The first attempts were toward the perfecting of a system of measuring music in time, and the outcome was the Perfect System, a thoroughly arbitrary and unnatural scheme of triple values. That the natural division of a musical note is into two halves scarcely needs an explanation. We therefore divide our whole notes into half notes, the halves into quarters, the quarters into eighths, and so forth. But the mensuralists divided the whole note into three parts or two unequal parts, and each of these into three more. The standard note was the _longa_. It was theoretically held to contain in itself the triple value of the perfect measure. Hence it was called the _longa perfecta_. The first subdivision of the _longa_ in the perfect system was into three _breves_ and of the _breve_ into three _semi-breves_. But in those cases in which the _longa_ was divided into two unequal parts one of these parts was still called a _longa_. This _longa_, however, was considered imperfect, and its imperfection was made up by a _breve_. So, too, the perfect _breve_ could be divided into an imperfect and a _semi-breve_. Let us now consider the signs by which these values were expressed. The sign for the _longa_, or long, as we shall henceforth call it, was a modification of one of the old neumes called a _virga_, written thus [music sign]; that for the _brevis_ or breve came from the _punctum_, written thus [music sign]. The new signs were long [music sign] and breve [music sign]. The _semi-breve_ was a lozenge-shaped alteration of the breve, [music sign]. This seems simple enough until we come across the distressful circumstances that the same sign represented both the perfect and imperfect long, and that the perfect and imperfect breve, too, shared the same figure. The following table illustrates the early mensural notes and their equivalents in modern notation. [Illustration: Music]