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
Resonari fibris
Mira gestorum
Famuli tuorum
Solve polluti
Labii 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.
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: