THE BEGINNINGS OF POLYPHONY
The third dimension in music--'Antiphony’ and Polyphony; magadizing;
organum and diaphony, parallel, oblique--Guido d’Arezzo and his
reputed inventions; solmisation; progress of notation--Johannes Cotto
and the _Ad organum faciendum_; contrary motion and the beginning of
true polyphony--Measured music; mensural notation--_Faux-bourdon_,
_gymel_; forms of mensural composition.
In the preceding chapter we have tried to trace the perfecting of a
form of melody called plain-song. We have seen how the mass of the
Catholic Church was set to solo music. Apart from the highly expressive
quality which the music inevitably acquired because of the reality and
life of the new emotional religion, the plain-song of the mass did not
differ from the artistic music of the Greeks and the Romans, that is
to say, it brought forward no new means of effect or of expression. We
may say it was the adaptation of old and tried methods to new ends. We
can hardly suppose that the technique of composition had been advanced
by the early Christian composers beyond the point to which the Greeks
had brought it, nor that the art of music had been expanded during the
first centuries of the Christian era to greater proportions than the
Greeks had developed it. The theorists of the first nine centuries
made blunders in trying to systematize Christian song according to the
remnants of Greek theory which had been preserved; yet the Greek scales
were still in use, though misnamed by the theorists, and composers for
the church still conformed to them. But about the beginning of the
ninth century a new element appeared in music for the church which
the Greeks had left practically untouched and which was probably the
contribution of the barbarian peoples of northern and western Europe,
either the Germans or the Celts, namely, part-singing. To the single
plain-song melodies of the ritual composers added another accompanying
melody or part. The resultant progression of concords and discords
was incipient harmony, the practice of so weaving two and later three
and four melodies together was the beginning of the science or art of
polyphony.
I
Polyphony was practically foreign to the music of the Greeks. They
had observed, it is true, that a chorus of men and boys produced a
different quality of sound from that of a chorus made up of all men
or all boys, and they had analyzed the difference and found the cause
of it to be that boys’ voices were an octave higher than men’s; and
that boys and men singing together did not sing the same notes. This
effect, which they also imitated with voices and certain instruments
they called _Antiphony_, and they considered it more pleasing than
the effect of voices or instruments in the same pitch which they
called _Homophony_. The practice of making music in octaves was
called _magadizing_, from the name of a large harp-like instrument,
the magadis, upon which it was possible. But magadizing cannot be
considered the forerunner of polyphony, for, though melodies an octave
apart may be considered not strictly the same, still they pursue the
same course and are in no way independent of each other; and the effect
of a melody sung in octaves differs from the effect of one sung in
unison only in quality, not at all in kind.
The allegiance of theorists to Greek culture all through the Middle
Ages and the Renaissance has tended to conceal the actual origin
of polyphony, but as early as 1767 J. J. Rousseau wrote in his
_Dictionnaire de musique_, 'It is hard not to suspect that all our
harmony is an invention of the Goths or the Barbarians.’ And later: 'It
was reserved to the people of the North to make this great discovery
and to bequeath it as the foundation of all the rules of the art of
music.’
The kernel from which the complicated science of polyphony sprang
is simple to understand. One voice sang a melody, another voice or
an instrument, starting with it, wove a counter-melody about it,
elaborated by the flourishes and melismas which are still dear to the
people of the Orient. Some such sort of primitive improvisation seems
to have been practised by the people of northern Europe, and to have
been taken over by the church singers. The later art of _déchant sur le
livre_ or improvised descant was essentially no different and seems to
have been of very ancient origin. The early theorists naturally took
it upon themselves to regulate and systematize the popular practice,
and thereupon polyphony first comes to our notice through their works
in a very stiff and ugly form of music called _organum_, which in its
strictest form is hardly more to be considered polyphony than the
magadizing of the Greeks.
The works of many of the ninth century theorists such as Aurelian of
Réomé, and Remy of Auxerre, suggest that some form of part-singing
was practised in their day, though they leave us in confusion owing
to the ambiguity of their language. The famous scholar Scotus Erigena
(880) mentions organum, but in a passage that is difficult and obscure.
Regino, abbot of Prum in 892, is the first to define consonance and
dissonance in such a way as to leave no doubt that he considers them
from the point of view of polyphony, that is to say, as sounds that are
the result of two different notes sung simultaneously. In the works of
Hucbald of St. Amand in Flanders, quite at the end of the century, if
not well into the tenth (Hucbald died in 930 or 932, over ninety years
of age), there is at last a definite and clear description of organum.
The word organum is an adaptation of the name of the instrument on
which the art could be imitated, or, perhaps, from which it partly
originated, the organ; just as the Greeks coined a word from magadis.
