Hexachords

This change, however, was made after the scale was divided into a system of octaves instead of hexachords. ❋ Edward MacDowell (1884)

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 ❋ Edward MacDowell (1884)

Furthermore, as there were six of these syllables, he arranged the musical scale in groups of six notes instead of four, hexachords instead of tetrachords. ❋ Edward MacDowell (1884)

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. ❋ Edward MacDowell (1884)

The first change in the _tetrachord_ system of reckoning tones and dividing the scale was made by Guido d'Arezzo (first half of eleventh century), who divided it into hexachords or groups of six notes each. ❋ Edward MacDowell (1884)

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. ❋ Edward MacDowell (1884)

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. ❋ Edward MacDowell (1884)

He also expanded the system of disjunct tetrachords from the enchiriadis notation into a system of overlapping hexachords, retaining the key feature of the tetrachords -- the half step between the two middle notes. ❋ Unknown (2009)

The next three hexachords were repetitions of the first three, namely, G A B C D E, C D E F G A, F G A B [flat] C D; the last was again a repetition of the first, G A B C D E. ❋ Edward MacDowell (1884)