Augmented Diminished Dementia
Most folks are fine when it comes to playing major chords. And they can handle most minor chords as well. And you can usually trust them not to panic (too much) when faced with sevenths (dominant, major or minor) and the odd ninth, add nine, suspended fourth or plain old sixth that might happen their way.
But augmented and diminished chords are, as the cliche goes, another kettle of fish. Just the names, “augmented” and “diminished,” give one pause. Do I need a special degree or extra study to employ one of these chords?
Not at all! You may not know it, but augmented and diminished chords are not all that much harder to learn than “ordinary” chords. Chances are that they are simply unfamiliar to you, since they don’t tend to pop up in songs all that often. They used to, though! Pop songs of the thirties and forties were filled with them. Motown and groups like the Beatles used them in the sixties. How often you come across these chords really depends on what type of music you listen to. And for the songwriter, these chords can open so many doors that it’s positively overwhelming!
So let’s take a look at them, how they’re formed and the functions they can serve. If you’re capable of counting to twelve, you’re capable of understanding and using these marvelous chords.
Leading You By The Ear
First, if you aren’t familiar with how chords, be they major, minor, augmented or diminished, are formed, then you might want to take a moment and peruse two old columns of mine called The Musical Genome Project and The Power of Three. I think you’ll find both pieces an easy read. And while you’re at it, take the time to go over Five To One, as the ideas there are going to be essential to the topic at hand.
And if you’re ready, let’s take a look at an old friend, the C major scale:
You may not have thought about this much before, but which note ends the C major scale? Depending on your personality, you either said “C” or “B” and I’m willing to bet that the majority of you picked the first answer. Either answer is fine; one could just as easily argue that there is no end of the scale – it just goes on and on…
But those of you who went with “C” probably did so for a good reason. It sounds like we’ve finished the scale. If you end on B, then you’re likely to feel that the scale is incomplete, that it’s hanging there waiting for an ending. Don’t take my word for this! Sing it or play it and hear for yourself.
This is the sense of “home” that we discussed ages ago in Five To One. And whether you know it or not, a lot of that sense of home relies on the B note, or rather, on the fact that the interval between B and C is a half step and not a whole step. In the study of music theory, half steps are often referred to leading tones. They serve to direct a voice, a melody, a solo or a chord to a specific destination. If that destination gives us a sense of home (and if not totally a sense of home, then at least a sense of respite), then we call that resolution. We even briefly touched on this in A La Modal, when we looked at the use of the C major scale in The Israelites and heard how the use of the half-step between C and C# gave us a wonderful sense of completion.
Believe it or not, most of you are already aware of how this sense of home works, even if you feel you can’t put it into words. This is why chord changes like F to C and G to C sound more complete; there’s more of a sense of finality than, say, Am to C. It’s because of the use of leading tones:
I’ve marked the leading tones here with little slash marks (“/” or “\”), which illustrate the movement of the notes. I also added G7 to this chart, to remind you of the discussion in Five To One about why G7 to C sounds even stronger than G to C – you’re using two leading tones instead of one. Is everyone with me so far? Okay, then, let’s take a look at augmented chords.
But first, I want to plant this in your brain because we’re going to want to look at it a lot in the very near future. Remember that, in Western music anyway, there are a total of twelve chromatic steps going from C to C:
That number, twelve, is going to become very important to us! So keep it in your hat, as they say, and don’t even bother to ask me who they are! By the bye, I can assume you all know that C# (number 2 in this chart) is the same as Db, right? Likewise, Eb is D#, F# is Gb, G# is Ab and Bb is A#. Got it? Good!
So now let’s take a look at Caug. As you read in The Power of Three, one makes an augmented chord by taking the root, adding a major third (the note two full step up from it) and then adding another major third. If it’s easier, just think about adding a half step to the fifth. Either way, you’ve got C, E and G# and it looks like this:
Since an augmented chord has the raised fifth, and since, in this case it’s G#, it’s a fairly safe bet that your ears want it to lead you to an A note. More often than not, an augmented chord will resolve to the fourth (F in the key of C) or the sixth (Am in the key of C. Check out these progressions and see if you don’t agree:
And these progressions are even more striking when you start with the C chord:
Can you hear how you build the tension when you change from the G in the C chord to the G# in the Caug? And then how the tension drains away when you finally get to that A note in either the Am or the F? This is a great thing for songwriters. You can use it as a melody line or, more striking still, use it as accompaniment as the melody holds on a single note common to all chords. And you don’t have to stop there! Check out this progression:
I’ve deliberately used the Fmaj7 here so that we can have sustained tones on the first two strings, namely the open E on the first string and the C note (second fret) on the B string. We start with the C to Caug to Am that we used in Example #6 and then raised the A note an additional half step to Bb, which gives us C7. Then we slip back down to A of the Fmaj7, lower that a half step to get the FmMaj7 (quite the chord, no?) and then finally get back home to our C chord.
Another thing I should point out here is that a lot of writers will use the C6 or Am7 chord (both of these chords use the same four notes: C, E, G and A) instead of plain old Am. As with so much else in music, it all depends on your own taste.
Sadly, outside of jazz, one is hard pressed to find augmented chords used with any regularity. You may find the occasional song (or songwriter – John Lennon regularly peppered his work with a well-placed augmented chord or two) where they pop up. In jazz, you’ll often find the seventh added to them. There is a moveable chord form for this and it looks like this:
Kudos to those of you who, having read my column, Moving On Up, can see the reasoning behind this. We’ve taken our E shape and adjusted the fifth, which is on the B string, accordingly moving it up a half step. The root of this chord is on both of the E strings (first and sixth), while the third is on the G and the seventh is on the D.
