When the sixth is taken and struck with the sixth it becomes a discord. Its preparations and resolutions are Fifth as a as follows. It is prepared in the eighth, sixth, and third, and resolved by the third and sixth, if the treble keeps on and the bass rises a fourth or falls a fifth, or the bass rises one degree, or the bass rises a sixth or falls a third. And, also, if the treble falls one degree and the bass rises one degree, or it rises a sixth or falls a third.

5D2

In closing our remarks on the artificial discords we think it proper to observe, that the natural resolution of the semidiapente, flat or defective fifth, is for the bass to rise one degree after it, and for the upper part to fall one, the parts thereby meeting in a major third.

The natural method of resolving the tritonus, or sharp fourth, is for the bass to fall one degree and for the upper part to rise one, whereby the parts meet in a minor sixth.

Discords by In our remarks on discords we have hitherto confined ourselves to their mere preparation and resolution, supposition. But there is another way in which they may be and are constantly used without such regular preparation and resolution, though they are then no longer considered in the light of discords but passing or transient notes. They are, nevertheless, discords; that is the second and seventh, as also the fourth, if used in only two parts, but not so in three or four parts, for the fourth then is a perfect concord, unless made a discord by the fifth, as we have seen above.

If we make use of the discords of the second, seventh, and fourth, and their replicates, or octaves in divisions, or diminutions as passing notes, it will be necessary to take care that the notes which fall on the accented parts of the bars be concords; but those in the unaccented parts may be discords if we take care to proceed to them by degrees upwards or downwards, and that thereafter our progress to a concord be upwards or downwards by degrees.

Music.

And here it is right to notice with respect to those divisions which touch a discord after a concord, and thereon Marie immediately return to the concord that was struck before the discord, that if the discord ascend by a single degree from the concord, and then by falling a single degree return to it, we must then skip upwards if we wish to go by a leap to the note that follows the concord. If, however, the discord fall a single degree from its preceding concord, and then by rising a single degree return again to it, we must skip downward if we are desirous to go by leap to the note that follows the concord.

9:3
4

&c.

D: 3

4

Discords by supposition may be used in the first half of the bar as well as in the second half, taking care that if we use them in the first accented part of the bar, they must also be used in the second half, and only in descending. This method is used in basses that sing as a treble part, and is of importance in bass instrumental accompani

Thus if discords by supposition are employed on the first and second accented parts of the bar, it must be when the notes of the real or plain harmony skip by thirds, descending; in which case, in this division the two accented notes, which are the first and third in the bar, begin by supposition a degree higher than the real notes and are therefore discords, which afterwards descending a degree are followed by the concords on the unaccented parts of the bar, which are in reality the notes of the skip.

To illustrate this in numbers which will be sufficiently intelligible, suppose that the skip of the real sounds is from the third to the unison. Then, to bring in the discords by supposition as passing notes on the first and second accented parts of the bar, a note must be taken higher than the third, which gives a fourth for the first accented part, the third then follows on the first unaccented part; then taking a second, being one note higher than the unison on the second accented part, the unison itself follows after on the last unaccented part of the bar. Hence the skip of a third descending from the third to the unison, is fourth, third, second, unison by supposition. If from the fourth to the second, it must be fifth, fourth, third, second. From the fifth to the third, it makes sixth, fifth, fourth, and third. From the sixth to the fourth, we have seventh, sixth, fifth, and fourth. From the seventh to the fifth, it will be eighth, seventh, sixth, and fifth. And from the eighth to the sixth, we must place ninth, eighth, seventh, and sixth. It is hardly necessary to state that with the replicates or octaves the same arrangements must take place.

Though we have thus far only mentioned the rules for employing discords by supposition where the plain or real notes proceed by skips of thirds, it is evident from what has been said that discords by supposition may be equally used in skips that proceed by fourths, fifths, sixths, sevenths, eighths, &c., both ascending and descending; but in this case we can only bring them in on the second accented part of the bar, and that by the division of the two notes that define the skip into four notes, whereof the first must keep its place on the firs accented part of the bar, the other three ending gradually on the last note of the skip, thus making as it were a divided third. In the example below, the first line contains the plain notes, and the second the treble by supposi

Music. tion; and in the second appended example, the second line contains the plain bass notes, and the third the bass Music. by supposition.