenced on one of four
finals (D, E, F, G) some chants moved almost exclusively in the tonal space above the
final, and others descended frequently beneath it and used fewer notes above the final.
The tonal space was delimited by eight modal scales, four of which were “authentic,”
corresponding to the first category, and the remaining four were “plagal,” corresponding
to the second. In the fully elaborated system, each scale was composed of a species of
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