There are three types of movement between two voices: Contrary,
oblique, and similar. Since our intention is to create independent
melodic lines in each of the voices, it is most desirable to proceed in
contrary motion whenever possible. Oblique motion is next best for
independence, and finally similar motion is least desirable. Considering
all of the above be aware, nevertheless, that parallel thirds and
parallel sixths are not only acceptable but are also a very pleasing sound.
When choosing your doubling for a first inversion chord, observe how that doubling is approached. Doubled notes are best approached in contrary motion; next best is oblique motion, and then similar motion. Also it is well advised to leave the doubled notes first when proceeding on to the next chord.
Consider the above example. In the first chord the tenor and bass are doubled. Going to the next chord the tenor moves upward and the bass moves upward. This is similar motion (shown by the S after the chord). In the second chord the bass and soprano are doubled. To get to this doubling the soprano came from the same note and the bass moved upward. This oblique motion is signified by the O over the chord. Now the two A's (bass and soprano) move in opposite direction to each other, so this doubling is left by contrary motion, the C after the chord. The doubling in the next chord (soprano and alto) is approached in contrary motion, shown by the C over the chord. The O after the chord represents the motion of soprano and alto in leaving their doubling. Finally the C over the last chord shows that the doubling between bass and tenor is approached in contrary motion.