PG Music Home Forums General Discussion Off-Topic Theory Question - Cdim7 in key of C

I have a music theory question. Not a trick question or anything, just wondering.

Most common chords in pop/jazz songs can be tied to the original key, so that they "make sense". For example, in the key of C, all the diatonic chords (Cmaj7,Dm7,Em7,Fmaj7,G7,Am7,Bm7b5) make sense in the key. And we can also add the chords for Cm (Cm7,Dm7b5,EbMaj7,Fm7,Gm7,AbMaj7,Bb7). Then we can add dominant 7 chords that "approach" chords that are a 4th above, adding these to the key of C... C7,D7,E7

Also, C#dim7 makes sense in that it is like an A7b9 without the root.

It helps to know how the chord fits in to the key. For example, if you can think of a C#Dim7 like an A7b9, it makes a progression like C6|C#dim7|Dm7|G7 in to a simpler one CMaj7|A7|Dm7|G7

But how about a chord like Cdim7 (or its similar cousins Ebdim7,F#dim7. They occur commonly in the key of C, but how are they related to the key of C?

For example, these are common chord progressions:

C | Cdim7 | Dm7 | G7
C | Ebdim7 | Dm7 | G7
F | F#dim7 | C/G | A7

Is the Cdim7 related to some other chords in the key of C in some way?

I've always read there are two ways to look at a dim chord.

One is as an incomplete dom7. So a Bdim is basically a G7 without the root. But... I'm not seeing that in your examples.

The other is as a passing chord with no tonal center. In that context, each note of the diminished chord can be considered equally valid root. So a C#dim7 (C#,E,G,Bb) could be written with any of the notes as the root. What really matters is the note that the chord is leading to - optimally you want the notes to move smoothly to the target.

That makes sense for where it's used for a brief duration, but again, not for your examples, where it's held for a whole measure.

So... That sort of leaves that dim chord to be explained some sort of passing chromatic motion.

With the first two examples:

C | Cdim | Dm7 | G7
C | Ebdim | Dm7 | G7

if you treat the Cdim6 as a Ebdim6, they're the same chord - a double chromatic suspension resolving to the Dm7:

C -> C
Eb -> D
Gb -> F
A -> A

With the last progression,

F | F#dim | C/G | A7

I see this as more a passing bass note, along the lines of:

Fmaj7 (Am/F) | F#dim (Am/F#) | C/G | A7

So I'm not sure they're "related" to the key of C, in the sense that they're diatonic. But I'm a dilettante, not a practitioner.

In many instances a Cdim7 in the key of C can be used as a D7, F7, Ab7 or B7. All dependent on what comes before, after and the melody. C///|Cdim///|Dm7 could become C///|Ebm7///|Dm7 or C///|Ebm7/Ab7/|Dm7 There are a thousand more possibilities. Later, Ray

Hi Peter,

Here's my take on it:

C | Cdim7 | Dm7 | G7 -- A popular sub for Rhythm Changes in the early era, I tend to think of the Cdim7 here as sub for Am also, but in this case Am6ALT that includes the b5 and b9 w/o root. Am6b5b9 A bit dense, though, so I save such for the wild stuff, would likely make more palatable harmony to go with the full diminished there, which would drop that b9 concept for the A. When it was used in Rhythm Changes it freed up the Bass player to stay on the C for the first three bars, then leaving the choice to drop a half step for the V7 chord, yielding a G7/B, or just play the root after the three C notes.

C | Ebdim7 | Dm7 | G7
Forces Bass note to be the b5 of that Amin7 sub above, retaining the 6th of the A chord, but this time the third of the A chord is impied Major rather than minor. I can be accused of grabbing such a sub where it seems appropriate to play that Am7 in the typical I, vi, ii, V7 as I,VI, II, V7. (ala the first two lines of Rhythm Changes in the original, but without the iii sub for the I the second time around.)

