Half diminished vii/x chords

feature requests
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In the current version of Hookpad vii/x chords are always fully diminished. While I understand that viio7/x is a bit more common, I come across quite a lot of viiø7/x, too.

I think it’s very unfortunate that the only way to transcribe these chords is to either label them as borrowed from a parallel mode or wrongly label them as viio7/x.

Transcribing a chord as ♯ivø7(lyd) instead of viiø7/V implies that it was arbitrarily borrowed from lydian without serving any particular function. I don’t think that is in line with Hooktheory’s emphasis on functional harmony.

My suggestion would be to implement a button that lets you switch between fully diminished and half diminished chords when using the vii/x feature, or at least make viiø7/x available via the search bar.

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If you want to enter a secondary iiø7/x V7/x (a minor 2-5), you can search for ii/(anything in major), insert the result, flat its fifth, then change the target chord manually if it didn’t happen to be from major. Secondary iiø7s are pretty common in my experience, and this at least gets you something resembling the notation with the correct meaning.

Not sure why only major target chords are in the search database – another bug report I’ve been meaning to write eventually.

Sadly, only major scale secondaries are in the search database too, with the unfortunate exception of the 7 chord, so searching for vii/… only gets you the fully diminished version. Your only option for a viiø7/x is some convoluted notation.

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I wasn’t actually referring to secondary ii chords with this request, but I’m glad you brought them up! Since there isn’t a button for them in the Inspector I was just assuming that it wouldn’t be possible to find them via the search function either.

I actually think it’s really weird that there’s a button for something as rare as a secondary IV chord, but not for the secondary ii chord which is obviously super common.

I’m not even sure if I’ve ever seen the IV/x function being used in a tab where it actually made sense. Usually when I see them it’s stuff like IV/IV instead of bVII, which just doesn’t make much sense, especially if there isn’t even a diatonic IV chord in the progression. I would even go as far as to say that since these chords don’t have any strong resolution tendency on their own, they only make sense if they’re followed by a secondary dominant.

In any case, thanks a lot for the reply! I’m glad that I finally know how to notate secondary ii chords. The only thing that really bothers me about manually flattening the 5th is that it creates this really absurd roman numeral - iiø7(♭5)/x. I might actually write a bug report about that.

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Yeah, IV/IV chords are pretty rare, but not unheard of. In case you’re curious, here are a few I keep in my notes as good examples of plagal progressions. Some even have a IV/♭VII (♭III) chord:

Many of these are analyzed in mixolydian to avoid secondary IVs, but I still think of them as plagal.

I wish any chord from any mode could be used as a secondary chord, not only to access the wide variety of common cadences, but to be able to experiment and come up with new ones. Here are a few more cadences that are impossible to notate correctly when used as secondaries:

  • ♭VI ♭VII I (mario)
  • IV iv I (minor plagal?)
  • iv7 ♭VII7 I (backdoor)

Others like ♭II6 V i (neapolitan) are sort of possible using the new tritone substitution feature, but it only halfway describes the intent. A secondary phrygian II would be a better option if it were available.

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@neurozero
Thank you for providing all of these examples, but honestly I have to disagree about them being secondary IV chords. The purpose of secondary harmony is tonicization, but in my opinion a plagal cadence is much too weak of a harmonic movement to be suitable for tonicization.

Playing I - bIII - bVII doesn’t shift the tonal center to bVII, it just evokes the parallel minor mode. Unlike with a secondary authentic cadence where we retroactively recognize the functional relationship once the tonicized chord is being played, with secondary plagal cadences our brain only recognizes how the two chords belong to the same key. There is no resolution happening. So in my opinion labeling a bIII as IV/bVII doesn’t add any useful information, but instead obscures the fact that this chord is borrowed from the parallel minor mode.

The 4th relationship becomes quite obvious when you play the secondary plagal cadence back to back with a diatonic plagal cadence like in “Leave A Light On” (IV - I - bIII - bVII), but I’m not sure if this really justifies calling it a IV/bVII. I mean you wouldn’t label an ascending fiths progression as IV - IV/V - IV/ii - iv/vi - iv/iii, would you?

