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Primer on Diminished Passing Chords

Discussion in 'General Instruction [BG]' started by FretlessMainly, Jan 20, 2014.

  1. FretlessMainly

    FretlessMainly

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    **NOTE** If you have no knowledge of theory, then this post will likely make your brain hurt, but if you have a working knowledge of diatonic chord function and the ability to construct or analyze chords, then perhaps this may be of interest.
    ____________________________

    I thought I'd add a quick discussion of two concepts that get discussed here on occasion: diminished chords and chord substitution. I did a search and I didn't find any recent threads on this topic, but my apologies if it has been discussed before.

    A "passing" chord can be viewed as a chord outside the key that functions to connect two chords in the key. One common example is that of the diminished 7th (dim7) chord that chromatically connects two chords in the key. Keeping it simple in C Major, let's look at an equally basic chord progression: I ii V I. In C Major, we have:

    | CMaj7 | Dmin7 | G7 | CMaj7 |

    We can use a passing dim7 chord to flavor this up a bit:

    | CMaj7 | C#dim7 | Dmin7 | G7 | CMaj7 |

    The questions that arise are generally these:

    1. Why did I choose to locate the chord where I did? and
    2. Why does this chord "work?"

    The most basic answer to question #1 is that chromatic root motion can be an effective tool (but more on how this particular use of the dim7 chord need not necessarily be viewed as chromatic root motion).

    The answer to question #2 lies in the relationship of the dim7 chord to the Dominant 7th (Dom7) chord.

    The dim7 chord is constructed from the root with three successive intervals of a minor 3rd. Starting on C# as in my example, doing this gives us this:

    C# E G Bb (note that mixing sharps and flats is appropriate in this context, because if you go to the key of C# Major to determine which chord tones are altered, you'll find that a dim7 chord consists of the Root (C#), b3 (E), b5 (G), and bb7 (Bb). Now, someone may say that the bb7 should be Cbb, not Bb. OK, go knock yourself out; sure, technically you are correct (but either way, we must mix sharps and flats in this case).

    The dim7 chord is unique (I believe it's unique in this respect) in that every note in a dim7 chord is also the root of the chord. By this I mean that there are only three dim7 chords and each serves as four "different" dim7 chords. In other words, our C#dim7, which contains C# E G and Bb contains the exact same notes as Edim7, Gdim7, and Bbdim7. The next four dim7 chords are found by moving up a half-step from any of these notes while the last set of four are found by moving up one more half-step.

    In any case, let's address question #2: The reason why this C#dim7 works so well in this simple progression is because it is nearly identical to the secondary Dominant of the ii chord (Dmin7). A secondary Dominant is a chord that is outside of the key, but functions as a legitimate V7 that resolves to a chord that is in the key. Using our example, the A7 is a secondary Dominant of the Dmin7:

    | CMaj7 | A7 | Dmin7 | G7 | CMaj7 |

    Notice that the A7 slots in directly in place of our passing dim7 chord. Why? To answer this question, let's break down the C#dim7 and the A7:

    C#dim7: C# E G Bb
    A7: A C# E G

    The two chords have three of four notes in common. This is always a strong indicator of "Hey, I've got a good chord substitution possibility here." But what about the notes that are not common to the two chords? These notes are the Bb in the C#dim7 and A in the A7. At first glance, this may seem to be a problem; however, it is not. It turns out that the Bb in the C#dim7 chord is the b9 of the A7 chord (more correctly, the b9 (or b2) of the A Major scale from which an A7 chord can be evaluated). The A7 chord is constructed as 1 3 5 b7 of the A Major scale.

    The reason why the Bb is "beneficial" here is that the V chord when resolving to a minor chord is very often voiced as V7(b9). Thus, our C#dim7 effectively functions as a chord substitution for A7(b9) resolving to a Dmin7. The only note missing is the A natural.

    Thus, a dim7 chord can be used effectively as a substitution for a V chord that resolves to a min7 chord. The way I generally choose which dim7 chord is to base it on the b9 of the dom7 chord. This brings up my final point, to which I alluded earlier: using my method, if I want to add a substitution for the Dom7 chord in this progression I posted earlier (with the b9 extension added to the A7):

    | CMaj7 | A7(b9) | Dmin7 | G7 | CMaj7 |

    I would choose Bbdim7. Let's construct a Bbdim7 chord:

    Bb Db Fb Abb (or G). Note that these notes are enharmonically equivalent to C# E G Bb. It's up to you whether you want to emphasize the chromatic root motion (C C# D), thus thinking of the chord primarily as a C#dim7, or if you prefer to call it an Edim7, and Gdim7, or a Bbdim7. These are all voicings (or inversions, if you prefer) of the same chord.