F | F#dim7 | C/G | A7

Now we are steering away from the Rhythm Changes type of sub. If the following bar were to be Dm, this might make a way to get there rather than the old two five one method. "Five to Five" modulation in the last two bars.


There's that old school jazzer's rule of thumb that if a chord shares two or more notes with another, then it likely can be used as a sub. Well, if the given Melody doesn't create a clam problem.

--Mac

I've always looked at the Cdim7 in the key of C as a VI chord. Works for me and makes sense(in my mind, anyway) diatonically. It's probably more complicated than that, but I can play it much better than I can explain it.

An enharmonic chord, and it can resolve many ways. IN 4 iterations. I usually view it as passing to an Am or Dm. I think it's the way your think of all dim7 chords. Then there is the 9th theory, and that's some complicated and makes me shake my head.

I'll have to get out my wife's music books after and have a peek. I'd ask her but when she forgets those 15 years of theory culminating in 4 an university, I get a dirty look when I ask a hard one.

There is also a world of difference in it's treatment from classical to jazz in my mind.

Jazz to me spends more times with resolving in unpredictable ways, which can lead to interest. And the chord can mess with one's head using triads and the inversions.

Somewhere I hear the C#dim7 and F#dim7 going back and forth in classical music but I just don't remember where. I'll have to mess with that and get back to you if the light comes on.

Jazz was part of my new year's resolution, for the 5th time, it seems to go in circles.
Gee that was obtuse.

Thanks Peter for thoughtful discussion, I actually gained useful insight from this thread (now if it will only stick)

It even forced me to go do some re-reading (and count notes on fingers and toes to follow ) too bad no real final "academic" answer (just left with a somewhat resolved chord!)

Larry

Hi Peter,

From my understanding of classical harmony, there are primarily two ways that the diminished chord is treated.

1. The diminished triad resolves to an inversion of a chord that has its root a perfect 4th higher (perfect 5th lower). This is the standard resolution for discords (dim, aug, 7, etc).

2. As you've already indicated, the diminished 7th acts as dominant harmony (without the dominant present and what would normally be the major 3rd up from the dominant as the chord's root note). For example, in the key of C major or C minor, Bdim7 is usually considered a variation of the dominant 7th (G7 chord) that has B as its root note rather than G. In this way (in the key of C), Bdim(7) leads to some inversion of C.

Arguably, though, this second point can be considered as a special case of point 1. For example, Bdim7 is enharmonically equivalent to Ddim7. The 4th above D is G and thus Ddim7 will resolve to a G chord. This, in turn, can be resolved to C (in C major or minor). So Ddim7-G7-C can be condensed to become Bdim7-C.


CONSIDERING POINT #1 ABOVE
In the key of A minor, chord ii (Bmb5 = Bdim triad) resolves to E (or E7) which, in turn, usually resolves to Am. (This is the standard ii-V-i progression in minor mode. This is also in keeping with the notion that chord ii is a variation of subdominant harmony.)

This principle can also be applied to secondary dominants. For example, consider the below progression in C major.

C-Dm-G7-C

When considering possible chords to lead to the Dm, the secondary dominant of D is A7 and so the progression could become ...

C-A7-Dm-G7-C

Equally, borrowing from minor mode harmony, the diminished triad a perfect 4th below D could also lead to Dm (using point #1 above). This gives C-Amb5-Dm-G7-C. Like A7, this diminished triad has the A root note. For this reason, I think of the above progression as the diminished variation of dominant harmony. Diminished triads often sound better when played as an inversion rather than root position. So putting the Amb5 in second inversion gives …

C-Amb5/Eb-Dm-G7

Extending the Am5b and Dm chord into chords of the 7th then gives …

C-Adim7/Eb-Dm7-G7

(Where the dim7 uses the principle of stacking notes that are successively a minor 3rd apart (as found in the seventh chord formed on the second note of the harmonic minor scale). Thus the musical distance from the root note to the top note is a diminished 7th: e.g. C-Eb-Gb-Bbb; and the notes C -> Bbb = a diminished 7 interval.)

