The system seems to us clumsy and inadequate. We cannot but ask ourselves why Guido did not choose the natural limit of the octave for his groups instead of the sixth. However, it was a great improvement over the yet clumsier system of the tetrachords, and was of great service to musicians down to comparatively recent times. One may find no end of examples of its use in the works of the great polyphonic writers. As a help to students in learning it, the system of the Guidonian Hand was invented, whereby the various tones and syllables of the hexachords were assigned to the joints of the hand and could be counted off on the hand much as children are taught in kindergarten to count on their fingers. That Guido himself invented this elementary system is doubtful, though his name has become associated with it. [Illustration: THE GUIDONIAN HAND.] Guido must also be credited with valuable improvements in the art of notation. In his day two systems were in use. One employed the letters of the alphabet, capitals for the lowest octave, small letters for the next and double letters for the highest. This was exact, though difficult and clumsy. The other employed neumes (see Chap. V) superimposed over the words (of the text to be sung) at distances varying according to the pitch of the sound. This, though essentially graphic, was inaccurate. Composers were already accustomed to draw _two_ lines over the text, each of which stood for a definite pitch, one for F, colored red, and one for C, a fifth above, colored yellow, but the pitch of notes between or below or above these lines was, of course, still only indefinitely indicated by the distance of the neumes from them. Guido therefore added another line between these two, representing A, and one above representing E, both colored black. Thus the four-line staff was perfected. It has remained the orthodox staff for plain-song down to the present day. This improvement of notation, in addition to the hexachordal system and the invention of solmisation, have all had a lasting influence upon music, and through his close connection with them Guido of Arezzo stands out as one of the most brilliant figures in the early history of music. III