This beautiful movement from Schumann's String Quartet in A minor, quite apart from æsthetic considerations, affords a most inspiring model of style for the student, for it abounds in suspensions, syncopations, accented passing notes and subtle chromatic effects.

CHAPTER IX

Double Counterpoint

$119. It is necessary now to learn something of that form of counterpoint known as "double counterpoint," not only because its practice affords valuable mental training, but because it is an integral part of the structure of such common forms of composition as the pianoforte invention, the fugue, and in most cases of the sonata and of the symphony.* Furthermore, a free and incidental use of double counterpoint is often made where the average listener would not recognize it as such, although he might be aware of some carefully planned design in the harmonic structure. In Sullivan's well-known hymn tune, "Onward, Christian Soldiers," for instance, the sopranos and the tenors answer each other in double counterpoint.

B

Likewise in the opening measures of Chopin's Ballade in Ab major there is free double counterpoint between two of the voices; for example,

two measures

B

etc.

B

$120. By double counterpoint, therefore, we mean “invertible counterpoint "; that is, when two melodies, written to be played or sung together, are capable of inversion, either being above or below the other, they are said to be

*In almost any symphony may be found interesting examples of double counterpoint. The first movement of Tschaikowski's Sixth Symphony is suggested as a movement likely to inspire the student. The first and second movements of Brahms' Second Symphony are also rich in examples.

in double counterpoint. The inversion may take place at any interval, but the two kinds which are most used, and are of the greatest practical advantage to the student, are double counterpoint at the octave and at the fifteenth. Double counterpoint is also triple or quadruple, according as we have a combination of three or four melodies, any one of which may be the highest, the lowest, or an inner part. In this brief manual we shall treat only of double counterpoint at the octave and the fifteenth, for two or for three voices. Those who are interested in double counterpoint at the less usual intervals are referred to the exhaustive treatises of Dubois, Prout and Bridge.

$121. Double counterpoint at the octave and at the fifteenth are virtually identical as far as harmonic considerations are concerned, the only practical difference being one of position; that is, in double counterpoint at the octave the two melodies in their first grouping are not to be more than an octave apart, and the inversion is made by placing the original lower voice up an octave, or the original higher down an octave, while in either case one voice remains as it is: for example,

In this example the inversion is made by placing the original melody up an octave, while the contrapuntal voice retains its original position.

Subject

HANDEL. Te Deum in Bb

Inversion

In the above example, on the other hand, the upper voice is placed an octave below. Observe in both these examples that the distance of an octave between the subject and the counterpoint is never exceeded. In double counterpoint at the octave, whenever the two voices in the original grouping are more than an octave apart, no real inversion can take place by the change of only one of the voices, but merely a contraction; for example, suppose that we wish to invert the following phrase

A

Be

by placing the lower voice an octave higher. As the voices at exceed the interval of an octave, it is evident that here no inversion can be made; for example,

B

A

Here the latter part of voice A is still above voice B, although the distance between the voices is contracted

The objection is sometimes made to double counterpoint at the octave that the limitation of range hampers effective writing, that the necessity for not exceeding the distance of an octave between the parts is fatal to freedom of movement. Doubtless this is true to some extent, yet as Handel in the chorus, "We worship God," in "Judas Maccabæus," did not seem to be fettered by the limitation,

or Mozart in his Mass in C minor, it will be well for the student in early exercises to cultivate his ingenuity by the formation of a melodious counterpoint without exceeding the limit of an octave.

$122. In double counterpoint at the fifteenth (double octave), the inversion is ordinarily made by raising the lower voice an octave and at the same time lowering the upper an octave. As a result, the position of the voices is often much better than if only one had been changed, and in the original grouping the limit of an octave need not be preserved; for example, in the following phrase,

etc.

as the two voices are sometimes more than an octave apart, it is clear that no continuous inversion can be made by lowering the upper voice an octave or by raising the lower. If the upper voice is lowered two octaves, the register is too low, while if the lower is raised two octaves, it is too high. By moving each voice an octave, however, and in opposite directions, a perfect inversion is secured and both voices are in a convenient position; for example,

*Let the student write out the inverison for each of these examples.