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Specially in jazz, it is common to approach a chord that is not the root by its diatonic 2-5, or simply its 5 (secondary dominant). When approaching a minor, it will be a ii7b5 - V7, and, in major, a ii7 V7. My question is, is there such thing as a secondary dominant of the 7th degree, specially a 2-5 of 7?

If so, what quality of 2 and 5 will it be since the chord being approached is not a major nor a minor, but a half diminished?

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In this video:

Jens Larsen says "I actually don't know of any songs that have a cadence to the seventh degree, but if I was to add a cadence to that one I would say [the half diminished chord] is a minor chord, and then I would make a minor cadence. So that [would be] C# half diminished to F#7 to B half-diminished."

I think he's got a good idea. It makes sense to me because if we think about a half-diminished chord as sounding like a chord built on the seventh degree of the major scale, then the "ii" of that chord would seem to be a major 7th chord one half-step above, the Imaj7 chord. But a half-step up isn't really a ii because it's not a 5th above the V/vii. If we raise the root only of the Imaj7 chord and keep the other notes diatonic, then we get a half-diminished 7th chord as our "ii" chord.

It's a hack, but if you really wanted to add a ii-V in front of a half diminished chord, this is probably the best way to do it. You could also try a fully diminished 7th chord for the "ii" chord.

All that said, I think what the other answers are getting at is no matter what you play in front of a half-diminished chord, it's never going to sound like a ii - V - i progression, because the quality of the final chord is going to change the sound enough that it will end up in its own sonic territory.

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In your first sentence I think you meant to say “tonic”, not “root”.

Taking the ii chord out of the equation for now, a secondary dominant chord is typically a dominant chord resolving down a 5th to a chord other than I or i. If using 7th chords secondary dominants are all non-diatonic to the original key and can use any chord as their target, including the chord built on the 7th degree in either major or minor. However the chord built on the 7th degree in major does not work well as a target chord because of its dissonance. It is better not to think of secondary dominants as diatonic to the scale degree they are approaching, but rather simply a 7th chord resolving to a non-tonic chord such as V7/ii, V7/iii, etc. the reason for this is because it is usually a fleeting moment in a progression and not actually a modulation.

The iim7 or iim7b5 is not a part of a secondary dominant. However it can be added before a secondary dominant in a chord progression if desired. It is more common to use iim7b5 going to a minor chord and ii7 when going to major but there are many instances of the opposite being done. It is up to the composer or arranger to use the one of their preference when creating a chord progression.

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    I understand what you mean, and don't want to quibble, but V resolving to vi is not resolving to I or i, but it is not a secondary dominant. Even if a dominant doesn't resolve to a tonic, we still need to theoretically relate it to a tonic. If that tonic isn't the prevailing tonic, then the dominant is secondary. Commented Mar 14, 2023 at 20:49
  • @MichaelCurtis If what I wrote is unclear please point it out but I did not refer to V resolving to vi, or to the diatonic V at all. In the context of my answer that would be V7/vi-vi, i.e. E7-Am in the key of C. Commented Mar 14, 2023 at 20:59
  • "a secondary dominant chord is simply a dominant chord resolving to a chord other than I or i" Commented Mar 14, 2023 at 21:01
  • V vi is a dominant resolving to a chord other that I or i, but it is not a secondary dominant. Commented Mar 14, 2023 at 21:02
  • "...any chord as their target, including the chord built on the 7th degree in either major or minor." So what chord specifically would be the dominant to viio in major? Commented Mar 14, 2023 at 21:10
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II - V - I a regular cadence with the subdominant being replaced by a functionally equivalent chord.

So then let us ask if there can be secondary tonality on the VII. First we see that clearly in minor this is significantly easier than in major, as VII in minor is a major chord, but in major it is a diminished chord. That one is considered as characteristic and will imply a dominant or a subdominant function, will thus be hard to be considered as a secondary tonality.

But in minor we have a slight similar problem: The natural 7th chord on the VII would be a dominant 7 and thus again imply a resolution. One can of course go by the mysterious ways of jazz and claim that dominant 7 chords do not imply a resolution, or one could alterate the 7th, so you’d sharpen the 6th of the original tonic.

The other question is how we can get a sort of dominant for the VII. This requires a leading tone, so a half step above and below. In minor this could only be that sharpened VI, in major this can only be I.

