Equalism
In De musica, Aribo clearly associates a 2:1 ratio with the tenor and also with the significative
letters found in the ancient rhythmic notation of Gregorian chant.
Aribo Scholasticus, De musica (up to 1078)
Latin: Scriptores ecclesiastici de musica sacra potissimum, ed. Martin Gerbert, Vol 2, p215
English: A Reply to Father Smits van Waesberghe, S.J. by Dom Gregory Murray
in Caecilia, vol 88, no.1, Spring 1961
The earliest surviving chant manuscripts to show musical notes written on lines date from the
period of Aribo. By the time he was writing, it appears that (at the very least) the composition
of new chants no longer made such a feature of long and short notes. These seem to have
been replaced by a single durational length, with the apparent exception of Guido's
proportional 'tenor'. The survival of non-rhythmic notations of chant from certain areas of
Europe may indicate that, in those areas, this was the case even for singing existing chant.
The speed of organum singing in the ninth-century Musica et scolica enchiriadis is described
as being slow.
Musica enchiriadis
Latin: Patrologia cursus completus, series latina, ed. J. P. Migne, vol 132, p974
Scolica enchiriadis
Latin: Patrologia cursus completus, series latina, ed. J. P. Migne, vol 132, p999
A remark by Hucbald (c.840/50-930) in his De organo has been interpreted by some as
pointing towards the use of a slow speed of organum being a factor in the loss of a
rhythmical contrast between longs and shorts. If all one-note syllables of chant originally had
a long duration which contrasted with syllables containing two notes of short duration, and if
such chant was slowed down so much that the short notes became long notes, then all the
ordinary one note syllables would become even longer, perhaps undesirably so. This might
then have led to the now very long notes being shortened to the length of the other, shorter
notes. Hucbald appears not to advocate any equalist approach.
De organo, Hucbald
Latin: Scriptorum de musica medii aevi nova series a Gerbertina altera,
ed. Edmond de Coussemaker, vol 2, p75
The longs and the shorts were certainly still being notated in the area of Nonantola in Italy
until the 12th century. The triple-time rhythmic modes were developed then and spread for a
time throughout Europe. The beat of ecclesiastic song was thereby cut into three short
notes rather than two as previously.
A tenor is the length of a note which is in
equal proportion if two notes are made
equal to four and their length [ie, 4] is in
inverse proportion to their number [ie, 2].
So it is that in the old antiphonaries we very
often find the letters "c", "t", "m", indicating
respectively "celeritas" (quick), "tarditas"
(slow), and "mediocritas" (moderate). In
olden times great care was observed not
only by the composers of the chant but also
by the singers themselves to compose and
sing proportionally. But this idea has
already been dead for a long time, even
buried.
Thus in fact, by two or many singing as one
in a moderately paced, properly measured
and concordant slowness which is
particular/proper to this song, you will see a
sweet harmony being born out of this
mixture of sounds.
Nonetheless, it is brought forth in a
moderately paced slowness, which is very
much its own, and, having been attended to
with concordant diligence, there will be most
honourable sweetness of chanting.
We correctly put dots and dashes for the
distinguishing of short and long notes
although, as it is said, it is proper that a
melody so grave of this sort be so slow that
a rhythmic ratio is hardly able to be
preserved in it. May there in any case be
such a distribution.
Tenor dicitur mora vocis, qui in aequis
est, si quatuor vocibus duae
comparantur, et quantum sit numerus
duarum minor, tantum earum mora sit
maior. Unde in antiquioribus
antiphonariis utrisque c. t. m. reperimus
persaepe, quae celeritatem, tarditatem,
mediocritatem innuunt. Antiquitus fuit
magna circumspectio non solum cantus
inventoribus, sed etiam ipsis cantoribus,
ut quilibet proportionaliter et invenirent
et canerent. Quae consideratio iam
dudum obiit, imo sepulta est.
Sic enim duobus aut pluribus in unum
canendo modesta duntaxat et concordi
morositate, quod suum est hujus meli,
videbis nasci suavem ex hac sonorum
commistione concentum.
Verumtamen modesta morositate edita,
quod suum est maxime proprium, et
concordi diligentia procurata,
honestissima erit cantionis suavitas.
Sane punctos ac virgulas ad
distinctionem ponimus sonorum brevium
ac longarum, quamvis hujus generis
melos tam grave, ut dictum est, esse
oporteat, tamque morosum, ut rhitmica
ratio vix in eo servari queat. Sit utique
descriptio talis.