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.