In our age of utilitarian inspiration the imperfections of such a system of notation in which the two most frequent signs had a twofold significance would be remedied by the invention of other signs; but the theorists of that day found it easier and more natural to supplement the system with numbers of rules whereby the exact values of the notes could be determined. For example, a long followed by another long was perfect; a long followed by a breve was imperfect and to be valued as two beats. But a long followed by two _breves_ was perfect, for the two _breves_ in themselves made up a second perfect three, since one was considered as _recta_ and the other as _altera_. A long followed by three _breves_ was obviously perfect, since the three _breves_ could not but make up a perfect measure. Similar rules governed the valuation of the _breve_. Three _breves_ between two longs were not to be altered, four _breves_ between two longs also remained unaltered, since one of them counted to make up the imperfection of the preceding long. But five _breves_ required alteration, the first three counting as one perfect measure, the last two attaining perfection by the alteration of the second of them. _Semi-breves_ were also subject to the laws of perfection and alteration and were governed by much the same laws as governed the _breves_. One who had mastered all these laws was able to read music with more or less certainty, though it must have been necessary for him to look ahead constantly, in order to estimate the value of the note actually before him.