Since Adim7 = Cdim7 = Ebdim7 = Gbdim7, it's often easier to name a diminished 7th chord by its bass note since its less confusing to interpret this visually. This gives …

C-Ebdim7-Dm7-G7 where Ebdim7 is really Adim7/Eb.

Also, Adim7 and Cdim7 are equivalent chords – that is, contain exactly the same notes – so the the above chord progression could also be written as …

C-Cdim7-Dm7-G7 which is C-Adim7/C-Dm7-G7

(To my mind, both Cdim7 and Ebdim7 are alternative ways of expressing Adim7 and so are a form of secondary dominant harmony when they lead to a Dm(7) chord.)


CONSIDERING C/G HARMONY
The progression C-D7-G7-C, where D7 is a secondary dominant, can be decorated to become

C-D7/F#-G7-C

In cadential position, a variation of G(7) is C/G which is essentially a G chord with two suspensions (the C and the E). In this position, C/G behaves as dominant harmony and not tonic harmony. Thus the above chord progression could be elaborated to become (melody permitting) …

C-D7/F#-C/G-G7-C

As explained in point 1, the diminished chord a 4th below D could used to lead to D7. Using 7ths, this gives …

C-Adim7-D7/F#-C/G-G7-C

However, Adim7=Gbdim7, and Gbdim7 is enharmonically equivalent to F#dim7. Thus …

C-F#dim7-D7/F#-C/G-G7-C

Because there are now two successive chords on the F# bass, either one can be eliminated. Choosing the dim7 chord then gives ...

C-F#dim7-C/G-G7-C

Alternatively, since F# is the leading note of G major (or G minor), and since the cadential C/G is simply a variation of G(7), the same principle of Bdim7 leading to C in the key of C major can be applied and F#dim7 can lead to C/G (if one considers a temporary key change of G major).

In the progression ...

C-F#dim7-C/G-A7

... C/G is what theory people call a passing 6/4 chord (6/4 = second inversion and comes about from Bach's day when figured basses were used). Since the bass is G, it is still good music to think of this as a form of G chord. To me, C/G feels more like a dominant chord than a tonic chord because of the dissonant interval of a 4th between the bass (G) and the chord tone C. To my way of thinking, given the above, F#dim7 to C/G is a less obvious variation of secondary dominant harmony.


AUDIO FILE
For comparison purposes, I've put together this 4-part harmony audio file of some of the above chord progression.

...link here (approx. 360 kB)

The progressions are ...

1. C - Am - Dm - G7 - C

2. C - A7 - Dm - G7 - C

3. C - Adim7 - Dm - G7 - C

4. C - Cdim7 - Dm - G7 - C

5. C - Ebdim7 - Dm - G7 - C

To my ear,even though the various second chords in the progressions sound slightly different, there's enough similarity to show that the dim7 chords are all acting in a similar way to the secondary dominant A7. (The reason that the Ebdim7 sounds more noticeably different than the others is because the melody needed to change to accommodate Eb in the bass.)


SUMMARY
In all instances, the progressions have come about by considering (a) that a discord (in this case the diminished chord) classically resolves to a chord whose root is a perfect 4th higher or (b) that a dim7 chord can resolved to an inversion of a chord whose root is one semitone higher that the root of the dim7.

Hope this helps with some kind of insight,
Noel

A passing chord...

+1

I did a lot of theory study last year to try to get to the bottom of such questions.

Most stuff of course resolves modally, and therefore makes sewnse this way. Music is also often tension and release tension and release. So what of the tension part? Well there are varying degrees. To have tension one must overturn the expected chord, but this can be dome by one note two or three or even four. Whtat I came to realise is that any tension has its beauty IF it is resolved contextually.