    Sorry, longer than I expected. I hope I made myself clear.
  2. MalcolmAmos

    MalcolmAmos Supporting Member

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    Yes + 1,000. The study of how chords function and how we can use this to our advantage can keep us busy for the rest of our lives - well, for the rest of mine anyway. LOL.

    A recap. Both the V7 and the vii (m7b5) are both considered dominant chords. V7 wants to resolve right now. The m7b5 wants to resolve, but, being the minor leading tone diminished chord is not in a hurry to do so. If you want a more fluid movement use the vii chord.

    V7 if you want to resolve quickly.
    m7b5 if you want to use a turn-a-round to resolve to the tonic. vii-iii-vi-ii-V7-I OR if you want to move somewhere, in a fluid motion let the vii start the movement. The iii likes to move and the vi likes to tag-a-long with the iii. See how you could use that.

    As both the V7 and vii (m7b5) have the same task in life they can sub for each other. You decide if you want this done quickly or in a more fluid movement.

    Need a pull into the next chord? R-3-5-X. Let X be the V of the next chord. That V begs to get to the tonic root of the next chord. I can not do this on the fly and rely instead on the chromatic or diatonic run that Fretless talked about. But using the secondary dominant to pull you into the next chord is very effective.

    ii and IV both are sub-dominant chords thus the ii or IV can sub for each other, i.e. ii-V-I or I-IV-V - in both cases the sub-dominant wants to move to the dominant V chord.

    Yes, there is enough here to keep us busy for quite some time.
  3. Pacman

    Pacman Layin' Down Time Supporting Member

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    The m7b5 chord is *not* a dominant function chord. It is a ii chord in minor tonality, and functions as such. However this thread is talking about fully diminished (1 b3 b5 bb7) chords.
  4. the_stone

    the_stone

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  5. FretlessMainly

    FretlessMainly

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    I think I have the same answer for #1 and #3. The Cdim7 and the Cmin7(b5) both contain notes that resolve to the root or third of the Dmin7 from a half-step away, which is strong motion. The Cdim7 is really a possible reharm for Dmin7 since the chords have two notes in common (but it's not a really strong reharm):

    Cdim7 = C Eb Gb A
    Dmin7 = D F A C

    The Gb and the Eb in the Cdim7 resolve in downward half-step motion to the 3rd and root of Dmin7, respectively. The resolution would be much stronger if the half-step motion were counter to one another; in other words, one moved a half-step up and the other moved a half-step down (which is what happens with a V7 I). Same deal with the Cmin7(b5).

    As for #2, the chord you suggest is:

    A G Bb Db F, which reads to me as an A7(b9 b13), which would naturally resolve to a chord based on D, especially a Dmin(7).

    Well, a Bmin7(b5) is a possible reharm for a G7 chord, so it can function in that capacity. But agreed, its primary role is as the ii in a minor tonality. However, consider this:

    | Dmin7 | G7 | CMaj7 | and then reharm it this way:

    | Dmin7 | Bmin7(b5) E7(b9) | Amin7 | this is related to a deceptive cadence such as this:

    | Dmin7 | G7 | Amin7 |, so the whole bar of Bmin7(b5) E7(b9) serves a dominant function to the relative minor of CMajor.
  6. MalcolmAmos

    MalcolmAmos Supporting Member

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    Packman forgot we were talking about a major tonality.
  7. FretlessMainly

    FretlessMainly

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    I don't think so. It's true that the primary function of a min7(b5) chord is as the ii in a minor tonality. But playing a Bmin7(b5) on guitar, I can resolve it nicely to a CMaj7; it wants to go there. As you mention, it doesn't want to resolve as strongly as a G7 does, but with three common tones (the B and the F being the drivers) it is still dominant to a moderate extent. All that is missing is the circle of 4th/5ths root motion that you get with the G7.
  8. Pacman

    Pacman Layin' Down Time Supporting Member

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    I most certainly did not.



    Still going to disagree - Bm7(b5) is still functioning as a ii, to the E7(b9). (which is functioning as a dominant) If you take out the E7, to my ears it falls apart.

