Chapter 48

THE DIDACTIC OF MUSIC FROM THE FIFTH CENTURY TO THE FOURTEENTH.

I.

There is very little in the Roman writers upon music that is of interest. Macrobus, an expert grammarian and encyclopedist living at Rome at the end of the fourth or beginning of the fifth century, wrote a commentary upon the song of Scipio, in which he quotes from Pythagoras concerning the music of the spheres: "What hear I? What is it which fills my ears with sounds so sweet and powerful? It is the harmony which, formed of unequal intervals, but according to just proportion, results from the impulse and movements of the spheres themselves, and of which the sharp sound tempered by the grave sound produces continually varied concerts." (Cicero, "_De Republica_," VI.) Commenting upon this passage, Macrobus says that Pythagoras was the first of the Greeks who divined that the planets and the sidereal universe must have harmonic properties such as Scipio spoke of, on account of their regular movements and proportions to each other. We find in the writings of Macrobus an advance upon the musical theories of Ptolemy. He shows that contrary to the doctrine of Aristoxenus there is not a true half tone, and that the relation 8:9 does not admit of being equally divided. In place of the three symphonies of the octave, fourth and fifth, mentioned by his predecessors, he makes five, including the octave and the double octave. "Such," he says, "is the number of symphonies that we ought to be astonished that the human ear can comprehend them."

Another of the Roman writers upon music was Martinus Capella. His work is called the "Nuptials of Philologus and Mercury" ("_De Nuptiis Philologiæ et Mercurii_"). The little upon music which the book contains was only an abridgment of the Greek treatise of Aristides Quintilianus.

The most important of the earliest treatises upon music, and by far the most famous, is that of Boethius, as it is also the most systematic. The following summary is from Fétis' "History of Music," Vol. IV:

"Born at Rome between 470 and 475, Boethius made at home classical studies, and went, they say, to Athens itself, where he studied philosophy with Proclus. He was of the age of about thirty-five when, in 510, he was made president of the senate. Theodoric, king of the Ostrogoths, called him to himself, on account of his reputation for wisdom and virtue; he confided to him an important position in the palace, and intrusted to him many important diplomatic negotiations. Boethius did nothing which was not to his credit, but this made him only the more hostile to the interests of the courtiers; he was therefore overthrown and cast into prison, where he composed his 'Consolations of Philosophy.' He was put to death 524 or 526."

Boethius' treatise on music is divided into five books. It is a vast repertory of the knowledge of the ancients relative to this art. Its doctrine is Pythagorean. The first book is divided into thirty-four chapters. In the first he develops the thought of Aristotle, that music is inherent in human nature. He there renders the text of a decree which the Ephori of Sparta rendered against Timotheus of Miletus, but which better critics have regarded as fictitious. The second chapter establishes that there are three sorts of music: the worldly, which is universal harmony; the human, which has its source in the intelligence, which reunites and co-ordinates the elements; finally, the third kind is artificial, made by instruments of different sorts. The chapters following treat of the voice as the source of music; of consonances and their proportions; of the division of the voice and its compass; of the perception of sounds by the ear; of the correspondence of the semitones; of the division of the octave; of tetrachords; of the three genera--enharmonic, chromatic and diatonic; of intervals of sounds compared to those of the stars; of the musical and different faculties.

All the second book, divided into thirty chapters, is speculative, and devotes itself to the different kinds and relations of intervals, according to the different systems of theoreticians. The third book, in seven chapters, is a continuation of the subject of the second. It is particularly employed in refuting the errors of Aristoxenus. The fourth book, in eighteen chapters, is entirely relative to the practice of the art, particularly to the notation. It is in this book that Boethius makes known the Latin notation of the first fifteen letters of the alphabet without preparation, without the slightest explanation, and as if he had done something which any one concerned with music at Rome would readily understand, as a matter of course. There is not one word to show that it was new, or that he claimed the invention. It was undoubtedly the usual notation.