But obtaining that sharpened VI in minor is not much of a problem, as the minor mode allows for the raised VI as preparation for the raised VII. So we can then use I as a sort of secondary II or III as a secondary IV and thus do i - IV7 - VII. In fact this has the character of a common sequence used in baroque music, where you use repeated cadences, such as I - IV - VII - III - VI - II - V - I.

So what can be done in major? That diminished chord is somewhat of a problem, but we can have the major mode steal the #IV from the lydian mode to obtain an augmented 4th. This way we can spell the VII as a minor chord instead. Then the dominant here would be a sort of phrygian dominant, so bII - I (in terms of the tonic I - VII5#), so you can do something like iii - I - vii5#. Alternatively we can turn I into a I6 and interpret this as a neapolitan for VII, allowing us to do I6 - #IV - VII, although that one needs to borrow a few more notes.

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When you bring up II V I and secondary dominant, it muddies the waters...

  • ii7 V7 I in major
  • ii7b5 V7 I in minor

...neither of those progression involves a secondary dominant, both are diatonic for their respective modes.

Both of those progression can be called "roots by descending fifths"

Diatonically, roots by descending fifths to the seventh scale degree would be...

  • I IV viio in major
  • i iv ♭VII in minor

I see another problem in the wording of the question, because this, "secondary dominant", does not change in meaning, because of this "specially in jazz".

A dominant is a dominant, and it is a concept from the major/minor harmony system, where tonics are major or minor triads, and their dominants are major chords rooted a perfect fifth above the tonic root. Secondary dominant are dominants to any major/minor triads that are not the prevailing tonic. In the major/minor system a diminished triad can't be a tonic so there is no dominant to relate to that non-tonic chord.

Essentially, secondary dominants follow the function of diatonic harmony, the only difference is a temporary change of the tonic.

The two main thing jazz introduces to the tonic/dominant concept are:

  • extending the tonic chord with sevenths, sixths, etc.
  • tritone substitution of the dominant

...otherwise the basic tonic triad in jazz is still a major or minor triad.

You can look into people working with locrian harmony in jazz, where the "tonic" would be the diminished triad, but IMO it makes more sense to think of that as a kind of modal harmony and not a flavor of the major/minor system.

Ah, I overlooked the obvious: in minor ♭VII can have secondary dominant IV7 or V7/♭VII so the II V I to the seventh scale degree, in minor, would be i IV7 ♭VII. Of course that doesn't end on a diminished chord, so I think this isn't really what you are asking about.

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  • I’m not sure but I think current teaching in jazz theory is a bit different from this. I’ll have to check my notes. Commented Mar 14, 2023 at 20:29
  • You can (ii) V7 (almost) any chord in jazz, and when you do, the V7 you use is often dominant even when that dominant chord is not diatonic, so the concept of secondary dominants, AKA “applied chords” is relevant to jazz. Even if the V7 in a progression is diatonic to the key of the song or the key of the moment, it can sometimes be lumped in with all the applied V7 chords or applied ii V7 chord pairs. See viva.pressbooks.pub/openmusictheory/chapter/ii-v-i Commented Mar 14, 2023 at 20:35
  • Sure, you can modulate to/tonicize something like ♭II a chord not diatonic to the current key, but that new tonic is still a major/minor triad base. But the point is those tonics will not be a diminished chord. I tweaked my sentence to clarify that. Commented Mar 14, 2023 at 20:39
  • What is it you want me to see in that linked site? Is there an example of a purported dominant to a diminished chord? Commented Mar 14, 2023 at 20:43
  • I don’t totally agree with your first sentence. I also feel like I’ve seen a specific ii - V - i° progression that would answer this question but I can’t find it right now. Commented Mar 14, 2023 at 21:06
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You can certainly include viio in a 'cycle of 5ths' type progression. Whether you'd refer to the preceding chord as a 'secondary dominant' depends on how far you're prepared to stretch that definition! I doubt viio is likely to be heard as a tonic, even the most temporary kind of one. So my practical answer to "Is there such thing as a secondary dominant (or 2-5) of the 7th degree?" would have to be 'no'.

I would be delighted, however, to see a musical demonstration proving me wrong! But let's see some actual music, the theoretical nit-picking has run its course I think!

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