On Double Counterpoint

By observing the rules laid down in the first section on the subject of double counterpoint at the tenth, as well as the laws which ordain the necessity of employing contrary movement and oblique movement, triple and quadruple counterpoint at the tenth will be obtained.

Example of a double counterpoint at the tenth

In order to convert this double counterpoint into triple counterpoint, nothing is required but to add to these two parts the inversion of the upper part a tenth below, or that of the lower part a tenth above.

In order to obtain quadruple counterpoint, the following example of a double counterpoint at the tenth is first proposed:

Of this double counterpoint, a triple counterpoint is formed, by adding a third part at the distance of a tenth or a third from one or other of the two existing parts; and by inverting, alternately, each of these parts in the manner worked out in the example of a quadruple counterpoint at the octave.

By adding to this same double counterpoint the two parts in thirds, in the following manner, a quadruple counterpoint at the tenth will be obtained:

This counterpoint – at least, as it is combined in the above example – gives but few inversion exempt from reproach.