But before proceeding with the development of the early polyphony after the time of Guido, we have to consider two inventions in music which have been for centuries placed to his credit. In the first place he is supposed to have divided the scale, which, it will be remembered, had always been considered as consisting of groups of four notes called tetrachords placed one above the other, into overlapping groups of six notes called hexachords. The first began on G, the second on C, the third on F, and the others were reduplications of these at the octave. The superiority of this system over the system of tetrachords, inherited from the Greeks, was that in each hexachord the halftone occupies the same position, that is, between the third and fourth steps.[67] It is not certain whether Guido was the first so to divide the scale, but he evidently did much to perfect the new system. There has long been a tradition that he was the first to give those names to the notes of the hexachord which are in use even at the present day. Having noticed that the successive lines of a hymn to St. John the Baptist began on successive notes of the scale, the first on G, the second on A, the third on B, etc., up to the sixth note, namely, E, he is supposed to have associated the first syllable of each line with the note to which it was sung. The hymn reads as follows: _Ut_ queant laxis _Re_sonari fibris _Mi_ra gestorum _Fa_muli tuorum _Sol_ve polluti _La_bii reatum Sancte Joannes. Hence G was called _ut_; A, _re_; B, _mi_; C, _fa_; D, _sol_; and E, _la_. These are the notes of the first hexachord, and these names are given to the notes of every hexachord. The half-step therefore was always _mi_-_fa_. Since the hexachords overlapped, several tones acquired two or even three names. For instance, the second hexachord began on C, which was also the fourth note of the first hexachord, and in the complete system this C was C-_fa_-_ut_. The fourth hexachord began on G an octave above the first. This G was not only the lowest note of the fourth hexachord but the second of the third and the fourth of the second. Therefore, its complete name was G-_sol_-_re_-_ut_. The lowest G, which Guido is said to have added to perfect the system, was called gamma. It was always _gamma_-_ut_, from which our word gamut. The process of giving each note its proper series of names was called solmisation.