Later theorists did not fail to associate the mysteries of the perfect system of triple values with the Trinity, and thus sprang up the belief that the earlier mensuralists had had the perfection of the Trinity in mind when they allotted to the perfect _longa_ its measure of three values. Yet, clumsy as the system of triple values was, it was founded upon perfectly rational principles. It was the best compromise in music between several poetic metres, some of which, like the Iambic and Trochaic, are essentially triple; others, like the Dactylic and Anapæstic, essentially double. Music, during all the years while the mensuralists were supreme, was profoundly influenced by poetic metres. All these had been reduced by means of the triple proportion to six formulas or modes, and every piece of music was theoretically in one or another of these modes. Such a definite classification of various rhythms, besides being eminently gratifying to the learned theorists, was of considerable assistance to the singer in his way through the maze of mensural notation, who, knowing the mode in which he was to sing, had but to fit the notes before him into the persistent, generally unvarying, rhythm proper to that mode. Composers were well aware of the monotony of one rhythm long continued. They therefore interrupted the beats by pauses, and occasionally shifted in the midst of a piece from one mode to another. The pauses were represented by vertical lines across the staff, and the length of the pause was determined by the length of the line--the perfect pause of three beats being represented by a line drawn up through three spaces, the imperfect pause of two beats by one crossing two spaces and the others in proportion. The end was marked by a line drawn across the entire staff.