In my opinion secondary subdominant chords only make sense if they’re followed by a dominant chord. The iib5 might be an exception in some cases because of its inherent tension, but I haven’t played around with that enough to confirm that. Secondary mediant chords don’t make any sense if you ask me.

All of that being said, I’m not claiming that my perspective is correct and yours is incorrect. I’m just sharing my thoughts on this topic. :slight_smile:

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I totally agree that tonicizing anything with a IV/ is kinda impossible. IV has pretty much no dominant function, but I still think secondary IVs can be useful sometimes.

Haha this is kind of a crazy looking example, but yeah, I might, if the next chord were a iii or a plausible substitute, just as I might use V - V/IV - V/♭VII - V/♭III - V/♭VI for a descending fifths progression if ♭VI (or a plausible substitute) were the next chord.

Consider I - V - II - VI in the chorus from Head Over Heels by The Go-Go’s. It is just another rotation of IV - I - ♭III - ♭VII from Leave A Light On or I - V - IV/IV - IV in the Chord Crush theme, but when written this way, VI is not even available from any modes to borrow from. It could be written I - V - V/V - V/ii but that’s weird too. Maybe I - V - IV/vi - IV/iii does sorta make sense here since iii and I share two tones?

How do you explain the forward motion of progressions like this if not for the plagal cadence? The only non-plagal movement in these chord loops is effectively VI - I in all three of them, but VI is not remotely dominant. It might be a deceptive plagal cadence, if there is any such thing.

Thanks for checking out my examples, although I’m not sure they’re even that great now that I’m looking around again and finding way more of them. This conversation has definitely made me think.

In general I prefer secondaries over substitutions when possible, mostly because they often provide more insights. Of course it’s rarely the only way to describe a chord. One of the great things about music is the multitude of ways we can describe the same thing, and I love it when a songs use this to switch perspectives, creating interesting pivots that break expectations.

Last thing – sorry for the wall of text – I’m not sure why you brought up secondary mediant chords, maybe I missed a reference somewhere, but they do make some sense when considering negative harmony. It suggests both iii7 and III7 are dominant, with III7 being a little stronger of the two, though I don’t know of any examples in the wild. And back to plagals, it also suggests iv is dominant, but not IV.

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@neurozero
If we agree that secondary IV chords are not suitable for tonicization on their own, then it’s quite obvious that labeling chords as such although they’re not part of a secondary IV - V is a misuse of the concept of secondary harmony. See the definition of a secondary chord:
“A secondary chord is an analytical label for a specific harmonic device: the use of diatonic functions for tonicization.”

Roman numerals display how different chords relate to the key of a piece of music. You seem to be very interested in how neighbouring chords within a progression relate to each other, but I don’t think Roman numeral analysis is the appropriate tool to explicitly convey that sort of information. If we start labeling diatonic chords as secondaries, we’re essentially leaving the realm of tonal harmony with our analysis. You might be interested in JJay Berthume’s Harmonic Relativity approach. It completely abandons the concept of tonal harmony and really hones in on the chord to chord realtionships within a progression.

Funny that you bring up VI chords. I’ve been quite fascinated with VI and VII chords lately. I’m not exactly sure what point you’re trying to make with the example of Head Over Heals, though. It is an interesting fact that these three progressions are rotations of each other, but Head Over Heals is clearly in D. We can’t just arbitrarily analyse it in another key, just so we don’t end up with weird supermodal chords. Labeling the first three chords as IV/V - IV/ii - IV/vi doesn’t explain the VI chord at the end either.

If we insist on analysing this progression through the lense of functional harmony, I would think of it as a retrograde progression in which case I - V - V/V - V/ii would be the appropriate label. I don’t think this is a good approach though and we’re much better off accepting the fact that we’re sometimes leaving the realms of functional harmony when analyzing 20th century Pop music.

