So far the complexities of the mensural system of notation are not too difficult to follow with comparative ease. But the longs, the _breves_ and the _semi-breves_ were employed only in the notation of syllabic music; that is, of music in which each note corresponds to a syllable of the text. In those cases where one syllable was extended through several notes, another form of notation was employed. The several notes so sung were bound together in one complex sign called a ligature. The ligatures, like the longs and the breves, were adaptations of old neumatic signs. In the old plain-song the flourishes or melismas on single syllables were sung in a free rhythm; but the mensuralists were determined to reduce every phrase of music to exact rhythmical proportions, and these easy, graceful, soaring ornaments were crushed with the rest in the iron grip of their system. Hence the ligatures were interpreted according to the strictest rules. A few examples will serve to show the extraordinary complexity of the system. Among the old neumatic signs which stood for a series of notes two were of especially frequent occurrence. These were the _podatus_, [music sign], and the _clivis_, [music sign]. Of these the first represented an ascending series, the second--which seems to have developed from the circumflex accent--a descending series. It will be noticed that the clivis begins with an upward stroke to the first note, which is represented by the heavy part of the line at the top of the curve. The _podatus_ has no such stroke. Several other signs were derived from these two, and those derived from the _clivis_ began always with this upward stroke, and those from the _podatus_ were without it. Thus all ascending ornaments were represented by a neume which had no preliminary stroke, all descending ornaments by one with the preliminary stroke. This characteristic peculiarity was maintained by the mensuralists in their ligatures. The _podatus_ became [music sign], the _clivis_ [music sign]. In so far as the mensural system of notation was graphic, in that the position of the notes in the scale presented accurately the direction of the changing pitch of the sounds they stood for, there was no need of preserving in the ligatures such peculiarities of the neumatic signs. But, on the other hand, these peculiarities were needed to represent the mensural value of the notes in the ligatures, the more so because the mensuralists were determined to allow no freedom in the rendering of those ornaments in ligature, but rather to reduce each one to an exact numerical value. Hence we find two kinds of ligatures: those which preserved the traits inherited from their neumatic ancestors, and those in which such marks were lacking. The first were very properly called _cum proprietate_, the others _sine proprietate_; and the rule was that in every ligature _cum proprietate_ the first note was a _breve_, while in every ligature _sine proprietate_ it was a long.