CHAPTER VI

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:

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.

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:

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.

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:

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.

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.