Of Hucbald’s life little is known save that he was born about 840,
that he was a monk, a poet, and a musician, a disciple of St. Remy
of Auxerre and a friend of St. Odo of Cluny. Up to within recent
years several important works on music were attributed to him, of
which only one seems now to be actually his--the tract, _De Harmonica
Institutione_, of which several copies are in existence. This and
the _Musica Enchiriadis_ of his friend St. Odo are responsible for
the widespread belief that polyphony actually sprang from a hideous
progression of empty fourths and fifths. Both theorists, in their
efforts to confine the current form of extemporized descant in the
strict bounds of theory, reduced it thus: to a given melody taken
from the plain-song of the church the descanter or organizer added
another at the interval of a fifth or fourth below, which followed
the first melody or _cantus firmus_ note by note in strictly parallel
movement. The fourth seems to have been regarded as the pleasanter
of the intervals, though, as we shall see, it led composers into
difficulties, to overcome which Hucbald himself proposed a relaxation
of the stiff parallel movement between the parts. In the strict organum
or _diaphony_ the movement was thus:
[Illustration: Music]
Either or both of the parts might be doubled at the octave, in which
case the diaphony was called composite.
Just why the intervals of the fifth and fourth should have been chosen
for this parallel music, which is excruciating to our modern ears, is
not positively known. The simple obvious answer to the riddle is that
Hucbald and his contemporaries based their theories on the theories of
the Greeks, who regarded the fifth and fourth as consonances nearest
the perfect consonance of the octave and unison. But in that case
we have to ask ourselves why Hucbald and his followers regarded the
diaphony of the fourth as pleasanter than that of the fifth which they
none the less acknowledged was more nearly perfect. Dr. Hugo Riemann
has suggested a solution to this difficulty which is in substance
that organum was an attempt to assimilate elements of an ancient art
of singing practised by the Welsh and other Celtic singers. The Welsh
scale is a _pentatonic_ scale, that is, a scale of five steps in which
half steps are skipped. In terms of the keyboard, it can be represented
by a scale starting upon E-flat and proceeding to the E-flat above
or below only by way of the black keys between or by a similar
progression between any other two black keys an octave apart. In such
a scale parallel fourths are impossible, as indeed they are in the
Greek scales of eight notes upon which the church music was based; but
whereas the progression of the fourths in the Greek scales is broken
by the imperfect and very unpleasant interval of the tritone, in the
pentatonic scale it is interrupted by the pleasing major third. Such
a progression of fourths and thirds seems to spring almost naturally
from the pentatonic scales and was very likely much practised by the
ancient Welsh singers.[65] A comparison of two examples will make the
difference obvious.
[Illustration: Music]
The presence in the octatonic scale of the disagreeable tritone, marked
with a star in the example, forced even Hucbald and Odo to make some
provision for avoiding it. This consisted in limiting the movement
of the 'organizing’ voice. It was not allowed to descend below a
certain point in the scale. In those cases, therefore, in which the
_cantus firmus_ began in such a way that the organizing voice could
not accompany it at the start without sinking below its prescribed
limit the organizing voice must start with the same note as the _cantus
firmus_ and hold that note until the _cantus firmus_ had risen so that
it was possible for the organizing voice to follow it at the interval
of the fourth. In the same way the parts were forced to close at the
unison if the movement of the _cantus firmus_ did not permit the
organizing voice to follow it at the interval of a fourth without going
below its limit. The following example will make this clear:
[Illustration: Music]
In this case it will be noted that the movement of the parts is no
longer continuously parallel, but that there are passages in which
it is oblique. Indeed it is hardly conceivable that strict parallel
movement was ever adhered to in anything but theory. It is interesting
to observe how even in theory it had to give way, and how by the
presence of the tritone in the scale the theorists were practically
forced into a genuine polyphonic style. The strict style, as we have
already remarked, was hardly more polyphonic than the magadizing of
the Greeks; for, though the voice parts are actually different, still
each is closely bound to the other and has no independent movement
of its own; but in the freer style there is a difference if not an
independence of movement.
In connection with this example it is also well to note that through
the oblique movement the parts are made to sound other intervals than
the fourth or fifth or unison, which with the octave were regarded
for centuries as the only consonances. At the first star they are
singing the harsh interval of a second; immediately after they sing
a major third. By the earliest theorists these dissonances were
disregarded or accepted as necessary evils, the unavoidable results
of the restrictions under which the organizing voice was laid. But
if the free diaphony was practised at all it was to lead musicians
inevitably to a recognition of these intervals, and of the effect of
contrasting one kind with another. In the works of Hucbald and Odo and
their contemporaries, however, the ideal is theoretically the parallel
progression of the only consonances they would admit, the fourth,
fifth, and octave. Oblique movement was first of all a way to escape
the tritone, and the unnamed dissonances were haphazard. Thus we find
only the mere germ of the science of polyphony. The dry stiffness of
the music and the inadequacy of the cumbersome rules must lead one to
believe that learned men, true to their time, were doing what they
could to define a popular free practice within the limits of theory.
