the first, namely,
C D E F G A; the third, likewise overlapping the second,
commenced on F. In order to make this hexachord identical
in structure with, the first and second, he flatted the B,
thus making the succession of notes, F G A B[flat] C D. 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.

THE GAMUT.

[F: g, a, b, c d e c d e f g a f g a b- c' d' ]
[W: [Gamma] A B C D E C D E F G a F G a b c d ]
[W: (Ut re mi fa sol la) (Ut re mi fa sol la) (Ut re mi fa sol la)]
[Hexachords: (Hard Low) (Natural Low) (Soft Low)]

[G: g a b= c' d' e' c' d' e' f' g' a' ]
[W: G a b c d e c d e f g aa ]
[W: (Ut re mi fa sol la) (Ut re mi fa sol la)]
[Hexachords: (Hard High) (Natural High)]

[G: f' g' a' b-' c'' d'' g' a' b=' c'' d'' e'']
[W: f g aa bb cc dd g aa bb cc dd ee ]
[W: (Ut re mi fa sol la) (Ut re mi fa sol la)]
[Hexachords: (Soft High) (Hard Super Acute)]

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,