d also a notation consisting of letters written above the
words to which they applied; they made use of the first fifteen
letters of the alphabet in the same manner as the Greeks, but we do
not know whether they employed the same characters for the instruments
and the voices, or had different ones. The only example we possess of
the Roman notation from classical times, or in close tradition from
classical times, is that in "Boethius' Consolations of Philosophy."
From the fact of this being the only place where the Roman notation is
illustrated, certain writers have concluded that Boethius invented
it--a supposition which is utterly improbable. Boethius mentions the
Roman notation, and employs it, as also does Hucbald in certain of his
examples, but neither one of them explains it or gives any account of
its origin. We have simply to take it for granted that the Romans
transferred the letter notation of approximate pitch to their own
characters instead of using Greek letters. The following example from
Guido's book illustrates the appearance of the Roman notation as he
uses it:

[Music illustration: Fig. 31.

LETTER NOTATION OF GUIDO OF AREZZO, WITH DECIPHERING.

Qui tol-lis pec-ca-ta.]

The most curious notation of which we have a record was that of the
neumae, or neumes, which were employed by the ecclesiastical writers
mostly from about the sixth century to the twelfth. This writing, as
will be seen from the examples hereafter given, very much resembled
the curves and hooks of the modern shorthand. The learned Fetis thinks
that the characters were derived from the Coptic notation, and these
again from the hieratic notation of the ancient Egyptians. The neumes
signified mostly intonations, upward or downward slides of the voice,
and not absolute pitch.

[Illustration: Fig. 32.

NEUME NOTATION OF THE TENTH CENTURY.]

There are no clefs or other indications of the key, and it is little
better than sheer guesswork to attempt to decipher one of them, for
want of some one single base mark to reckon from. Accordingly, the
various commentators have rendered the old pieces in a variety of
ways. It is probable that the imperfections of this notation were
helped out, when it was in current use, by tradition, which
appropriated certain keys to each of the principal hymns of the
Church; this being understood, the singer found himself able to make
something intelligible out of a notation which, without the help of
traditi