The sudden untraceable advent of a new free style some hundred years or
more later goes to prove that the free descant of a genuinely musical
people was never actually suppressed or discontinued by the influence
of the theorists.
II
However, before considering the new diaphony, we have still to trace
the further progress of the organum of Hucbald and Odo. The next
theorist of importance was Guido of Arezzo. To Guido have been
attributed at various times most of the important inventions and
reforms of early polyphonic music, among them descant, organum and
diaphony, the hexachordal system, the staff for notation, and even the
spinet; but the wealth of tradition which clothed him so gloriously
has, as in the case of many others, been gradually stripped from him,
till we find him disclosed as a brilliantly learned monk and a famous
teacher, author of but few of the works which possibly his teaching
inspired. He has recently been identified with a French monk of the
Benedictine monastery of St. Maur des Fosses.[66] He was born at or
near Arezzo about 990, and in due time became a Benedictine monk. He
must have had remarkable talent for music, for about 1022 Pope Benedict
VIII, hearing that he had invented a new method for teaching singing,
invited him to Rome to question him about it. He visited Rome again a
few years later on the express invitation of Pope John XIX, and this
time brought with him a copy of the _Antiphonarium_, written according
to his own method of notation. The story goes that the pope was so
impressed by the new method that he refused to allow Guido to leave the
audience chamber until he had himself learned to sing from it. After
this he tried to persuade Guido to remain in Rome, but Guido, on the
plea of ill-health, left Rome, promising to return the following year.
However, he accepted an invitation from the abbot of a monastery near
Ferrara to go there and teach singing to the monks and choir-boys; and
he stayed there several years, during which he wrote one of the most
important of his works, the _Micrologus_, dedicated to the bishop of
Arezzo. Later he became abbot of the Monastery of Santa Croce near
Arezzo, and he died there about the year 1050. During the time of his
second visit to Rome he wrote the famous letter to Michael, a monk
at Pomposa, which has led historians to believe that he was actually
the inventor of a new division of the scales into groups of six notes,
called _hexachorda_, and a new system of teaching based on this
division.
The case of Guido is typical of the period in which he lived. Very
evidently an unusually gifted teacher, as Hucbald was a hundred years
before him, his influence was strong over the communities with which
he came into contact, and spread abroad after his death, so that
many innovations which were probably the results of slow growth were
attributed to his inventiveness. The _Micrologus_ contains many rules
for the construction of organum below a _cantus firmus_, which are not
very much advanced beyond those of Hucbald and Odo. The old strict
diaphony is still held by him in respect, though the free is much
preferred. To those intervals which result from the 'free’ treatment
of the organizing voice, however, he gives names, and he is conscious
of their effect; so that, where Hucbald and Odo confined themselves to
giving rules for the movement of the organizing voice in such a way
as to avoid the harsh tritone even at the cost of other dissonances,
Guido gives rules to direct singers in the use of these dissonances
for themselves, which, as we have seen, in the earlier treatises
were considered accidental. This marks a real advance. But there is
in Guido’s works the same attempt merely to make rules, to harness
music to logical theory, that we found in Hucbald’s and Odo’s; and it
is again hard to believe that his method of organizing was in common
practice, or that it represents the style of church singing of his
day. From the accounts of the early Christians, from the elaborate
ornamentation of the plain-song in mediæval manuscripts in which it is
first found written down, and from later accounts of the 'descanters’
we are influenced to believe that music was sung in the church with
a warmth of feeling, sometimes exalted, sometimes hysterical even to
the point of stamping with the feet and gesticulating, from which the
standardized bald ornamentation of Guido is far removed. Furthermore,
the next important treatises after Guido’s, one by Johannes Cotto, and
an anonymous one called _Ad Organum Faciendum_, deal with the subject
of organum in a wholly new way and show an advance which can hardly be
explained unless we admit that a freer kind of organum was much in use
in Guido’s day than that which he describes and for which he makes his
rules.
But before proceeding with the development of the early polyphony after
the time of Guido, we have to consider two inventions in music which
have been for centuries placed to his credit. In the first place he is
supposed to have divided the scale, which, it will be remembered, had
always been considered as consisting of groups of four notes called
tetrachords placed one above the other, into overlapping groups of
six notes called hexachords. The first began on G, the second on C,
the third on F, and the others were reduplications of these at the
octave. The superiority of this system over the system of tetrachords,
inherited from the Greeks, was that in each hexachord the halftone
occupies the same position, that is, between the third and fourth
steps.[67] It is not certain whether Guido was the first so to divide
the scale, but he evidently did much to perfect the new system.
There has long been a tradition that he was the first to give those
names to the notes of the hexachord which are in use even at the
present day. Having noticed that the successive lines of a hymn to St.
