Thus we have the following values and their corresponding rests: 

Maxima [Illustration] Longa [Illustration] Brevis [Illustration] Semibrevis [Illustration] Minima [Illustration] Semiminima or crocheta [Illustration] Fusa or crocheta [Illustration] Semifusa [Illustration]

The rests for the fusa and semifusa were turned to the left in order to avoid the confusion that would ensue if the rest [illustration] stood for [fusa].  Besides, the sign would have easily become confused with the C clef [illustration].

Signs for the changes of tempo, that is to say changes from quick to slow, etc., were introduced in the fifteenth century.  The oldest of them consists of drawing a line through the tempus sign [O|].  This meant that the notes were to be played or sung twice as rapidly as would usually be the case, without, however, affecting the relative value of the notes to one another.  Now we remember that the sign [C] stood for our modern [4/4] time; when a line was drawn through it, [C|] it indicated that two brevi were counted as one, and the movement was said to be alla breve.  This is the one instance of time signatures that has come down to us unaltered.

IX

THE SYSTEMS OF HUCBALD AND GUIDO D’AREZZO—­THE BEGINNING OF COUNTERPOINT

We have seen that by order of Charlemagne, Ambrosian chant was superseded by that of Gregory, and from any history of music we may learn how he caused the Gregorian chant to be taught to the exclusion of all other music.  Although Notker, in the monastery of St. Gall, in Switzerland, and others developed the Gregorian chant, until the time of Hucbald this music remained mere wandering melody, without harmonic support of any kind.

Hucbald (840-930) was a monk of the monastery of St. Armand in Flanders.  As we know from our studies in notation, he was the first to improve the notation by introducing a system of lines and spaces, of which, however, the spaces only were utilized for indicating the notes, viz.: 

    [Illustration]

His attempt to reconstruct the musical scale was afterwards overshadowed by the system invented by Guido d’Arezzo, and it is therefore unnecessary to describe it in detail.  His great contribution to progress was the discovery that more than one sound could be played or sung simultaneously, thus creating a composite sound, the effect which we call a chord.  However, in deciding which sounds should be allowed to be played or sung together, he was influenced partly by the mysticism of his age, and partly by a blind adherence to the remnants of musical theory which had been handed down from the Greeks.  As Franco of Cologne, later