Home, Away, and Diminished

[@urbster1]

this is so great. i love these mini lessons, thanks so much!!

[@Ambidextroid]

Interesting! The D-6 is like unaltered V9, the F-6 is iv-6 (or with G in the bass, Gb9sus4), the Ab-6 is like altered Vb9b13. But the B-6 I find unconvincing. While the other three examples are ubiquitous, this one I don't know a single example of, its the only one that doesn't work with G in the bass, and the only one that doesn't resolve to C. It can work as B-6/E (E9) to C6/A (A-7), but then its resolving to A minor rather than C major. The same thing applies to the ii-Vs that are implied by these chords: D-7 | G7 | C is your typical ii-V, F-7 | Bb7 | C is the backdoor, Ab-7 | Db7 | C is the tritone sub, but B-7 | E7 | C doesn't register to my ears as a functional resolution. At a stretch you could call it a deceptive cadence to C rather than A-, but my ears don't hear it as a deceptive cadence either. I am of the opinion that the resolution of F-6 to C is because of the backdoor resolution, and Ab-6 to C is because of the tritone sub resolution, but the way these resolutions work are quite different and the fact thay they are minor 3rds apart is a coincidence, so that completing the apparent sequence with B-6 is a fallacy - or at least expecting it to behave like the others is a fallacy. I believe the F-6 to C relationship can be explained by a combination of the deceptive cadence to the relative minor and the picardy third resolution. My way of understanding it is as follows: as there is ambiguity between the tonal centres of C minor and Eb major, a chord progression in Eb major can resovle to a C minor chord - for example F-7 | Bb7 | C-7 instead of F-7 | Bb7 | Eb, so called a deceptive cadence. And any chord progression in C minor that resolves to the tonic can resolve to C major instead, for example F-7 | Bb7 | C, so called a picardy third resolution. That explains the resolution of iv-6 to I, or bVII7 to I, or any number of other progressions that employ modal mixture between C and Eb. The Ab-6/G on the other hand is explained by the tritone substitution. Seeing as the tritone in Db7 resolves both to Gb and C, it opens a window between these two keys. The connection is not as strong as between C and Eb, as there are several avenues between Eb and C, whereas with Gb and C one has to pass through Db7. Placing G in the bass gives us the Gb9B13, which is really just a suspension of Db7 over G. The fact that these resolutions are minor 3rds apart does open up many possibilities including the central diminished chord, octatonic patterns and the family of dominants and so on, however I don't think the minor 3rds connection explains where the resolutions come from, I think it is just a coincidence that we can take advantage of. So I don't think it jsutifies or demands a resolution of B-6 or E7 to C. By the way I don't mean to suggest that you didn't know any or all of this already - I'm sure none of this is news to you, I just wanted to make sure I was making a comprehensive argument. I see and hear a lot about these minor 3rd relations and people use it to justify a resolution of Eb7 to C, which I have never really been on board with. I would be interested to know your thoughts.

[@KazTrumpet]

Thank you for your insightful comment! Please keep in mind that I treat 1(6) and all its inversions a home chord. Not a 1 triad. 1(6) 1(6)/3 1(6)/5 1(6)/6 These are all home chord to me. I hear four notes together as a unit. And all of the inversions are valid home chords. What I mean by this is : -1(6) is not 1 triad with the 6th added -1(6)/6 is not 6- triad with ♭7 added *triad is not the base. The four note chord is the base. This makes home feel like a mix of C major and A minor if I translate it into a triad language. 1(6), 1(6)/3, 1(6)/5, and 1(6)/6 are all home. And if you heard 7-6/3→ 1(6)/6 cadence convincing enough, then we’re on the same page! That being said, From a traditional way of thinking, Everything you’re saying makes sense to me. And I agree that 7-6/3→ 1(6) cadence is a less satisfying resolution than other options. I believe it is mainly due to the weak bass motion. My hierarchy of bass motions for a cadence is : Strong 5 → 1 (↓ fifth) 4 → 1 (↑ fifth) ♭2 → 1 (↓ semitone) 7 → 1 (↑ semitone) 2 → 1 (↓ tone) ♭7 → 1 (↑ tone) 3 → 1 (↓ third) ♭6 → 1 (↑ third) Weak 3 → 1 bass motion for a cadence is one of the weakest ones. For me, 4-6/3 → 1 is the most convincing cadence for 3 → 1 bass movement. However, 7-6/3 → 1(6)/3 is convincing enough to my ears as well. 7-6 → 1(6) and with any of the strong bass motions work in my opinion. 7-6/5 → 1(6) ✅ 7-6/♭2 → 1(6) ✅ My theory is that all of the away chords (2-6, 4-6, ♭6-6, 7-6) can be paired up with any of the 12 possible bass note. And they can all cadence to 1(6). If ♭6-6/5 → 1(6) makes sense to you? What about ♭6-6 → 1(6)？ This has a weak bass movement just like 7-6/3 → 1(6)