John the Baptist began on successive notes of the scale, the first on
G, the second on A, the third on B, etc., up to the sixth note, namely,
E, he is supposed to have associated the first syllable of each line
with the note to which it was sung. The hymn reads as follows:
_Ut_ queant laxis
_Re_sonari fibris
_Mi_ra gestorum
_Fa_muli tuorum
_Sol_ve polluti
_La_bii reatum
Sancte Joannes.
Hence G was called _ut_; A, _re_; B, _mi_; C, _fa_; D, _sol_; and E,
_la_. These are the notes of the first hexachord, and these names
are given to the notes of every hexachord. The half-step therefore
was always _mi_-_fa_. Since the hexachords overlapped, several tones
acquired two or even three names. For instance, the second hexachord
began on C, which was also the fourth note of the first hexachord, and
in the complete system this C was C-_fa_-_ut_. The fourth hexachord
began on G an octave above the first. This G was not only the lowest
note of the fourth hexachord but the second of the third and the fourth
of the second. Therefore, its complete name was G-_sol_-_re_-_ut_. The
lowest G, which Guido is said to have added to perfect the system, was
called gamma. It was always _gamma_-_ut_, from which our word gamut.
The process of giving each note its proper series of names was called
solmisation.
The system seems to us clumsy and inadequate. We cannot but ask
ourselves why Guido did not choose the natural limit of the octave for
his groups instead of the sixth. However, it was a great improvement
over the yet clumsier system of the tetrachords, and was of great
service to musicians down to comparatively recent times. One may find
no end of examples of its use in the works of the great polyphonic
writers. As a help to students in learning it, the system of the
Guidonian Hand was invented, whereby the various tones and syllables
of the hexachords were assigned to the joints of the hand and could be
counted off on the hand much as children are taught in kindergarten to
count on their fingers. That Guido himself invented this elementary
system is doubtful, though his name has become associated with it.
[Illustration: THE GUIDONIAN HAND.]
Guido must also be credited with valuable improvements in the art
of notation. In his day two systems were in use. One employed the
letters of the alphabet, capitals for the lowest octave, small letters
for the next and double letters for the highest. This was exact,
though difficult and clumsy. The other employed neumes (see Chap. V)
superimposed over the words (of the text to be sung) at distances
varying according to the pitch of the sound. This, though essentially
graphic, was inaccurate. Composers were already accustomed to draw
_two_ lines over the text, each of which stood for a definite pitch,
one for F, colored red, and one for C, a fifth above, colored yellow,
but the pitch of notes between or below or above these lines was,
of course, still only indefinitely indicated by the distance of the
neumes from them. Guido therefore added another line between these two,
representing A, and one above representing E, both colored black. Thus
the four-line staff was perfected. It has remained the orthodox staff
for plain-song down to the present day. This improvement of notation,
in addition to the hexachordal system and the invention of solmisation,
have all had a lasting influence upon music, and through his close
connection with them Guido of Arezzo stands out as one of the most
brilliant figures in the early history of music.
III
Hardly a trace has survived of the development of music during the
fifty years after the death of Guido, about 1050. The next works which
cast light upon music were written about 1100. One is the _Musica_
of Johannes Cotto, the other the anonymous _Ad organum faciendum_
mentioned above. In both works a wholly new style of organum makes its
appearance. In the first place, the organizing voice now sings normally
above the _cantus firmus_, though the whole style is so relatively
free that the parts frequently cross each other, sometimes coming to
end with the organizing voice below. In the second place, contrary
movement in the voice parts is preferred to parallel or oblique
movement; that is, if the melody ascends, the accompanying voice, if
possible, descends, and _vice versa_. Thus the two melodies have each
an individual free movement and the science of polyphony is really
under way. Moreover, they proceed now through a series of consonances.
There are no haphazard dissonances as in the earlier free organum of
both Hucbald and Guido. The organizing voice is no longer directed only
in such a way as is easiest to avoid the hated tritone, but is planned
to sing _always_ in consonance with the _cantus firmus_. The following
example illustrates the movement of the parts in this new system:
[Illustration: Music]
Cotto is rather indifferent and, of course, dry about the whole
subject of _organum_. It occupied but a chapter in his rather long
treatise. But the 'Anonymus’ is full of enthusiasm and loud in his
praises of this method of part-singing and bold in his declaration of
its superiority over the unaccompanied plain-song. Such enthusiasm
smacks a little of the layman, and is but another indication of the
real origin of _organum_ in the improvised descant of the people,
quite out of the despotism of theory. The Anonymus gives a great many
rules for the conduct of the organizing or improvising voice. He has
divided the system into two modes, determined by the interval at which
the voices start out. For instance, rules of the first mode state
how the organizing voice must proceed when it starts in unison with
the _cantus firmus_, or at the octave. If it starts at the fourth or
fifth it is controlled by the rules of the second mode. There are
three other modes which are determined by the various progressions
of the parts in the middle of the piece. The division into modes and
the rules are of little importance, for it is obvious that only the
first few notes of a piece are definitely influenced by the position
at which the parts start and that after this influence ceases to make
itself felt the modes dissolve into each other. Thus, though the
enthusiasm of the Anonymus points to the popularity of the current
practice of organizing, whatever it may have been, his rules are but
another example of the inability of theory to cope with it. Still this
theoretical composition continued to claim the respect of teachers and
composers late into the second half of the twelfth century.
