a melody previously learned by
ear and therefore enabled the singer (the system was used for vocal
music only) to differentiate between that particular melody and the
dozens of others which he probably knew. Neume notation was used mostly
in connection with the "plain-song melodies" of the Church, and since
the words of these chants were sung as they would be pronounced in
reading, the deficiency of the neume system in not expressing definite
duration values was not felt. But later on with the rise of so-called
"measured music" (cf. invention of opera, development of independent
instrumental music, etc.), this lack was seen to be one of the chief
disadvantages of the system.

The elements of neume-writing as given by Riemann in his Dictionary of
Music are:

"(1) The signs for a single note: Virga (Virgula) and Punctus (Punctum).
(2) The sign for a rising interval: Pes (Podatus). (3) The sign for a
falling interval: Clinis (Flexa). (4) Some signs for special manners of
performance: Tremula (Bebung), Quilisma (shake), Plica (turn), etc. The
others were either synonyms of the above-named or combinations of
them...."

Since music in the middle ages was always copied by hand, it will
readily be understood that these neumae were not uniform either in shape
or size, and that each writer made use of certain peculiarities of
writing, which, although perfectly intelligible to himself, could not
readily be interpreted by others (cf. writing shorthand). Here then we
observe the greatest weakness of the neume system--its lack of
uniformity and its consequent inability accurately to express musical
ideas for universal interpretation.

Examples of several neumes are given merely in order to give
the beginner a general idea of their appearance.

Virga [virga symbol] or [virga symbol]. Punctus [punctus
symbol] or [punctus symbol]. Pes [pes symbol] or [pes symbol].
Clinis [clinis symbol] or [clinis symbol].

As music grew more and more complex, and especially as writing in
several parts came into use (cf. rise of organum, descant, and
counterpoint), it became increasingly difficult to express musical ideas
on the basis of the old notation, and numerous attempts were made to
invent a more accurate and usable system. Among these one of the most
interesting was that in which the words of the text were written in the
spaces between long, parallel lines, placing the initial letters of the
words _tone_ and _se