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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?

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  • All seventh chords will have a major or minor second and/or a tritone, which is a much stronger dissonance than the only-sometimes-dissonant perfect fourth. Also, the fourth in a 6-4 triad is "exposed"; whereas, in a seventh chord there is an intervening consonant third to "soften" the fourth (and create the stronger dissonance of a second). – Aaron Sep 25 '20 at 20:44
  • Also, consider a G6-4 triad moving to a C6-3 triad. Both chords contain a fourth. In this case it's not about resolving the fourth but resolving the leading tone. – Aaron Sep 25 '20 at 20:48
  • @Aaron But only one of those chords has a fourth with the bass, no? – Richard Sep 25 '20 at 20:50
  • In my triad example, yes, fair enough. – Aaron Sep 25 '20 at 20:54
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    Rereading your title, there are rules for resolving seventh chords in second inversion. For a dominant seventh chord, the resolution of the tritone predominates: the leading tone resolves upward to the tonic, and the chordal seventh resolves downward to the scalar third. The root becomes the fifth of the chord of resolution, and the chordal fifth may resolve upward to the scalar third or downward to the root. – Aaron Sep 25 '20 at 20:57
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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.

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  • or to put it another way, are there any examples pre Chopin where the fourth above the bass in a 643 chord was actually treated differently to that in a 64? – user71850 Sep 26 '20 at 18:50
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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

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  • Do you mean "first-inversion triads" in your last paragraph? And I agree with your upper paragraph, but ultimately my question is: why aren't we bothered by the treatment of the fourth in seventh chords like we are for triads? – Richard Sep 25 '20 at 20:55
  • Yes, I meant first-inversion. Edit forthcoming. Thanks. I'll take a look at the resolutions of the fourths; however, there are no parallel fourths here, just an oblique one. – ttw Sep 25 '20 at 21:23
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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.

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    Did you mean the 4th comes the fifth of the succeeding chord? – Michael Curtis Sep 28 '20 at 12:34
  • ReFaSoTi => DoMiSoDo. Thank you, Michael. (The fourth is the root of the actual 34 chord... ) – Albrecht Hügli Sep 29 '20 at 19:38

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