A treatise by Guy, Abbot of Chalis, about this time, is concerned with
essentially the same problems and presents no really new point of view.
He is practically the last of the theorizing organizers. Organum gave
way to a new kind of music. In the course of over two hundred years
it had run perfectly within the narrow limits to which it had been
inevitably confined, and the science of it was briefly this: to devise
over any given melody a counter-melody which accompanied it note by
note, moving, as far as possible, in contrary motion, sinking to meet
the melody when it rose, rising away from it when it fell, and, with
few exceptions, in strictest concord of octaves, fifth, fourths, and
unison. Rules had been formulated to cover practically all combinations
which could occur in the narrow scheme. The restricted, cramped art
then crumbled into dust and disappeared. Again and again this process
is repeated in the history of music. The essence of music, and, indeed,
of any art, cannot be caught by rules and theories. The stricter the
rules the more surely will music rebel and seek expression in new and
natural forms. We cannot believe that music in the Middle Ages was not
a means of expression, that it was not warm with life; and therefore we
cannot believe that this dry organum of Hucbald and Odo, of Guido of
Arezzo, of Guy of Chalis, which was still-born of scholastic theory, is
representative of the actual practice of music, either in the church
or among the people. On the other hand, these excellent old monks
were pioneers in the science of polyphonic writing. Inadequate and
confusing as their rules and theories may be, they are none the less
the first rules and theories in the field, the first attempts to give
to polyphony the dignity and regularity of Art.
Meanwhile, long before Guy of Chalis had written what may be taken as
the final word on organum, the new art which was destined to supplant
it was developing both in England and in France. Two little pieces,
one _Ut tuo propitiatus_, the other _Mira lege, miro modo_, have
survived from the first part of the twelfth century. Both are written
in a freely moving style in which the use of concords and discords
appears quite unrestricted. Moreover, the second of them is distinctly
metrical, and in lively rhythm. It is noted with neumes on a staff
and the rhythm is evident only through the words, for the neumes gave
no indication of the length or shortness of the notes which they
represented, but only their pitch. Now in both these little pieces
there are places where the organizing voice sings more than one note to
a note of the _cantus firmus_ or _vice versa_. So long as composers set
only metrical texts to music the rhythm of the verse easily determined
the rhythm in which the shorter notes were to be sung over the longer;
but the text of the mass was in unmetrical prose, and if composers,
in setting this to music in more than one part, wished one part to
sing several notes to the other’s one, they had no means of indicating
the rhythm or measure in which these notes were to be sung. Hence it
became necessary for them to invent a standard metrical measure and a
system of notation whereby it could be indicated. Their efforts in this
direction inaugurated the second period in the history of polyphonic
music, which is known as the period of measured music, and which
extends roughly from the first half of the twelfth century to the first
quarter of the fourteenth, approximately from 1150 to 1325.
IV
Our information regarding the development of the new art of measured
music comes mainly from treatises which appeared in the course of these
two centuries. Among them the most important are the two earliest,
_Discantus positio vulgaris_ and _De musica libellus_, both anonymous
and both belonging to the second half of the twelfth century; the _De
musica mensurabili positio_ of Jean de Garlandia, written about 1245;
and at last the great _Ars cantus mensurabilis_, commonly attributed to
Franco of Cologne, about whose identity there is little certainty, and
the work of Walter Odington, the English mathematician, written about
1280, _De speculatione musices_. As the earlier theorists succeeded
in compressing a certain kind of music within the strict limits of
mathematical theory, so the mensuralists finally bound up music in an
exact arbitrary system from which it was again to break free in the
so-called _Ars nova_. But the field of their efforts was much larger
than that of the organum and the results of their work consequently of
more lasting importance.
The first attempts were toward the perfecting of a system of measuring
music in time, and the outcome was the Perfect System, a thoroughly
arbitrary and unnatural scheme of triple values. That the natural
division of a musical note is into two halves scarcely needs an
explanation. We therefore divide our whole notes into half notes, the
halves into quarters, the quarters into eighths, and so forth. But the
mensuralists divided the whole note into three parts or two unequal
parts, and each of these into three more. The standard note was the
_longa_. It was theoretically held to contain in itself the triple
value of the perfect measure. Hence it was called the _longa perfecta_.