If you’re implying that the chromatic harmony in this song only works because of the plagal relationships between the chords I will just point you to the solo section where the VI chord is sandwiched between bVII and V and it still sounds just as good. As for the “forward motion” aspect - I don’t think there’s anything special about plagal relationships. I think how much “momentum” a progression creates is mostly dependent on how much overlap there is between neighbouring chords. I - vi feels rather calm and static, whereas I - IV has a lot more energy, but you can get the same effect from progressions like I - ii or I - bVII. I would even say you get the same effect from chromatic mediant relationships like I - bVI.

Feel free to share more examples if you think you’ve found better ones. Would be intersting to see if you could still convince me in the end haha. You don’t need to apologize for writing so much. I’m a huge music nerd myself and I love talking about this stuff.

I brought up secondary mediants, because you said you would like to have all chords available as secondaries. If we assume that any chord containing at least 2 unstable scale degrees automatically serves dominant function, then a iii7 would be a viable dominant substitute, but I don’t think that theory holds up in practice. I agree that iv is moderately dominant in major keys, maybe III7 too, but iii7? No way. I generally think that negative harmony is more of a gimmick than anything else. It’s fun to play around with and it can certainly be very inspiring, but I don’t think it’s useful for serious music analysis.

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So a secondary IV - V is ok but a secondary IV alone or in sequence is not? I guess I could get on board with that. I’m not saying I won’t still abuse the notation, but I’ll be thinking about this while I do it! I also still think secondary options should be unrestricted, both for extended tonicizations and to access the various cadences idiosyncratic to each mode.

My ideal Hookpad would let you enter chords in whatever way you like, whether a secondary from a specific mode, raising or lowering a whole chord by any interval, negating a chord, or raising or lowering any tone by any interval, including its root, third, and seventh, as well as allow stacking of operations. It would then suggest a list of equivalent simplified names you could choose to either replace the convoluted way you found the chord, or display it on a second (or third) line as an alternative name that highlights different harmonic perspectives or modulation opportunities. This would let you easily enter harmonic relatives, extended tonicizations, planing/side slipping, various forms of diminished chords, etc without having to think up it’s canonical name or click on 100 different things, and the app will do the heavy lifting, reducing it down like one might an algebraic equation.

With Head Over Heels, I think I was just pointing out that modal mixture doesn’t always work to describe these sorts of progressions. If the stack of plagals really is incidental, I don’t think harmonic relations fully explain them either, since as you point out this one does have a well defined key center. Maybe its just because we tend to hear the first chord as the tonic, but I kind of like your retrograde progression explanation too. Also relating harmonic momentum to the number of tones that change - I’d never considered that before but it makes a lot of sense, in fact it seems kinda obvious now that you’ve pointed it out!

I learned of harmonic relativity here, where he calls it chord relationships. He also provides a couple tables where he attempts to describe each interval for major and minor chords. Even though both Berthume and Berkemeier say each one is subjective, their descriptions still seem to agree, and Berkemeier’s extended list also seems about right to me. I’d love to see a list that includes augmented and diminished chords, and I’m curious if anyone has explored how sevenths combine – whether it is a union or intersection of emotions, whether the upper or lower triad is more significant, or if it is even more nuanced than that.

As for dominant substitutes, I think iii7 totally works. It’s just a Vadd6 with the 6 in the bass. It just isn’t as useful since it shares so many tones with its target, and I probably wouldn’t use it myself with so many better options. From what I know of negative harmony (pretty much only this), dominant chords must have at minimum one unstable tone and one leading tone, and the presence of a modal tone indicates a tonic chord. iii7 then is both dominant and tonic, which I think describes it pretty well.

