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The image above (from Korean composer Byung Dong Paik's Theory of Harmonics, page 227) shows Deceptive Cadence progressions of Secondary half-diminished 7th chord

As you can see, the progression in the image above resolves the Secondary half-diminished 7th chord to a substitution chord.

But the substitution chord comes out as a second inversion, and what happens after that doesn't make sense.

The progression on the left side of the image seems to make sense. The bass goes in sequence and the 4th stays. This is one of the progress of the second inversion.

but, on the right side of the image, the base is sequential but the 4th of the ii46 jumps down from V.

Is this some kind of second inversion 'cadence progression?' (i46->V) but I don't even know if vi, which is the substitution chord of i , can do cadence progress because of the second inversion. (vi46->V)

In the image, ii46 is followed by V and then I. I is V in F and if vi46->V proceeds, shouldn't 'I' come immediately after ii46? In my opinion, this doesn't make sense either.

So I hope someone can tell me how it went.

  • is the iii64 acting like a V chord which goes to a deceptive resolution? iii64 often replaces V.
    – user35708
    Commented Aug 24, 2022 at 11:39
  • @armani Oh no, I see. I think you're right... If you leave it as an answer, I'll pick it up.
    – guss2222
    Commented Aug 24, 2022 at 12:03
  • As to "shouldn't I come after ii46," remember that regardless of what cane before, ii chords are almost always used just before the dominant.
    – nuggethead
    Commented Aug 24, 2022 at 12:05
  • @nuggethead It seems that the answer has already been found. I didn't think that a substitution chord (vi=I) of another key would also form a substitution chord (iii=V) in the original key. I guess I asked a stupid question.
    – guss2222
    Commented Aug 24, 2022 at 12:10
  • @guss2222 not at all a stupid question! I am.not convinced your.book explained it well enough, or marked the chords clearly enough to avoid confusing people!
    – nuggethead
    Commented Aug 24, 2022 at 12:31

2 Answers 2


Is this book using the term "substitution chord?" I think that concept will just add an unnecessary layer of complexity.

One way to think about these 6/4 chords is contrapuntally. They resolve like passing 6/4 chords, bass moving down by step to a root position chord.

In terms of root progression things look complicated, but you can break it down into simpler pieces by understanding a simple progression can take the insertion of a secondary dominant before nearly any chord, and technically a dominant can resolve deceptively to nearly any non-tonic chord. When you consider those two points of harmonic elaboration, the harmony reduces to mostly root progression by descending fifths, the fundamental type of progression.

  • A typical second inversion passing progression should perfect 4th in chord is stay in place. But the right side of the image is not.
    – guss2222
    Commented Aug 25, 2022 at 3:21
  • 1
    You're being too literal, too much textbook thinking. A passing 6/4 to a V would be a ii chord, and the chord in question is a ii6/4. The critical part of a passing 6/4 is not literally holding the root of the 6/4 to become the fifth of the next root position chord, it's the step-wise motion of the bass moving through the fifth of the 6/4 chord. Commented Aug 25, 2022 at 12:43
  • These 6/4 chords are clearly, and easily explain as passing 6/4 chord or simply as common contrapuntal motions. Commented Aug 25, 2022 at 12:45
  • This is how I look at it: if the D5 in the penultimate bar was repeated or held until beat 3 for the V chord and then it descended to B4, would you be satisfied that ii6/4 is a passing 6/4? Commented Aug 25, 2022 at 13:02
  • A typical second inversion passing progression I was talking about is the same book as the example in the main text. and yes Your last example is how the book says it. And I asked a similar question about the second inversion before, and I knew that the rest of the voices other than the bass and 4th do not have to move like the example in the book, but the 4th and the bass should only move as set. In other words, I thought I had some flexibility in thinking with the second inversion question I asked earlier, but if you're right, I guess it wasn't.
    – guss2222
    Commented Aug 25, 2022 at 13:07

The fourth and third last chords look like it had a quick modulation to the sub-dominant key. How else do you explain the B flat?

You also have a E resolving like a leading tone should which strengthens this idea.

It also looks like a normal leading tone chord with its seventh added. Just one in F major.

  • I already wrote this example 'progressions of Secondary half-diminished 7th chord'. 'viiø43/IV' stands for Secondary half-diminished 7th, which has a leading tone and is resolved in ii46. In other words, what you are describing is something I already know and not what I asked. What I'm curious about is that the ii46 is a second inversion inversion, but it's not a normal second inversion progression.
    – guss2222
    Commented Aug 25, 2022 at 12:44

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