I have also found that the dimininished scale has its own logic. It is unsettled, unless it returns to the root (no perfect fifth). However, it can reproduce it's own structure on every second note - so as to potentiallly nominate that note as new root. This gives it a kaelidoscopic patternating quality, a kind of daisy chaining property that is not possessed by the major or minor scales but is also present in the whole tone scale. Certain harmonic structures can be based on this rather that the conventional modal thinking. So sometimes the diminished functions to imply another, non modal context. Think Debussy.

Obviously it also has a role as a tension in modal harmony as cited above in various manners

This has already been touched upon but I'll add it anyway. I like doing this for practice to work myself through the various keys.

Dim7ths can also be used as pivot chords to effect a modulation to remote keys, so any note of a dim7th can be lowered a semitone to make a dominant 7th, which can then be used as a V7-1 cadence in the new key.

So if for some reason you wanted to go from C major key to Bb Minor Key, you could play the C dim7th chord and then lower the Gb to F to get an F7th chord, which can then proceed to the tonic chord of Bb Minor.

Even though not all are effective, we can end up with 4 major and 4 minor key modulations just from the one dim7. Very handy if you are stuck trying to get to an unrelated key.

I like experimenting with dim7ths, they are interesting chameleons.

(The C-Cdim7-Dm7-G7 is a really nice sounding progression isn't it.)

People without a lot of experience blowing the Rhythm Changes and chording same are likely to miss the point because of that.


--Mac

Yes, Rhythm Changes (key Bb), uses that dim7 a lot....

the second bar can be

| Dm7 C#dim7 | Cm7 F7 |

for that one, I've thought of the C#dim7 as an A7b9/C# .

Then a few bars later (Bar 6), when it comes up again ...

| Eb6 Edim7 | , we have that same chord again (Edim7 is similar to C#dim7 and Bbdim7).
But in this case I think of the Edim7 just like a Eb7b9 (ie no real change of chord).

To all who have posted:

Thanks for all the helpful input.

As indicated in the posts, it (Cdim7 in key of C) is an interesting chord. Sounds so musical and correct for the key of C, yet doesn't have an obvious reason why it belongs.

Used in lots of songs (e.g. Embraceable You, Rhythm Changes etc.)

I always thought that all musics actually consist of various forms of Tension--->Release.

That can be rhythmic as well as melodic as well as harmonic.

Use of the Cdim7 in C changes a C7 to a C7 that also has a b5 and #9 in it, one way to look at it.

The two primary "supertension" notes.


--Mac

Embraceable You is a good example. In the second bar, (key of C), Ebdim is the correct chord. A good sub is Am7b5/D7b9/ Later, Ray

,
A most interesting question, Peter. I could think of it as a variant ii7 (am7), since it fits that place in the rhythm changes so well. But really the Gb kind of disqualifies it as an A-anything. It is more than a passing chord, since it does not go to C#, or contain a C#. It certainly fits in the 'tension/release' model which Mac mentioned, but I dont' think that quite answers the question you asked.

Hmmm....you got me puzzling now...I know it sounds good, but...

Am7 = the vi in key of C though.

I think the Cdim7 moving to Dm7 sounds good because it's resolving as it should and in a way our ears are expecting.

Dim7th chords are classified as chromatic harmony and usually if you chromatically alter a note, it resolves in the same direction as it was altered. If you sharpen a note it will resolve upwards and if you flatten a note it will resolve downwards.

So for example, if you changed C Major chord to C augmented, the G# should resolve up a semitone to A. When we play Caug Chord then F Major chord, the release of tension from the G# to the A sounds right and pleasant.

In Cdim7 the Eb and Gb are, as already mentioned, appoggiaturas to D and F, so by lowering the the Eb and Gb a semitone to D and F, the result is smooth and they are resolving in a theoretically (what a horrible word to spell!) correct way.

The resulting Dm7 (C,D,F,A) releases the tension in a way that is expected and "comforting" to our ears.

Nice!