The first subdivision of the _longa_ in the perfect system was into
three _breves_ and of the _breve_ into three _semi-breves_. But in
those cases in which the _longa_ was divided into two unequal parts one
of these parts was still called a _longa_. This _longa_, however, was
considered imperfect, and its imperfection was made up by a _breve_.
So, too, the perfect _breve_ could be divided into an imperfect and a
_semi-breve_.
Let us now consider the signs by which these values were expressed. The
sign for the _longa_, or long, as we shall henceforth call it, was a
modification of one of the old neumes called a _virga_, written thus
[music sign]; that for the _brevis_ or breve came from the _punctum_,
written thus [music sign]. The new signs were long [music sign] and
breve [music sign]. The _semi-breve_ was a lozenge-shaped alteration of
the breve, [music sign]. This seems simple enough until we come across
the distressful circumstances that the same sign represented both the
perfect and imperfect long, and that the perfect and imperfect breve,
too, shared the same figure. The following table illustrates the early
mensural notes and their equivalents in modern notation.
[Illustration: Music]
In our age of utilitarian inspiration the imperfections of such a
system of notation in which the two most frequent signs had a twofold
significance would be remedied by the invention of other signs; but the
theorists of that day found it easier and more natural to supplement
the system with numbers of rules whereby the exact values of the notes
could be determined. For example, a long followed by another long was
perfect; a long followed by a breve was imperfect and to be valued as
two beats. But a long followed by two _breves_ was perfect, for the two
_breves_ in themselves made up a second perfect three, since one was
considered as _recta_ and the other as _altera_. A long followed by
three _breves_ was obviously perfect, since the three _breves_ could
not but make up a perfect measure. Similar rules governed the valuation
of the _breve_. Three _breves_ between two longs were not to be
altered, four _breves_ between two longs also remained unaltered, since
one of them counted to make up the imperfection of the preceding long.
But five _breves_ required alteration, the first three counting as one
perfect measure, the last two attaining perfection by the alteration
of the second of them. _Semi-breves_ were also subject to the laws of
perfection and alteration and were governed by much the same laws as
governed the _breves_. One who had mastered all these laws was able
to read music with more or less certainty, though it must have been
necessary for him to look ahead constantly, in order to estimate the
value of the note actually before him.
Later theorists did not fail to associate the mysteries of the perfect
system of triple values with the Trinity, and thus sprang up the belief
that the earlier mensuralists had had the perfection of the Trinity in
mind when they allotted to the perfect _longa_ its measure of three
values. Yet, clumsy as the system of triple values was, it was founded
upon perfectly rational principles. It was the best compromise in
music between several poetic metres, some of which, like the Iambic
and Trochaic, are essentially triple; others, like the Dactylic and
Anapæstic, essentially double. Music, during all the years while the
mensuralists were supreme, was profoundly influenced by poetic metres.
All these had been reduced by means of the triple proportion to six
formulas or modes, and every piece of music was theoretically in one
or another of these modes. Such a definite classification of various
rhythms, besides being eminently gratifying to the learned theorists,
was of considerable assistance to the singer in his way through the
maze of mensural notation, who, knowing the mode in which he was
to sing, had but to fit the notes before him into the persistent,
generally unvarying, rhythm proper to that mode. Composers were well
aware of the monotony of one rhythm long continued. They therefore
interrupted the beats by pauses, and occasionally shifted in the midst
of a piece from one mode to another. The pauses were represented by
vertical lines across the staff, and the length of the pause was
determined by the length of the line--the perfect pause of three
beats being represented by a line drawn up through three spaces, the
imperfect pause of two beats by one crossing two spaces and the others
in proportion. The end was marked by a line drawn across the entire
staff.
So far the complexities of the mensural system of notation are not too
difficult to follow with comparative ease. But the longs, the _breves_
and the _semi-breves_ were employed only in the notation of syllabic
music; that is, of music in which each note corresponds to a syllable
of the text. In those cases where one syllable was extended through
several notes, another form of notation was employed. The several notes
so sung were bound together in one complex sign called a ligature.
The ligatures, like the longs and the breves, were adaptations of
old neumatic signs. In the old plain-song the flourishes or melismas
on single syllables were sung in a free rhythm; but the mensuralists
were determined to reduce every phrase of music to exact rhythmical
proportions, and these easy, graceful, soaring ornaments were crushed
with the rest in the iron grip of their system. Hence the ligatures
were interpreted according to the strictest rules. A few examples
will serve to show the extraordinary complexity of the system. Among
the old neumatic signs which stood for a series of notes two were
of especially frequent occurrence. These were the _podatus_, [music
sign], and the _clivis_, [music sign]. Of these the first represented
an ascending series, the second--which seems to have developed from
the circumflex accent--a descending series. It will be noticed that
the clivis begins with an upward stroke to the first note, which is
represented by the heavy part of the line at the top of the curve.
