recurs after G and so on, was established by an anonymous Milanese treatise of ca. 1000 called Dialogus
de musica, once attributed erroneously to Abbot Odo of Cluny.
Hucbald sought to ground his theory as far as possible in the chant itself. He grasped that the “four
finals” used in actual singing formed a tetrachord in their own right (T–S–T), and he showed how the
scale of the first mode could be built up from it by means of disjunct replication: TST–(T)–TST. He
defined the four finals in a manner that resonates fully with our modern notion of a tonic: “Every song,” he
wrote, “whatever it may be, however it may be twisted this way and that, necessarily may be led back to
one of these four; and thence they are termed ‘final,’ because all things which are sung may take an ending
in them.” By relocating the tetrachord of the four finals (D–E–F–G) on its fourth note rather than its first
(or, to speak technically, by conjunctly replicating it: T–S–T/T–S–T), he deduced the tetrachord G–A–B–
C.
FIG. 3-3 The Abbey of St. Amand, where Hucbald lived and worked, as it looked in the eighteenth century. This painting was
made by J. F. Neyts shortly before the abbey was destroyed, an early casualty of the French Revolution.Thus he was able to rationalize within the new modal system the old singer’s practice of adjusting the
note B to avoid the tritone with F. In effect he admitted two versions of B (the hard and the soft, as they
came to be known) into the system (Ex. 3-3) to account for the pitches actually called for by the Gregorian
melodies.
EX. 3-3 Disjunct and conjunct replication of the T-S-T tetrachord (the tetrachord of the four finals) as described by HucbaldMODE CLASSIFICATION IN PRACTICE
As continually emphasized in this discussion, modal theory arose out of an attempt at classifying the
existing Gregorian chant, particularly the antiphons, as an aid to mastering an enormous body of material