The fifth book of this treatise has for its object the determination of intervals by the divisions of a monochord, and a refutation of the systems of Ptolemy and Archytas. We here find this proposition, remarkable if we recall the time when the author lived, that: "If the ear did not count the vibrations, and did not seize the inequalities of movement of two sounds resonating by percussion, the intelligence would not be able to render account of them by the science of numbers." After Boethius there is nothing in Roman literature concerning music. Notwithstanding that Italy fell under the dominion of the Goths and Lombards after 476, it preserved Greek traditions in music to the end of the sixth century.

Cassiodorus, who lived still in 562, aged almost 100 years, left a souvenir for music in the fifth chapter of his treatise on the "Discipline of Letters and Liberal Arts" (_De Artibus ac Disciplinis Litterarum_). He enumerates the fifteen modes of Alypius as not having been abandoned, and establishes them in their natural order, calling them tones. Here also we find the classification of six kinds of symphonies, about 300 years after this enumeration, first realized in notes by Hucbald. He gives a series of fourths and of fifths, occasionally for two voices, occasionally with the octave added. These are the most important of all the things concerning music to be found in that part of Cassiodorus' book dedicated to music.

In the seventh century the first, or perhaps the only author who wrote upon music was Bishop Isidore, of Seville. In his celebrated treatise on the etymologies or origins ("_Isidori Hispaniensis Episcopi Etymologiarum, Libri XX_") divided into twenty books, chapters XIV to XXII of the third book relate to music. These are the chapters published by the Abbé Gerbert, under the name of "_Sentences de Musique_," in the collection of ecclesiastical writers upon this art, after a manuscript in the imperial library at Vienna. While many of these chapters contain nothing more than generalities and pseudo historical anecdotes concerning the inventors of this art, this is not the case with the nineteenth chapter, the sixth in Gerbert's edition, for here he speaks "Of the First Division of Music, called Harmony." The definitions given by St. Isidore have a precision, a clearness not found in other writers of the Middle Ages. "Harmonic music," says he, "is at the same time modulation of the voice, and concordance of many simultaneous sounds. Symphony is the order established between concordant sounds, low and high, produced by the voice, the breath or by percussion. Concordant sounds, the highest and the lowest, agree in such way that if one of them happens to dissonate it offends the ear. The contrary is the case in diaphony, which is the union of dissonant sounds." Here we find St. Isidore employing the term diaphony in its original sense, as a Greek word, meaning dissonance--a sense exactly opposite to that of Jean de Muris.

The Venerable Bede was the light of the eighth century, and the glory of the Anglo-Saxons. His treatise upon music, however, deals in theories and generalities, throwing no light upon the music of his day. The elevation of his ideas may be seen in the following sentence, with which he introduces his subject: "It is to be remarked that all art is contained in reason; and so it is that music consists and develops itself in relations of numbers." ("_Notandum est, quod omnis ars in ratione continetur. Musica quoque in ratione numerorum consistit atque versatur._")

Only two treatises upon music have come down to us from the ninth century. The first is by a monk, named Aurelian, in the abbey of Réomé or Montier-Saint-Jean, in the diocese of Langes, who appears to have lived about the year 850. His book, called "_Musicæ Disciplina_," in twenty chapters, is a compilation of older anecdotes and theories, throwing no light upon the actual condition of the art in his day. The sole remaining work of this period was by Rémi, of Auxerre, who had opened the course of theology and music at Rheims in 893, and afterward at Paris in the earlier years of the tenth century. His book, like the preceding, is wholly devoted to the ideas of the ancients.

II.

This brings us to the first writer on music, during the Middle Ages, whose work throws any important light upon the actual practice of the art in the period when it was written, namely, Hucbald, a monk of the convent of St. Armand, in the diocese of Tournay, in French Flanders. Gerbert gives two treatises upon music, as having come down to us from this author. Nevertheless there is reason to doubt the genuineness of one of them--whereof presently. The first of these, the so-called "Treatise," from a manuscript in the library of the Franciscan convent at Strassburg, collated with another from Cesene, bears this title: "_Incipit Liber Ubaldi Peritissimi Musici de Harmonica Institutione_." The other is called "_Hucbaldi Monachi Elonensis Musica Enchiriadis_," or "Manual of Music, by the Monk Hucbald." The former work is of little interest, and if a genuine production of Hucbald's, probably belongs, as M. Fétis suggests, to his earlier period, when he was still teaching at Rheims, along with his former classmate, Rémi, of Auxerre.

