In music theory we talk a lot about HOW to do certain things: build chords, analyze progressions, etc. But as you progress in music theory you will find that we also talk more about how certain things FUNCTION.

For example, consider your clothes. Whatever we may be wearing, we have certain items that are mostly FUNCTIONAL: socks to keep our feet warm, snaps and buttons to close up the front of jackets, laces for our shoes, etc. Some things function the same way for everyone, regardless of what we wear, so we can standardize them in a certain way. This is different from things that are DECORATIVE: jewelry, hair clips, nose rings.

In music theory, certain CHORDS have a specific function. Root position chords are stable, and serve to stabilize a tonal center and provide a strong chord to move away from or come back to in a progressions. And first inversion chords can be substituted for their root position counterparts to achieve a more smooth bass line, or to make the bass line more interesting:

The first example above is how the bass line would sound if all the chords were in root position, but the bottom is what Haydn wrote: more interesting bass line, more interest in the harmony when you alternate between root (stable) chords and first inversion (less stable) chords.

So what about second i

nversion chords? Second inversion chords have three specific functions: PASSING, PEDAL, and CADENTIAL.

PASSING SECOND INVERSION CHORDS

Second inversion chords allow the bass line to move stepwise in one direction on these less stable chords as it travels to stronger root position chords:

PEDAL SECOND INVERSION CHORDS

These second inversion allow to bass line to stay STATIC, perhaps while more elaborate music goes on in the higher voices, but still allows for a change in harmony:

CADENTIAL SECOND INVERSION CHORDS

These are definitely the most common kinds of second inversion chords. They almost always appear in the pattern I6/4 -- V -- I at the end of a phrase or a piece of music:

See how in the example above, when we add a I6/4 chord to before the V, we can extend the cadence and allow for another chord. This puts more tension in the second-to-last chord--the dominant--before finally resolving to I. And because of its placement next to the V chord, the I 6/4 actually serves a DOMINANT function.

Here is the portion of our textbook that discusses second inversion chords: http://musictheory.pugetsound.edu/mt21c/TheCadentialSixFourChord.html