Here’s a list of the rest of the dominant chords, as predicted by negative harmony. I find it curious that the remaining columns (hollow, avoid, stable, and modal) can be arranged to display this sine wave shape, and that Locrian, Phrygian, Aeolian, Ionian, and Lydian each have three dominants while Dorian and Mixolydian have none, though I have no idea if these observations are significant in any way:

​█▂█▂██▂█▂█▂▉█▂█▂██▂█▂█▂▉█   UL   HASM
​ •   ⋆  ⋆  ⋆ •   ⋆  ⋆  ⋆    1&   ⋅1⋅⋅    ♭II7
​⋆•   ⋆  ⋆   ⋆•   ⋆  ⋆   ⋆   11   ⋅1+⋅    ♭IIΔ     Loc  Phr
​⋆ •  ⋆  ⋆   ⋆ •  ⋆  ⋆   ⋆   21   ⋅⋅+⋅     iiᶱ7    Aeo
​  ⋆ •  ⋆   ⋆  ⋆ •  ⋆   ⋆    +1   ⋅⋅11    iii7     Ion  Lyd
​  ⋆ •   ⋆  ⋆  ⋆ •   ⋆  ⋆    +2   ⋅⋅⋅1    III7
​   ⋆ •  ⋆  ⋆   ⋆ •  ⋆  ⋆    12   ⋅⋅⋅+     ivᶱ7
​⋆  ⋆ •  ⋆   ⋆  ⋆ •  ⋆   ⋆   11   ⋅⋅1+     iv7     Loc  Phr  Aeo
​  ⋆  ⋆ •   ⋆  ⋆  ⋆ •   ⋆    &1   ⋅⋅1⋅      V7     Ion
​  ⋆   ⋆•   ⋆  ⋆   ⋆•   ⋆    11   ⋅+1⋅      VΔ     Lyd
​  ⋆   ⋆ •  ⋆  ⋆   ⋆ •  ⋆    12   ⋅+⋅⋅    ♭viᶱ7
​ ⋆   ⋆  ⋆ •  ⋆   ⋆  ⋆ •     1+   11⋅⋅   ♭vii7     Loc  Phr
​  ⋆  ⋆  ⋆ •   ⋆  ⋆  ⋆ •     2+   1⋅⋅⋅   ♭VII7     Aeo
​  ⋆  ⋆   ⋆ •  ⋆  ⋆   ⋆ •    21   +⋅⋅⋅    viiᶱ7    Ion
​  ⋆   ⋆  ⋆ •  ⋆   ⋆  ⋆ •    11   +1⋅⋅    vii7     Lyd
​█▂█▂██▂█▂█▂▉█▂█▂██▂█▂█▂▉█   UL   HASM

Key:

          +  &     Δ = major 7 (not tritone substitution!)
triads    0  1     Stable    P1 P5    Modal   m3 M3    Leading  m6 M7     
sevenths  1  2     Unstable  M2 P4    Hollow  M6 m7    Avoid    m2 TT

I’m curious what has piqued your interest in VI and VII? Here are the rest of the supermodal chords, which I also find pretty interesting. I couldn’t figure out any clever arrangement of the columns here, so I just left them the same as above. Note that a couple of these (♭II, II, ♭V) are available as triads, just not as the specific seventh listed:

​█▂█▂██▂█▂█▂▉█▂█▂██▂█▂█▂▉█   UL   HASM
​ •  ⋆  ⋆   ⋆ •  ⋆  ⋆   ⋆    ⋅+   ⋅111    ♭iiᶱ7
​ •  ⋆   ⋆  ⋆ •  ⋆   ⋆  ⋆    ⋅&   ⋅1⋅1    ♭ii7
​ •   ⋆  ⋆  ⋆ •   ⋆  ⋆  ⋆    1&   ⋅1⋅⋅    ♭II7
​ ⋆•   ⋆  ⋆   ⋆•   ⋆  ⋆      1⋅   1&⋅⋅     IIΔ
​ ⋆ •  ⋆  ⋆   ⋆ •  ⋆  ⋆      ⋅⋅   1&⋅1   ♭iiiᶱ7
​  ⋆ •   ⋆  ⋆  ⋆ •   ⋆  ⋆    +2   ⋅⋅⋅1    III7
​   ⋆•   ⋆  ⋆   ⋆•   ⋆  ⋆    ⋅2   ⋅⋅⋅&    IIIΔ
​   ⋆ •  ⋆  ⋆   ⋆ •  ⋆  ⋆    12   ⋅⋅⋅+     ivᶱ7
​ ⋆  ⋆ •  ⋆   ⋆  ⋆ •  ⋆      ⋅⋅   12⋅+     ♭v7
​ ⋆  ⋆ •   ⋆  ⋆  ⋆ •   ⋆     ⋅⋅   12⋅+     ♭V7
​  ⋆   ⋆ •  ⋆  ⋆   ⋆ •  ⋆    12   ⋅+⋅⋅    ♭viᶱ7
​   ⋆  ⋆ •  ⋆   ⋆  ⋆ •  ⋆    ⋅2   ⋅+⋅1    ♭vi7
​ ⋆  ⋆  ⋆ •   ⋆  ⋆  ⋆ •      ⋅⋅   11+1     VI7
​ ⋆  ⋆   ⋆•   ⋆  ⋆   ⋆•      ⋅+   11⋅1     VIΔ
​ ⋆  ⋆   ⋆ •  ⋆  ⋆   ⋆ •     ⋅+   11⋅1   ♭viiᶱ7
​   ⋆  ⋆  ⋆ •   ⋆  ⋆  ⋆ •    ⋅1   11⋅+    VII7
​   ⋆  ⋆   ⋆•   ⋆  ⋆   ⋆•    ⋅1   11⋆+    VIIΔ
​█▂█▂██▂█▂█▂▉█▂█▂██▂█▂█▂▉█   UL   HASM

