, and
circumflex. Then we know from Ptolemy, Boethius, and Alypius
that letters were used to designate the different tones; but as
there is no music extant in this notation to prove the theory,
we need not trouble ourselves with it.

The system of Aristophanes, however, was destined to become the
nucleus from which our modern notation sprang. We know that
an elementary idea, clearly expressed, has more chances of
living than has a more complicated system, however ingenious
the latter may be. Now this system is so plain that we will
find it is common to many aboriginal peoples, for instance
the American Indians have a system very similar.

In the period now under consideration (from the third to the
tenth century), music was noted in this way: an upstroke of
the pen meant a raising of the voice, a downstroke lowered it,
a flat stroke meant a repetition of the same note, thus [/ \ -]
[G: c' g' c' c']. Gradually it became necessary to indicate
the contour of the melodies with more accuracy; therefore the
circumflex was added [Over-slur] [G: g' c'' g'] and reversed
[Under-slur] [G: g' e' g']. Still later a sign for two steps was
invented [Step] [G: e' g' b'] and when the progression was to
be diatonically stepwise the strokes were thicker [Thick Step]
[G: g' a' b']. So this notation developed, and by combining
the many signs together, simple non-rhythmic melodies could be
indicated with comparative clearness and simplicity. The flat
stroke for a single note [-], indicating [G: b'], eventually
became smaller and thicker, thus [Thick -]. By combining these
different signs, a skip of a third and back came to be noted
[Crenellation], and if the note came down on a second instead
of the original note it became [Podium] [G: g' b' a']. The
_quilisma_ ([Upper Mordent]) indicated a repetition of two
notes, one above the other, and we still use much the same
sign for our trill. Also the two forms of the circumflex,
[Over-slur] [Under-slur], were joined ([Turn]) and thus we
have the modern turn, so much used by Wagner.

Now while this notation was ingenious, it still left much
to be desired as to pitch. To remedy this a red line was
drawn before writing these signs or _neumes_, as they were
called. This line represented a given pitch, generally E;
above and below it were then written the signs for the notes,
their pitch being determined by the relative position they held
in regard to the _line_. Thus [Podium, Turn, Upper Morden