To the lowest note of this scale, which was foreign to the Greek system, he gave a special name, _gamma_, after the Greek letter G. From this we get our word for the scale, the gamut. The other notes remained the same as before, only that for the lowest octave capital letters were used; in the next octave, the notes were designated by small letters, and in the last octave by double letters, aa, bb, etc., as in the following example. [F: g, g G: a g' | a' g'' ] [W: Capitals. : Small letters | Double or very small letters] PRESENT SCALE. [F: c,, | c, | c G: c' | c'' | c''' | c''''] [W: C_ | C | c : c' | c'' | c''' | c''''] [W: Contra | Great | Small : 1st | 2nd | 3rd | 4th ] Following out his system, he applied the newly acquired syllables to each of the hexachords--for instance, the lowest hexachord, G A B C D E, which was called hard, became _ut re mi fa sol la_; the second, which was called natural, C D E F G A, also became _ut re mi fa sol la_; and the third, which was called soft, F G A B[flat] C D, became likewise _ut re mi fa sol la_. The next three hexachords were treated in the same manner; the last or seventh hexachord was merely a repetition of the first and the fourth. 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.