First-inversion triads are used for a number of purposes, including to smooth bass lines and to provide melodic motion in repeated chords.
First-Inversion Triads for Smooth Bass Melodies
Triads in root position establish stability in the chorale and are considered anchor positions, but if all chorales or hymns were composed only of root positions, bass lines would be disjointed. Stepwise movement would be possible only with adjacent chords that are a step apart (IV to V, V to vi, etc.). One of the reasons first inversions are employed is to provide smooth bass lines with a musical balance of steps and skips.
Figured bass consists of a bass part (single line) with figures (mostly numbers) below to indicate the type of harmony. It is a contrapuntal, intervallic shorthand method of showing the harmony (along with nonharmonic tones). The numbers 6 and 6/4 refer to intervals above the bass note, but they imply others such as 3, 8, or an additional 6 or 4 to fill out the four voices. Figured-bass numbers do not denote specific arrangements; they do not indicate what note should be placed in a particular voice (soprano, alto, or tenor).
First-Inversion Triads to Provide Melodic Motion
Not only do first-inversion triads diminish the angularity of a bass line, but they may also add another ingredient not available to root positions—they provide an opportunity to incorporate melodic motion in the bass melody.