he tonality of plain song, and symphony, or
the singing of many voices at different intervals--in other words,
harmony.

In treating the scale he divides it into tetrachords, precisely
according to the Greek method, as far as known to him, and he nowhere
appears to perceive the inapplicability of this division to the
ecclesiastical modes. For representing the sounds of the scale,
divided into four tetrachords, Hucbald proposed the Greek letters,
which in effect, would have been a notation of absolute pitch, with
the farther disadvantage of ignoring the harmonic principles of unity
already discovered, and in fact involved in his own method of
enlarging a two-voice passage by adding a third at the interval of an
octave with the lowest.

He recognizes six kinds of symphony; in reality he employs only three,
the others being reduplications. His symphonies are those of fourths,
fifths and octaves. In all parts of his work but one he uses the term
diaphony as synonymous with symphony; _there_ he gives its ancient
meaning of dissonance.

He proposed a sort of staff notation, upon which all the voices could
be represented at once. The following illustration represents his
staff and his diaphony, or harmony:

[Illustration: POLYPHONIC NOTATION OF HUCBALD.]

The initial letters, T and S, at the beginning of the lines in the
preceding staff indicate the place of the steps (tones) and half steps
(semitones).

[Music illustration: DECIPHERING OF ABOVE.

Sit glo-ri-a Do-mi-ni in sae-cu-la lae-ta-bi-tur
Do-mi-nus in o-pe-ri-bus su-is.]

M. Fetis gives a two-voice parallelism in fifths, which is
progressively enlarged to three voices by adding an octave to the
lower voice; and then to four by doubling the original upper voice in
the octave above. Thus:

[Music illustration: Tu pa-tris sem-pi-ter-nus es fi-li-us.]

In addition to mechanical progressions of parallel motion in this way,
Hucbald in another place gives an account of a so-called "roving"
organum, in which, while parallel progressions of fourths and fifths
still are found, there are also other intervals, while the beginning
and the end must be in unison. This form of the harmony of
simultaneous sounds has in it much of the character of counterpoint,
especially in the restriction that the voices must begin and end in
unison. This roving organum, or free organum, was also known as
"profane" or "secular" organum, in contradistinction to the "sacred
organ