[@Ambidextroid]

@@KazTrumpet I just can't hear vii-6/V → I(6) or vii-6/♭II → I(6) as a resolution at all personally! The maj7th in vii-6/V sounds like it's fighting any dominant function. I think this note in particular (the ♭V scale degree) is the culprit. If you look at it from the point of view of the diminished chord, you can see how this note would cause problems: in the key of C, if you start with Ab dim7 and raise either of the notes Ab or D by a semitone, you still maintain the F-B tritone that implies a G7. If you raise the note B by a semitone that's not a problem because then you have F-C implying a sus (or ii) chord. But if you raise the note F, you are losing the most fundamental note of the G7. vii-6/♭II sounds like it could be a iv-6/V in the key of Gb which is something, but still doesn't register to me as a resolution to I(6). ♭V is the only scale degree I don't think works as an alteration on a V chord. ♭vi-6 → I(6) does make some sense to me as a resolution because it's like a iv-6 in the key of Eb which wants to resolve to Ebmaj, and thus could also resolve to Cmin, so it can resolve backdoor-like to Cmaj instead. Then you could almost think of it as a double backdoor, like the backdoor of the backdoor, which ends up being the same key as the tritone sub since it's removed from the original key by two minor thirds. To apply that logic to the vii-6 chord, it would have to be a triple backdoor, or a backdoor to the tritone sub, which I guess is too many levels of abstraction for my brain to register as a functional resolution. I see what you mean by the weak bass motion stuff, but I'm not convinced that it's the primary explanation for why the vii-6 isn't as strong as the others. For example I hear ♭vi-6 → I(6) as a much stronger resolution than vii-6 → I(6) despite having the same strength bass movement.

[@KazTrumpet]

@ Another explanation is Negative Harmony. 5(7) has the same amount of pull to 1(6) as 4-6 does to 1(6). In other words, 4-6 is the reflection of 5(7) in the key of 1(6) 5(7) ≒ 4-6 Same can be said for ♭2(7) ♭2(7) ≒ 7-6 7-6 is the reflection of ♭2(7). 7-6 has the equivalent pull to 1(6) as ♭2(7) does to 1(6). This is the most satisfying explanation I know for why 4-6 → 1(6) works. More satisfying than your double backdoor explanation. I just think.. if you are able to stretch you’re thinking that much for 4-6 → 1(6), what’s holding you from stretching a little bit more for 7-6 → 1(6)? (It’s the ♯4 note rubbing against 4 isn’t it? The thing is you don’t need the 4. Instead of 4 → 3 resolution you have ♯4 → 5 resolution.) And another point you made about the sus, I would say is If you are at peace with 4-6/5 → 1(6), that means you accept the suspended 4th of 5(7). ♯4 note is exactly the same. It’s a suspended major 7th. I think the fundamental difference between you and me is how we define cadences. For you, it’s a 5 → 1 resolution and coming up with explanations to fit the 5 → 1 model. I get where you are coming from because I used to think that way too. But that way of thinking is limiting as you are already having to bend rules for sounds that you can hear but not quite explain with the model. For me, I think of cadences more gesturally. It’s tension and release. Tension → Release So I don’t even define the tension chord as a dominant. I call it away chords. Love your comments. It makes me really think about it.

[@KazTrumpet]

@ I actually need to explore 5(7) chords more. In jazz, I rarely hear a straight 5(7) chords resolving to 1. Unless it’s in this inversion 5(7)/4 → 1/3 or something. I also think major scale has tension and release built-in to it, and it doesn’t feel at home. Pentatonic scale feels like a home scale to me.

[@Ambidextroid]

