as they were called
(which were simply a series of notes forming a little melody
sung to two or three words), the voice was rarely called upon
to progress more than the interval of a sixth, and so this
solmization, as the new system was called, was very valuable;
for one had only to give the pitch, and _ut_ always meant the
keynote, _re_ the second, _mi_ the third, etc., etc. In time
_ut_ was found to be a difficult syllable to sing, and _do_
was substituted. This change, however, was made after the scale
was divided into a system of octaves instead of hexachords. The
improvement in singing soon made the limits of the hexachords
too small to be practical; therefore another syllable was added
to the hexachordal system, _si_, and with this seventh note
we have our modern scale. From this we see that the scale in
present use is composed of octaves, just as the older scales
were composed of hexachords, and before that tetrachords. Just
as in mediaeval times each hexachord commenced with _ut_,
so now every octave of our tonal system commences with _do_.

Before leaving the hexachordal system, it may be as well to
explain the mode of procedure when the voice had to go beyond
the interval of the sixth. We know that the first of every set
of six notes was called _ut_, the second, _re_, the third,
_mi_, etc. When the voice had to go beyond _la_, the sixth
note, to B[natural], that sixth note was always called _re_,
and was considered the second note of a new hexachord. If,
on the other hand, the voice had to go beyond _a_, to B[flat],
the fifth note was called _re_, since the syllables _mi fa_
must always come on the half-tone.

In a study of our system of writing music, it may be as well to
begin with the derivation of our sharps and flats. Observing
the third hexachord on our list we see that in order to make
it identical in structure with the first and second, the B had
to be lowered a semitone. Now the third hexachord was called
soft. The B[flat] in it was accordingly called a soft B or
B _molle_, which is still the name in France for a flat, and
_moll_ in German still means minor, or "soft" or "lowered." For
the fourth hexachord, which was called hard, this B was again
raised a semitone. But the flatted B was already indicated
by the letter _b_ or round _b_, as it was called; hence this
B natural was given a _square_ shape and called B _carre_,
[illustration]. The present French word for natural (when it
is specially