The _podatus_ has no such stroke. Several other signs were derived
from these two, and those derived from the _clivis_ began always
with this upward stroke, and those from the _podatus_ were without
it. Thus all ascending ornaments were represented by a neume which
had no preliminary stroke, all descending ornaments by one with the
preliminary stroke. This characteristic peculiarity was maintained
by the mensuralists in their ligatures. The _podatus_ became [music
sign], the _clivis_ [music sign]. In so far as the mensural system of notation
was graphic, in that the position of the notes in the scale presented
accurately the direction of the changing pitch of the sounds they
stood for, there was no need of preserving in the ligatures such
peculiarities of the neumatic signs. But, on the other hand, these
peculiarities were needed to represent the mensural value of the notes
in the ligatures, the more so because the mensuralists were determined
to allow no freedom in the rendering of those ornaments in ligature,
but rather to reduce each one to an exact numerical value. Hence we
find two kinds of ligatures: those which preserved the traits inherited
from their neumatic ancestors, and those in which such marks were
lacking. The first were very properly called _cum proprietate_, the
others _sine proprietate_; and the rule was that in every ligature _cum
proprietate_ the first note was a _breve_, while in every ligature
_sine proprietate_ it was a long. If the ligature represented a series
of _breves_ and _semi-breves_, the preliminary stroke was upward from
the note, not to it, thus: [music sign].
Further than this we need not go in our explanation of notation
according to the mensural system. The mensuralists had their way and
reduced all music to a purely arbitrary system of triple proportion,
and their notation, though bewildering and complex, was practically
without flaw. The reaction from it will be treated in the next chapter.
Meanwhile we have to consider what forms of music developed under this
new method.
V
Regarding the relations of the voice parts, one is struck by the new
attitude toward consonance and dissonance of which they give proof. In
the old and in the free organum only four intervals were admitted as
consonant--the unison, the fourth, the fifth, and the octave. The third
and the sixth, which add so much color to our harmony, were appreciated
and considered pleasant only just before the final unison or octave.
The mensuralists admitted them as consonant, though they qualified them
as imperfect. For, true to the time in which they lived, they divided
the consonants theoretically into classes--the octave and unison
being defined as perfect, the fourth and the fifth as intermediate,
the third and later the sixth as imperfect. So far did the love of
system carry them that, feeling the need of a balancing theory of
dissonances, these were divided into three classes similarly defined
as perfect, intermediate, and imperfect. We should, indeed, be hard
put to-day to discriminate between a perfect and an imperfect discord.
Of the imperfect consonances the thirds were first to be recognized,
the minor third being preferred, as less imperfect, to the major. The
major sixth came next and the last to be consecrated was the minor
sixth, which, for some years after the major had been admitted among
the tolerably pleasant concords, was held to be intolerably dissonant.
The fact that these concords, now held to be the richest and most
satisfying in music, were then called imperfect is striking proof of
the perseverance of the old classical ideas of concord and discord
inherited from the Greeks. Again, one must suspect that theory and
practice do not walk hand in hand through the history of music in the
Middle Ages.
The admission of thirds and sixths even grudgingly among the consonant
intervals is proof that through some common or popular practice of
singing they had become familiar and pleasant to the ears of men. We
have already mentioned the possible origin of organum in the practice
of improvising counter-melodies which seems to have existed among the
Celts and Germans of Europe at a very early age. There is some reason
to believe that in this practice thirds and sixths played an important
rôle; in fact, that there were two kinds of organizing or descant,
one of which, called _gymel_, consisted wholly of thirds, the other,
called _faux-bourdon_, of thirds and sixths. These kinds of organizing,
it is true, are not mentioned by name until nearly the close of the
fourteenth century, but there is evidence that they were of ancient
origin. Whether or not these were the popular practices which brought
the agreeable nature of thirds and sixths to the attention of the
mensuralists has not yet been definitely determined. The reader is
referred to Dr. Riemann’s _Geschichte der Musiktheorie im IX-XIV
Jahrhundert_ (Leipzig, 1898), and the 'Oxford History of Music,’ Vol.
I, by H. E. Wooldridge (Part I, p. 160), for discussions on both sides
of the question. The word gymel was derived from the Latin _gemellus_,
meaning twin, and the _cantus gemellus_, or organizing in thirds, in
fact, consists of twin melodies. _Faux-bourdon_ means false burden,
or bass. The term was applied to the practice of singers who sang the
lowest part of a piece of music an octave higher than it was actually
written. If the chord C-E-G is so sung then it becomes E-G-C, and
whereas in the original chord as written the intervals are the third,
from C to E, and the fifth, from C to G, in the transposed form the
intervals are the third, from E to G, and the sixth, from E to C, of
which intervals _faux-bourdon_ consisted. The origin of this 'false
singing’ offered by Mr. Wooldridge,[68] though properly belonging in a
later period, may be summarized here.
