From the works of Boethius (_circa_ 400) and others, he had derived and accepted the Pythagorean division of the scale, making thirds and sixths dissonant intervals; and so his perfect chord (from which our later triad gets its name of _perfect_) was composed of a root, fifth or fourth, and octave. Hucbald, as I have already explained, changed the Greek tone system somewhat by arranging it in four regular disjunct tetrachords, namely: [F: (g, a, b-, c) (d e f g) G: (a b c' d') (e' f+' g' a')] This system permitted the addition of a fifth to each note indiscriminately, and the fifths would always be _perfect_; but in regard to the octaves it was faulty, for obvious reasons. As his system of notation consisted of merely writing T for tone and S for semitone between the lines of his staff, it was only necessary to change the order of these letters for the octave at the beginning of each line. With the fourth, however, this device was impossible, and therefore he laid down the rule that when the voices proceeded in fourths, and a discord (or augmented fourth) was unavoidable, the lower voice was to remain on the same note until it could jump to another fourth forming a perfect interval: [F: {g b} {g b} {g a} {g b} {d a} {d g} {c f} {c e} {a, d} {g, c}] This at least brought into the harmony an occasional third, which gradually became a recognized factor in music. We probably know that the year 1000 was generally accepted as the time when the world was to come to an end. In the _Bibliotheque Nationale_ in Paris there is a manuscript containing the prophecy which had been handed down for many centuries; also the signs for the notes to which it was to be sung, viz.: [Figure 07] The text is: The Judge will speak and the earth shall tremble with awe. The stars shall be destroyed and the glory of the moon shall die, the mountains shall be crushed and the world with all in it shall utterly perish. With the opening of the eleventh century, such was the relief from this fear which had been oppressing Christendom, that even the church reflected it in such strange rites as the _Feast of Asses_ (January 14th), which was a burlesque of the Mass. In this travesty of the Mass a young girl, dressed to represent the Virgin, riding on an ass and carrying a child in her arms, was conducted to the church door. Upon being admitted and riding up the aisle to the altar, the girl tethered the ass to the railing and sat on the steps until the service was finished. The _Credo_, _Gloria_, etc., all ended with a "hee-haw," and at the conclusion of the service the officiating priest brayed three times, and was answered by the congregation. The mixing of the vernacular with Latin in this service is the first instance of the use of any language but Latin in church music.