@@KazTrumpet When I am considering cadences I am always using my ear first, and trying to find the most intuitive resolution. When I hear iv-6 my ear tells me that I am in a minor key and the most intuitive point of resultion is i (minor), as a plain old minor plagal cadence. But seeing as major chords are more stable, you can resolve minor harmonies to major tonics, with the picardy third (which of course they were doing way back even when tonality was in its infancy). To be clear, the way I see iv-6 → I(6) resolution is not a "double" backdoor, just a regular backdoor - in other words, its just a plain old picardy third. I agree that the double backdoor idea really is a stretch, and thinking about it now I can say I don't believe it works. However in that case I was referring to ♭vi-6 → I(6) which can already be explained as an inversion of the ♭II7 → I(6), i.e. the tritone sub. No double backdoor needed. Personally I think explaining iv-6 → I(6) as a minor plagal cadence with a picardy third, and ♭vi-6 → I(6) as a tritone sub with the 5th in the bass is more satisfying than invoking negative harmony! And doesn't require "bending the rules". I don't mean to say that my explanation is "why it works" and yours is "not how it works" or anything like that, I don't even believe there necessarily is a "why". My thoughts are not an attempt to explain where the cadence comes from, but rather to find some tonal framework that allows me to explore related sounds. If I think of an F-6 → C(6) as a picardy third resolution then I can see that F-6 is contained in the E♭maj tonality, and it tells me that really anything in E♭ can resolve to C. This then then tells me that, for example, if I ever see a ♭VI maj7 chord (in this case A♭maj) then instead of thinking of it as borrowing the I chord from A♭, I can think of it as borrowing the IV chord from E♭, which lets me use a whole bunch of ideas and language that I'm already familiar with from other contexts. For example if I was playing a tune like Night and Day with the progression A♭maj → G7 → Cmaj, it looks like ♭VI → V → I in the key of C, but it could also be a IV → III7 → vi progression in the key of E♭, but using a picardy third for the final chord. I know all sorts of ways to move from IV to III7, so I can apply those movements to ♭VI → V, hence the ♭VI is more a lydian sound than an ionian sound. Now I can think of a ♭VI → V as essentially a variation on the backdoor progression. So I can at least say that I find my explanation of iv-6 → I(6) as a picardy third resolution to be useful as a framework for improvising. If you use negative harmony as your framework for understanding iv-6 → I rather than seeing it as a piardy third, you end up with a whole different set of explanations and options that come from it, and in my opinion this approach is more limiting. While my picardy third explanation suggests the iv-6 → I is functioning like a plagal cadence, the negative harmony explanation would suggest that its functioning as a negative counterpart to a perfect cadence. With the picardy third explanation, iv-6 has more of a subdominant function (which can resolve to I as a plagal cadence), your explanation suggests it has more of a dominant function. With my framework you could have either iv-6 → V → I as a subdominant to perfect cadence OR iv-6 → I as a plagal cadence , while the negative harmony approach suggests iv-6 → I already is like a perfect cadence, and a negative harmony version of a IV → V → I would be something like v-♭6 → iv-6 → i which just doesn't register to my ears as a functional progression. When it comes to negative harmony, I have never been conviced. I have always seen it as an interesting pattern, but I haven't seen an example of a progression or cadence (that my ears find satisfying) that can be explained by negative harmony but not also explained by normal harmony. If you have any good examples I would genuinely be really interested! But the only negative chord substitution that my ears can register is the iv-6 subbing for the V, and I think that can already be explained by normal tonality. Now as for the sus thing, I disagree that those can be seen as the same thing! The reason I am happy to suspend the 4th in a V chord is because it's part of the findamental tritone to maj third resolution. The C major scale has a semitone between B and C, and between E and F. If we accept that resolution my semitone is the strongest, and that resolution by contrary motion is the strongest, then we can see that there is only one place in the C major scale where both of these things are possible at once - the tritone between F and B resolving by contrary motion to the maj3rd/min6th between C and E. There are only two triads that contain the notes C and E: Cmaj and Amin, hence why ionian and aeolian are the only two modes that really act as tonal centres. In my opinion this tritone to third resolution is the most findamental aspect of tonal music, so the notes E, F, and B, C are the most important notes for resolution to the tonic. I accept the suspended C in a Gsus chord because that C still implies the C major tonality. The C wants to resolve down by semitone to B to form that fundamental B-F tritone. If you suspended the 7th instead, I would say that you wouldn't raise it to F#, you would drop it to E. Then the E wants to resolve up by semitone to the F forming the B-F tritone, and you maintin those important semitones (EF and BC). The reson I think F# or G♭ doesn't work here is because you end up with the fundamental semitones in this resolution being F, G♭ and B, C. And these two semitones can't exist together in any diatonic tonality. You end up with a 4th resolving to a 5th rather than a tritone resolving to a maj3rd. I do accept that the ♭5 scale degree CAN work over a V chord, for example B7/G resolving to Cmaj is a beautiful resolution, but that's quite different because its no longer like a V7 → I in the key of C, it's more like a I → IV in the key of G, and takes advantage of the ambiguity between the I and IV chords. In this case, the B7 is like a III7 chord resolving up to IV. I'm so sorry for that incredibly long comment lol, once I start talking about my thoughts on music I can't stop. I don't necessarily need to be able to understand how a resolution works to accept that it is a legitimate resolution, at the end of the day the ear is king - yet, I just cannot hear the vii-6/V resolving to I, even if there is some way of explaining it... Explanations like negative harmony seem like logical frameworks but they just don't agree with my ears. But stuff like picardy thirds, tritone subs and secondary dominants have been enough for me to understand most anything that my ears tell me is right.