By the first quarter of the fourteenth century the methods of descant
had become thoroughly obnoxious to the ecclesiastical authorities and
the Pope, John XXII, issued a decree in 1322 for the restriction of
descant and for the reëstablishing of plain-song. The old parallel
organum of the fifth and fourth was still allowed. Singers, chafing
under the severe restraint, added a third part between the cantus
firmus and the fifth which on the written page looked innocent enough
to escape detection, and further enriched the effect of their singing
by transposing their plain-song to the octave above, which, as we
have seen, then moved in the pleasant relation of the sixth to the
written middle part. Thus, though the written parts looked in the book
sufficiently like the old parallel organum, the effect of the singing
was totally different. However, this explanation of the origin of the
term _faux-bourdon_ leaves us still unenlightened as to how the sixth
had come to sound so agreeably to the ears of these rebellious singers.
Having perfected a system of notation, and having admitted the
intervals pleasantest to our ears among the consonances to be allowed,
having thus broadly widened their technique and the possibilities of
music, we might well expect pleasing results from the mensuralists.
But their music is, as a matter of fact, for the most part rigid and
harsh. Several new forms of composition had been invented and had been
perfected, notably by the two great organists of Notre Dame in Paris,
Leo or Leonin, and his successor, Perotin. It is customary to group
these compositions under three headings, namely, compositions in which
all parts have the same words, compositions in which not all parts
have words, and compositions in which the parts have different words.
Among the first the _cantilena_ (_chanson_), the _rondel_ and _rota_
are best understood, though the distinction between the cantilena and
the rondel is not evident. The rondel was a piece in which each voice
sang a part of the same melody in turn, all singing together; but,
whereas in the rota one voice began alone and the others entered each
after the other with the same melody at stated intervals, until all
were singing together, in the rondel all voices began together, each
singing its own melody, which was, in turn, exchanged for that of the
others. Among the compositions of the second class (in which not all
parts have words), the _conductus_ and the _organum purum_ were most in
favor. Both are but vaguely understood. The _organum purum_, evidently
the survival of the old free descant, was written for two, three, or
even four voices. The tenor sang the tones of a plain-song melody in
very long notes, while the other voices sang florid melodies above it,
merely to vocalizing syllables. The _conductus_ differed from this
mainly in that such passages of florid descant over extended syllables
of the plain-song were interspersed with passages in which the
plain-song moved naturally in metrical rhythm, and in which the descant
accompanied it note for note. In the _conductus_ composers made use of
all the devices of imitation and sequence which were at their command.
Finally, the third class of compositions named above is represented by
the Motet.
The Motet is by far the most remarkable of all forms invented by
the mensuralists. In the first place, a melody, usually some bit of
plain-song, was written down in a definite rhythmical formula. There
were several of these formulæ, called _ordines_, at the service of the
composers. The tenor part was made up of the repetition of this short
formal phrase. Over this two descanting parts were set, which might be
original with the composer, but which later were almost invariably two
songs, preferably secular songs. These two songs were simply forced
into rhythmical conformity to the tenor. They were slightly modified
so as to come into consonance with each other and with the tenor at
the beginning and end of the lines. Apart from this they were in no
way related, either to each other or to the tenor. So came about the
remarkable series of compositions in which three distinct songs, never
intended to go together, are bound fast to each other by the rules of
measured music, in which the tenor drones a nonsense syllable, while
the descant and the treble may be singing, the one the praises of the
Virgin, the other the praises of good wine in Paris. This is surely
the triumphant _non plus ultra_ of the mensuralists. Here, indeed, the
rules of measured music preside in iron sway. Not only have the old
free ornaments of the early church music been rigorously cramped to a
formula and all the kinds of metre reduced to a stiff rule of triple
perfection, but the quaint old hymns of the church have been crushed
with the gay, mad songs of Paris down hard upon a droning, inexorable
tenor which, like a fettered convict, works its slow way along. A
reaction was inevitable and it was swift to follow.
L. H.
FOOTNOTES:
[65] See Riemann, _Handbuch der Musikgeschichte_, I², p. 144 ff.
[66] See article by Dom Germain in _Revue de l’art chrétien_, 1888.
[67] Strict 'imitation’ would be extremely difficult in the
tetrachordal system. A subject given in one tetrachord could not be
imitated exactly in another, because the tetrachords varied from each
other by the position of the half-step within them. Compare, for
instance, the modern major and minor modes. The answer given in minor
to a subject announced in major is not a strict imitation. If, on the
other hand, the answer to a subject in a certain hexachord was given in
another hexachord, it would necessarily be a strict imitation, since in
all hexachords the half-step came between the third and fourth tones,
between _mi_ and _fa_.
[68] _Op. cit._, Part II.