The essence of the hexachord system is that each hexachord includes only one semitone—between mi and fa. A series of seven overlapping hexachords completed the gamut of formally recognized musical tones, a span of two and one-fourth octaves, containing the notes of the C major scale plus B♭.

What made a hexachord soft?

A melody moving a semitone higher than la (namely, from A to the B♭ above) required changing the la to mi, so that the required B♭ becomes fa. Because B♭ was named by the "soft" or rounded letter B, the hexachord with this note in it was called the hexachordum molle (soft hexachord).

How does the Guidonian hand work?

The Guidonian hand is another of his inventions, it is a system of assigning each part of the hand a certain note, thus, by pointing to a part of his hand, a group of singers would know which note was indicated and sing the corresponding note.