I can even provide a list of all 48 diatonic seventh chords if you like! I tend to agree though about the usefulness of negative harmony though. Other than finding questionable alternative dominants, I’m not really sure what else to do with it.

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@neurozero
There’s absolutely nothing wrong with abusing theoratical concepts for private purposes, but when we’re submitting an analysis to a public platform I think we should stick to the generally agreed upon definitions of harmonic devices. :slight_smile:

Interesting - I didn’t realize only two scale degrees are considered to be unstable in negative harmony. I haven’t encountered this way of classifying scale degrees before, but to be honest I’m not a fan. I mean “avoid”? What year are we in? 1720? And what is hollow supposed to mean? I personally consider every note that is a half step away from any note within the tonic triad to be unstable. For minor keys that would include m2, M2, d4, A4, m6 and M7. For major keys that would include m2, A2, P4, A4, m6 and M7. I think it’s really redundant to distinguish between unstable notes and leading notes. Also I just watched a small section of that 12tone video and I couldn’t disagree more about the 3rd scale degree not being a point of resolution. Dominant seventh chords wouldn’t be a thing if that was the case.

I think I stumbled upon VI and VII chords when I started delving more into 20th century Pop music, especially the 60s. I find them rather refreshing as I’ve gotten pretty used to the sound of the usual modal interchange options. I think what makes III, VI and VII special is that they provide a somewhat familiar sound due to their frequent use as applied dominants to diatonic chords, so they’re not nearly as jarring as most other supermodal chords, but still create a pleasant surprise when they don’t resolve as expected. I would even put II into the same category, since it’s used as V/V much more often than as a modal interchange chord, so it provides the same surprising effect when it doesn’t resolve to V.

Also I think it’s really fascinating how playing a major chord instead of the diatonic minor option actually introduces a certain amount of bitter sweetness into the progression, because it essentially tonicizes a minor chord (with the exception of II), even if it doesn’t resolve that way. I also just love the fact that there’s just no logical explanation for these chords from a tonal harmony perspective - neither functionally nor modally. They just work due to habituation through decades of functional harmony.

♭v and ♭vi are pretty cool as well, although I’ve gotten a bit tired of them by hearing them so much in certain genres. I don’t really see any use for the rest of the supermodal chords in a tonal harmony context though. Sure, some of them might occur from time to time when techniques like planing are being used, but I don’t think it’s justified to call those supermodal, since they’re simply functioning as neighbouring/ passing chords in that context.

You can get pretty interesting results when applying negative harmony to common chord progressions. There’s a whole youtube channel dedicated to negative harmony covers of popular music. At the very least these are pretty entertaining, but some of them are actually kind of inspiring. But as I said it’s more of a gimmick for when you’re bored or in need of inspiration.

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