The tetrachord beginning with the first note, C, gives the beginning of the Mixolydian scale as well as that
of the adjusted Lydian with B-flat: TTS. (In view of what we have observed about the F mode with B-flat,
we could call this the major tetrachord.) If one begins on the second note of the hexachord, one gets the
beginning of the Dorian scale, TST (we can call it the minor tetrachord). And by beginning on the third
note one derives the essence of the Phrygian, STT. For all practical purposes, this model implies, there
are only three finals—not four—and their scales are best thought of as beginning on C, D, and E. It was a
step in the direction of what we call major-minor tonality.
Hermann appears to have been unaware of the fact, but his conceptual module had already been
abstracted from the chant itself as part of a great pedagogical breakthrough—perhaps the greatest in the
history of the literate tradition of music in the West. For it was precisely this breakthrough that at last
made “sight-singing” possible and put Western music on a literate footing in truly practical terms. Its
importance would be hard to overestimate.
The man responsible for this signal achievement was the same Italian monk, Guido of Arezzo, who
around 1030 (in the prologue to an antiphoner) first proposed placing neumes on the lines and spaces of a
ruled staff to define their precise pitch content. Guido used special colors, later replaced by alphabet
signs, to denote the C and F, “key” lines—claves in Latin—that have semitones below them; these letters
survive as our modern “clefs.” We, who still rely on his inventions nearly a thousand years later, owe him
a lot, as did all the generations of Western musicians preceding us. No wonder he was a legend in his own
time, and by now is something of a myth, a musical Prometheus.
FIG. 3-5 Guido of Arezzo instructing his pupil Theodal at the monochord, from a twelfth-century manuscript in the Austrian
National Library, Vienna.
The actual Guido lived from about 990 to about 1033 and specialized for most of his fairly brief life
in the training of choirboys. Like many teachers of ear training, he was ever on the lookout for melodies
(in his case, chiefly chant antiphons) with which to exemplify the various intervals. Imagine his
excitement, then, when (as he tells us) he chanced upon a tune that could exemplify all of them. This was
the hymn Ut queant laxis (“So that tongues might loosen”), composed in the late eighth century by Paul the
Deacon, a monk at the Benedictine abbey of Monte Cassino, in honor of the abbey’s patron saint, John the
Baptist. This hymn tune is so constructed that the first syllable in each half-line is one scale degree higher
than the one that precedes it, the whole series exactly tracing out the basic hexachord from C to A (Ex. 3-