Now in the hymns, and also in the sequences, 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 marked) is becarre; the German word for major also comes indirectly from this, for dur means “hard.”