    I get what you're saying about the reharm of a G7, but it's more a rootless voicing to me, and still begs for the G.
  9. FretlessMainly

    FretlessMainly

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    Yes it's serving as a ii in a ii V to a i minor and yes it's a "rootless voicing" of a true Dominant chord. But it's at least 2/3rds of the important notes for establishing Dominance in a G7 (being to my ear, in order of importance, B and F and then........G). So it has dominant character, at least to my ear (and brain). I don't need the root so much. Maybe that comes, at least in part, from playing DB in a Jazz trio for several years where the pianist often omitted (if I recall what he told me correctly after some 14 years) the root in favor of the 9th and the 5th in favor of the 13th, particularly on Dom7 chords. That sound is very open and often ambiguous. When I felt of the mind to, I'd play the root, but often I'd play the root of the tritone sub to further muck up the waters - and often it sounded great. In that situation, a G7 chord would be voiced:

    Db in the bass, B F A E Which could be viewed as a partial voicing of a DbAlt7 (in other words, a Db7(#9#5) but no b9 or b5, which would really muddy the waters because those two notes are common to G7!).
  10. jblmusic1994

    jblmusic1994

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    The fully diminished C# to D is a dominant function. It would be considered a vii fully diminished 7 of 2 in C major.
  11. jblmusic1994

    jblmusic1994

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    Just because a chord isn't a dominant chord, doesn't mean it's role isn't dominant. V, V7 and vii fully diminished 7ths are all wanting to go immediately to I. Sometimes the vii will go to a V, but that's more of a prolonging of the dominant sound rather than a predominant or secondary dominant of V.
  12. davidhilton

    davidhilton Supporting Member

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    I think what Malcome may have meant to say is: In a major key, -7b5 chords have "dominant function" ...you know, like the I, iii, and the vi have "tonic" function...and the ii, and IV have sub dominant function...the V7 and the vii-7b5 have dominant function...thats what i think he meant...
  13. MalcolmAmos

    MalcolmAmos Supporting Member

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    As to the ii and IV being (having) sub-dominant tasks and the V7 and vii-m7b5 being (having) dominant tasks -- yes that is the point I was trying to make.

    Appreciate your post.
  14. MalcolmAmos

    MalcolmAmos Supporting Member

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    I think I probably was the first to do that. Yes, the 7th chord in the major key is a minor chord. Normally vii is all that is needed. I added the m7b5 to indicate it was a 1/2 diminished chord. Because we were talking about diminished chords, scales and keys. As to the - it was just a separation mark, perhaps (m7b5) would have been better.
  15. FretlessMainly

    FretlessMainly

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    Whenever discussing a min7(b5) chord, I refer to it as exactly that. In my mind, there's too much confusion generated when chords are discussed as triads rather than as four-note entities. In the triad world, the vii is a diminished triad, but the proper vii chord is min7(b5).

    You can't really discuss even something as basic as diatonic harmony without including the 7ths and since the primary function of a min7(b5) chord is as the ii chord in a minor tonality and one of the primary functions of the dim7 chord is as a substitution for a Dom7 chord, the concept of a diminished triad is confusing because I think it's best to learn harmonic theory in the context of how a chord functions. Thus, calling the vii chord "half-diminished" or referring to the vii triad as diminished clouds the functionality of the chord.
  16. Cycho

    Cycho

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    "The dim7 chord is unique (I believe it's unique in this respect) in that every note in a dim7 chord is also the root of the chord."

    I'm not quite sure what you mean here, but augmented chords are similar. One breaks up 12 semitones into four intervals of three semitones and the other breaks 12 semitones into three intervals of four semitones.
  17. the_stone

    the_stone

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    I can't tell who it is you're quoting, but what they're saying is that a diminished 7th harmony is symmetrical - just like with an augmented triad, the chord divides the octave up evenly into minor-third intervals.

    What's wrong is saying that every note is a "root of the chord." While every note that occurs in a fully diminished chord can function as a root, labeling a pitch as such is depended on the context in which the harmony is functioning and where it is resolving.
  18. the_stone

    the_stone

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    What is "negligent" is making a blanket statement saying that every pitch in a diminished 7th chord is a root note. What is correct is saying that a diminished chord is symmetrical, and that every pitch in a dim7 can function as the root note, depending on the surrounding context.

    I'm not sure why you feel the need to "accent" the root? Are the other pitches not as important, since in your words "they are also the root of the chord"?

    Would you care to divulge a theoretical text or other academic source you are referring to?
  19. davidhilton

    davidhilton Supporting Member

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    Just Berklee-speak...:cool:
  20. davidhilton

    davidhilton Supporting Member

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    Just tryin to keep it real playa!

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