Until now, crossing the parts has been forbidden for students. The crossing of parts is an exceptional process which one must use with great sobriety.
However, when its done for melodic interest of the parts, its effect is excellent, so long as these parts are returned to their natural order as soon as possible.
Sometimes, crossing is used to avoid or mitigate the bad effect of two fifths or two octaves:
Example: J.S. BACH. (Choral 40.)
but to use this means requires a lot of experience, as its insufficient or bad in many cases. Thus, the preceding example is good only when executed by voices or instruments with different timbres, making it possible to distinguish between the melodic succession of each part. On a keyboard instrument, this example produces the two consecutive fifths and two octaves.
Crossing parts is most often practiced between intermediate parts. Crossing with the outermost parts is rare, here’s why.
The upper part usually contains the main melody, and this melody could be stifled by a part that rises above it. As for the Bass, if another part descends below it, this part then becomes the Bass.
But, in general, the lower register of a higher part is much weaker than the medium register of the real Bass. On the other hand, the Bass in its upper register, has good strength and a character which makes it predominant. This results in a conflict of the following required rule:
RULE: When a part crosses with the Bass, each of these two parts (the Bass and the crossing part) must be treated in good Bass. Now, one of the principal conditions principal conditions of a good bass is preparing and resolving the perfect fourth (CH 7.1).
Note: This rule doesn’t apply when the two crossing parts have the same nature of pitch and timbre force.
Old Music Theory 