117. This important rule needs to be supplemented by another:—The modulation in the answer from dominant back to tonic must be made at the same point at which the modulation was made in the subject from tonic to dominant. This rule will be fully illustrated as we proceed.
118. The modulation in a fugue subject may be either expressed or implied. It is expressed when the leading note of the dominant key appears as a note of the subject, as in example, §57 (b). It is implied when, although the leading note of the new key is not actually present, the whole form of the melody, and especially its last notes, show more or less distinctly that they are looked at as belonging to the key of the dominant, and when they produce the mental effect of being in that key.
119. The examples now to be given will show what is meant by implied modulation—
It will be seen that in all these passages the mental impression of the last notes is unmistakably that of a modulation to the dominant; and it may be stated as a general rule that, whenever a subject ends with the descent from the submediant to the dominant of the tonic key, a modulation is implied, and these two notes are considered to be the supertonic and tonic of the dominant key.
120. Sometimes the great composers choose to consider a modulation as implied when there is no absolute necessity for it—
Here we see from the answer given by Bach that he implies a modulation in the second bar, though a real answer would have been perfectly correct. Had he regarded E as the third of C, he
