Chapter 11: The Rules Regarding the treatment of the Fourth (Diatessaron and Tritone).

The diatessaron is called a consonance by the theorists and a dissonance by the practicing musicians. Because of this the fourth plays a curious role, midway between the role of a consonance and a dissonance. In two voice writing, the fourth is always treated like a dissonance, but in three or more voice writing their are times at which the diatessaron is considered a consonance.

In particular, the diatessaron is only forbidden between the lower two voices in a multi-voice composition. If two voices are both consonant with the bass, but between them they have the interval of the diatessaron, this is considered a consonance. There are two common cases where this occurs.

Examples of consonant fourths (6 and 7)

First, if the descant is an octave above the bass and the countertenor is a diapente above the bass, then the interval between the countertenor and the descant will be a diatessaron. These three notes, as can be plainly heard, make a very pleasing sound and are considered a perfect consonance, despite the diatessaron between the upper two voices. Example 6 shows a typical usage. This consonance is frequently used at cadences.

Second, if the descant is a third above the bass and the countertenor is a sixth above the bass, then the interval between the countertenor and the descant may be a diatessaron. (Other times it will be a tritone, in which case it may be possible to correct the interval through the use of musica ficta). Example 7 shows this. Because both thirds and sixths are allowed to move in parallel motion, this consonance may also be used in parallel motion, but special care should be used to avoid the dissonance of the tritone.

Thus, the diatessaron between the upper two voices may be used as a consonance, although it is always a dissonance between the lowest two voices. Josquin des Prez does in his Motet Absalon Filli Mi uses the fourth as if it were an ordinary consonance, but this device must be used with great care.

In no account may the tritone be used as a consonance. In fact, there are special rules concerning the correction of tritones.

Correcting Tritones by musica ficta

The reason that the forth is considered dissonant, may be due to the fact that sometimes the fourth results in the tritone (which has a most harsh sound) instead the diatessaron. For this reason many practicing musician will not play a tritone when one occur, but will correct a tritone through the use of accidental music or musica ficta. Because in a tritone one voice always sings mi while the other voice sings fa, this is sometimes referred to as the mi-contra-fa rule.

Suppose that one voice has written b-duram mi while a second voice sings f fa ut above it, then the first singer would sing a b-molle fa instead, making a diapente instead of a diminished diapente. Similarly, if one voice has written b-duram mi while a second voice sings F fa ut below. Then the first voice would sing b-molle fa instead, making a diatessaron instead of a tritone. In each case, one singer can correct the false interval by singing a note one semitone lower than what is written. If one voice has written e la mi and another has b-molle fa, then the first voice should sing a semitone lower than written, flattening the note to make e-molle fa. And similarly in the various transposed hexachords.

In some cases, by the use of accidental music or musica ficta it is possible to correct the tritone and the the corrected interval is then consonant. If no such correction is possible, the tritone must be treated like a dissonance. As such, its use is only permitted as a passing tone, it is forbidden in syncopated dissonances.

Just as the introduction of musica ficta can correct a false interval, it can turn a true interval into false. Singers and composers must be careful not to color notes in such a way as to create a false interval such as the tritone.

Onward to: Chapter 12: On The Cadence.

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