The manual of Hucbald is not to be regarded as a complete treatise upon music. It has three principal subjects, namely: The formation of a new system of notation, the tonality of plain song, and symphony, or the singing of many voices at different intervals--in other words, harmony.

In treating the scale he divides it into tetrachords, precisely according to the Greek method, as far as known to him, and he nowhere appears to perceive the inapplicability of this division to the ecclesiastical modes. For representing the sounds of the scale, divided into four tetrachords, Hucbald proposed the Greek letters, which in effect, would have been a notation of absolute pitch, with the farther disadvantage of ignoring the harmonic principles of unity already discovered, and in fact involved in his own method of enlarging a two-voice passage by adding a third at the interval of an octave with the lowest.

He recognizes six kinds of symphony; in reality he employs only three, the others being reduplications. His symphonies are those of fourths, fifths and octaves. In all parts of his work but one he uses the term diaphony as synonymous with symphony; _there_ he gives its ancient meaning of dissonance.

He proposed a sort of staff notation, upon which all the voices could be represented at once. The following illustration represents his staff and his diaphony, or harmony:

The initial letters, T and S, at the beginning of the lines in the preceding staff indicate the place of the steps (tones) and half steps (semitones).

[Music illustration: DECIPHERING OF ABOVE.

Sit glo-ri-a Do-mi-ni in sae-cu-la lae-ta-bi-tur Do-mi-nus in o-pe-ri-bus su-is.]

M. Fétis gives a two-voice parallelism in fifths, which is progressively enlarged to three voices by adding an octave to the lower voice; and then to four by doubling the original upper voice in the octave above. Thus:

[Music illustration: Tu pa-tris sem-pi-ter-nus es fi-li-us.]

In addition to mechanical progressions of parallel motion in this way, Hucbald in another place gives an account of a so-called "roving" organum, in which, while parallel progressions of fourths and fifths still are found, there are also other intervals, while the beginning and the end must be in unison. This form of the harmony of simultaneous sounds has in it much of the character of counterpoint, especially in the restriction that the voices must begin and end in unison. This roving organum, or free organum, was also known as "profane" or "secular" organum, in contradistinction to the "sacred organum" already given, upon the sweetness of which Hucbald greatly prided himself.

Fétis has well said that Hucbald must be considered as one of those superior spirits who impress upon their epoch a movement in an art or science. Besides this, he merits particular mention in the history of music because his works are the first since those of Boethius--a period of four centuries--in which the art of music is treated systematically and without obscurity.

In the "_Epistola de Harmonica Institutione ad Rathbodum Episcopum Trevinesem_" ("Letter to Rathbodum, Bishop of Treves"), there is mention of the instruments of music during the seventh and eighth centuries. They are the cithara and harp as the stringed instruments; musetts, syrinx and organ among the wind instruments; cymbals and drums, instruments of percussion. In the tenth century there was a methodical treatise upon music in dialogue form, published by Odon, abbot of Cluny, who died in this monastery November 18, 942. This work, which was wrongfully attributed to Guido of Arezzo, contains a number of analyses of intervals showing an understanding of the exact dimensions of the various kinds of fourths, fifths, thirds and sixths. According to his doctrine, the intervals of the fourths, fifths and octaves are more natural for the voice than the others called thirds and sixths, because the former are invariable, while the latter may be larger or smaller by a half step. He makes a summary of ecclesiastical chant, mentioning the modes as established by St. Gregory, illustrating each of them by a selection from the "Plain Song." It is a fact significant of the unsettled condition of musical theory and the complete unconsciousness of musical amateurs that any essential change in the art was being undergone, that as late as 1000 or 1020 Adelbold, Bishop of Utrecht, published a treatise upon music in which the proportions of the tetrachords are calculated carefully according to the Greek theories, and demonstrated upon the monochord.

