Why are there particular "rules" for using triads in second inversion but not for using seventh chords in second inversion?

Question

In the Classical style, there are three correct uses of the six-four triad (or sometimes four; see When, if ever, are arpeggiated six-four chords really "real"?). The logic is that the interval of the fourth, historically a dissonance, needs to be correctly handled when it's between the bass and an upper voice.

So why do these same rules not apply to second-inversion seventh chords, which also have a fourth between the bass and an upper voice? The only difference between the two is that the second-inversion seventh chord has a third above the bass in addition to the sixth and fourth.

In other words, a second-inversion triad must be a passing, pedal, or cadential six-four. Why isn't this also true for second-inversion seventh chords?

Is there a historical reason why the triad is treated differently than the seventh chord? Perhaps an explanation from the thoroughbass tradition?

Or perhaps they do follow these same guidelines, but current theory textbooks don't make that clear enough?

Answer 1

In Bach-chorale style harmony the ‘rules’ about the dissonant fourths in seventh chords would seem to be the same as in triads. But... x43 was only ‘really’ used in this style as a passing chord, so the fourth above the bass was considered ok just as in the straight 64. Other examples that you’ll find of V43 are bass arpeggiations (typically involving V65) - the fourth ‘rule’ you alluded to and hence also ok. 43 can’t be used to substitute a cadential 64 - try it, you’ll be setting up a modulation away from your local tonic. It can’t be used as an auxiliary/pedal 64 substitution for the same reason. Those ‘rules‘ of course did not survive the 19th century.

Answer 2

From what I've read, the only things to worry about are the treatment of the seventh (resolve downward by step) and the root (move a fifth downward) while avoiding parallels. It's a combination of the rules ("common procedures" would be a better name) for triads in inversion and resolution of sevenths. One may follow these guidelines as closely as needed to get the sound desired. The second inversion V43 gets a nice (rather an ancient sound) of a major sixth expanding to an octave if moving to a I.

The only peculiarity seems to be that third inversion sevenths (4-2) chords tend to resolve to first inversion triads a fifth below (else the seventh doesn't fall.) There are probably some exceptions.

With respect to the fourth in the V43-I53 cadence, the following link suggests that it's a "weak" authentic cadence and not really suited for a final cadence but OK internally. http://www.sfcmtheory.com/harmony_supplements/chap_08.htm

Answer 3

Rules always are derived from the practice in a certain epoque:

The triad and its second inversion came up in the time of renaissance and early bar(counterpoint and through bass) while the tetrads and seventh chords have been developed later.

If you have a 34 passing chord (second inversion of any degree) the 3rd (=7th) will be leaded downwards, and the 6th (=lead tone) upwards, the 4th becomes the fifth (edited!) of the succeeding chord and the bass will continue its line. E.g. ReFaSoTi => DoMiSoDo.

The case of the ambivalent I46 = Vsus64 as tetrad doesn’t appear.