nomenclature, and in both cases the need gave rise to the
result as we have it to-day.

Out of the chaos of conflicting statements regarding the development of
music notation, the student may glean an outline-knowledge of three
fairly distinct periods or stages, each of these stages being intimately
bound up with the development of _music_ itself in that period. These
three stages are:

(1) The Greek system, which used the letters of the alphabet
for representing fixed pitches.

(2) The period of the neumae.

(3) The period of staff notation.

Of the Greek system little is known beyond the fact that the letters of
the alphabet were used to represent pitches. This method was probably
accurate enough, but it was cumbersome, and did not afford any means of
writing "measured music" nor did it give the eye any opportunity of
grasping the general outline of the melody in its progression upward and
downward, as staff notation does. The Greek system seems to have been
abandoned at some time preceding the fifth century. At any rate it was
about this time that certain _accent marks_ began to be written above
the text of the Latin hymns of the church, these marks serving to
indicate in a general way the progress of the melody. E.g., an upward
stroke of the pen indicated a rise of the melody, a downward stroke a
fall, etc. In the course of two or three centuries these marks were
added to and modified quite considerably, and the system of notation
which thus grew up was called "neume notation," the word _neume_
(sometimes spelled _neuma_, or _pneuma_) being of Greek origin and
meaning a _nod_ or _sign_.

This system of neumes was in some ways a retrogression from the Greek
letter system, for the neumes indicated neither definite pitches nor
definite tone-lengths. But it had this advantage over the Greek system,
that the position of the signs on the page indicated graphically to the
eye the general direction of the melody, as well as giving at least a
hint concerning the relative highness or lowness of each individual tone
(the so-called _diastematic system_), and this was a great aid to the
eye in singing, just as the relative highness and lowness of notes on
the modern staff is of great value in reading music at the present time.
Thus although the neumae did not enable one to sing a new melody at
sight as our modern staff notation does, yet they served very well to
recall to the eye the general outline of