III.

The most important writer upon music in the eleventh century, and one of the most famous in the history of the art, was a monk named Guido, living at Arezzo, in Tuscany, a Benedictine in the abbey of Pontose. He was a remarkably skillful teacher of ecclesiastical singing, both in his own monastery and at Rome, and in the effort to systematize the elements of music he introduced a number of important reforms, and is credited by later writers with many others which he did not himself originate, but which grew out of some of his suggestions. He is generally credited with having invented the art of solmization, the introduction of the staff, the use of the hand for teaching intervals, and the introduction of notes. He was not the first who introduced the staff. Hucbald, as we have already seen, employed the spaces between the lines for designating pitch. Between his time and that of Guido, one or more lines were introduced in connection with the neumæ, as will be more particularly illustrated in chapter XV. Guido, however, employed both the lines and the spaces, but instead of notes he wrote the Roman letters upon the lines and spaces according to their pitch. The notes were invented shortly after his time. For determining the correct pitch of the notes of the scale he explains the manner of demonstrating them upon the monochord. He mentions organum and diaphony, and remarks that he finds the succession of fifths and fourths very tiresome. The last treatise of the thirteenth century was written by John Cotton, an English monk, whose entire theory of music is made up from the Greek works.

This summary of the didactic writers between Boethius and Franco at Cologne fully confirms the justice of the remark, in the chapter previous, concerning the influence of the Church upon music. At the very time when a well marked beginning was being made in counterpoint by the old French school at Paris, and when the English, Welsh and Scandinavian musicians were in possession of an art of expressive melody resting upon a simple harmonic foundation, these writers can find nothing to say but to repeat over and over again their tedious calculations concerning the intonations of _nete hypate_ and the other Aristoxinean notes in the enharmonic and chromatic genera, which had been dead names in the art of music for more than ten centuries.

With the appearance of Franco at Cologne, there is something new in music. Late in the twelfth century he wrote a treatise upon measured music, the first one in all the history of the art, so far as we know, in which musical measure is treated independently of verse, and a notation given for representing it. He recognizes two kinds of measure--triple or perfect, and duple or imperfect. He gives four kinds of notes--the shortest being the _brevis_, an oblong note having twice the value of a whole note; a short stem affixed to this note doubled its value. It was then called the _longa_. A note head twice as long represented a still longer duration, called the _maxima_ or longest. There was also a _semibreve_, a diamond-shaped note which was used when two or more tones were sung to one syllable. There were no bars for indicating the place of the strong pulse in the measure, but a bar was used to show the end of the musical phrase belonging to a line of verse. The notation was made still more uncertain by the license of the breve in triple time being equal to three semibreves, and so in general each long note in triple measure being equal to three of the next class shorter. In short, the time notation was of the most crude and imperfect description, but it was at least a beginning, and all the theoretical writers upon music for the next two centuries rest in the precepts of Franco of Cologne, as a sure stronghold, where no false doctrine can find admission. Franco remarks, concerning the dissonances, that the imperfect dissonances, the thirds and sixths, go very well between two consonances, showing that in his time the third and sixth were still regarded as licenses in harmony to be explained or excused. The general principle that any dissonance is admissible when smoothly placed between two consonances is a fundamental law of modern counterpoint.

There was another Franco whose work has often been confounded with that of the celebrated master at Cologne. Franco of Paris was connected with the Sorbonne or with Notre Dame, and his writing had mostly to do with harmonic music. He classifies the consonances as--complete, the unison and octave; the incomplete, the major and minor thirds; the middle, the fourth and fifth. This is the first instance in musical theory where the third has been recognized as a consonance. Among the dissonances he classes the major and minor sixth as incomplete, and says concerning these two only that immediately before a consonance any incomplete dissonance goes very well. From the superior celebrity of the Cologne Franco the work of the Parisian master was overlooked for many years, and it is only through the investigation of Coussemaker that his real standing and importance have been ascertained.