Now, let’s put the augmented chord on hold for a moment and take a quick look at our second feature, if you will. Diminished chords also demonstrate the importance of leading tones; perhaps even more so than the augmented chords. Think back on Example #2 and ask yourself, what’s the difference between Bdim and G7? The Bdim contains the same notes except it has not G. In other words, it’s a G7 without a root. So it will always contain two leading tones in it, depending of course on the chord to which you intend to resolve. More on that in a moment…
First a quick bit of stuff that might be confusing. It’s rare to play pure diminished chords, that is, the root, minor third and flatted fifth, on the guitar. Because the instrument is, for the most part, tuned in fourths, it’s hard to create comfortable chord voicings that use adjoining strings. That’s not to say it can’t be done. Here’s a common moveable chord for pure diminished chords:
For this moveable chord, you only want to play the three strings indicated. The root is on the A string, while the flatted fifth is on the D string and the minor third is on the B string. This particular fingering leads itself very nicely to chord progressions like this:
This is a very common progression in jazz or old pop standards. You can hear this at the beginning of We’ll Meet Again or all throughout Ain’t Misbehavin’. And it’s a terrific example of leading tones, here in the bass notes. If you start with the C major chord and then only change the C note, moving it up a half step to C# while keeping the E and G intact, you’ve then got C#dim. This resolves to Dm, from which we go to Gaug7 that will bring us back to C.
But guess what? To a jazz player, this is not a diminished chord! He or she calls it a “half diminished” chord. Why? Well, I might need the wit of Nick Torres to figure this out but I highly suspect that jazz players insist that anything good enough to be called a chord should have four notes!
So let’s remember that our diminished chord is made by taking the root, adding a minor third to it and then another minor third, which gives us the flat fifth. By the way, this flat fifth is called the tritone. It’s as far away from the root as one can get. But more on that later. For now, on top of all that we’ve got so far, let’s stick another minor third:
Technically, in terms of the major scale, we’re adding the sixth to the chord, but in music theory terms we call this a diminished seventh. The diminished seventh can easily be played on the guitar. Here’s Cdim7:
And now we’re in for some real fun! Because of the make up of the diminished seventh chord, you have all sorts of ways to resolve it! Let’s look at a Cdim7 and see a few examples:
This is all a matter of the use of leading tones. When going from Cdim7 to C, for instance, we let the C note stand pat while the Eb lead us up to E while the Gb and A collapse in on the G note. I didn’t plot it out, but the A could just as easily lead up to the Bb and give us a C7. Or, in our second example here, the Eb could lead down to D, the Gb and A could collapse on G again and the C note could lead down to B, which would give us a G chord. We could also, as I hope you see, create G7, Gm or Gm7 just as easily.
And that’s just the tip of the iceberg! If you’re up for it, and I have to admit that this is a lot easier on a keyboard than on the guitar, try resolving from Cdim7 to any or all of the following chords: Db, Db7, Dbm, Dbm7, Eb, Eb7, E, Em, Gb, Gb7, A, A7, Bb, Bb7, Bbm, Bbm7 and B7. Even if you decide to take my word for it, just reading that list of possible resolutions should put you a little in awe of the possibilities of this chord. But wait, as they say, there’s more!!
More Fun With Numbers
Ask any of my friends and they will gladly tell you that my grasp of science and/or physics is, at best, more than slightly tenuous. Still, I will declare forever and a day that all the wonderful talk about wormholes and dimensional portals and all that sort of fanciful thought probably started with a musician who was under the spell of Augmented Diminished Dementia.
Remember I told you to hand on to the number twelve? Let’s take a look at something incredibly interesting. Let’s take the twelve tones of Example #3 and the Caug chord of Example #4. Remembering that the Caug chord is built with a root (C), a major third (E) and then another major third (G#), what happens if we add yet another major third to the equation?
Goodness, we’re back at the root! How on earth did that happen? We’ll grab a pencil and come join in the fun. The interval of the major third is two whole steps, or four half steps. So if we’re starting with note “1,” then the next note in our sequence will be “1” plus 4, which is “5” and we look on our master chart and low and behold, “5” is E. So far, so good! Adding four to “5” gives us “9” and wouldn’t you know it? G# is the note assigned to “9.” That’s our Caug chord, alright! So let’s add four to “9” and we’re up to “13,” which, being a half-step up from B puts us smack dab on the C note.
Remember again, our total number of chromatic notes is twelve. “13” is the same as “1” as far as we’re concerned here. And twelve, as I truly, sincerely (dare I say desperately?) hope you all know, is divisible evenly by four. Repeat with me from your childhood: “Twelve divided by four is three.” This means that each augmented chord is actually the same as two other augmented chords! They share the same notes! Again, don’t take my word for it! Do the math and see:
And do you know what that means? There are only four possible augmented chord combinations! Oh, each one has got three names (or more if you start changing your flats for sharps – for instance, G#aug, from this example, is the same as Abaug, no?), but I think you see where I’m coming from:
Now go back to our twelve chromatic tone chart in Example #3 (or Example #14, since it’s closer!) and see if we’ve left anyone out. Pretty wild, huh? I’m more than willing to bet that those of you who learned how to play, oh, Gaug, for instance, didn’t have a clue that you also learned how to play Ebaug as well.
And knowing this sort of thing can be gold to a songwriter. You’re writing a song in the key of C and you want to really go wild on the bridge. Instead of using the time-honored C7 to F approach, why not go to Caug? And then instead of going to F, think of Caug as Eaug and go to A without batting an eye. Your listeners will blink and wonder how you managed to transport them without their knowing!
If this isn’t wild enough for you, then let’s go back to the diminished seventh chord. Think about this – the diminished seventh, as we saw earlier is built upon a stack of minor thirds. So guess what happens when you throw another minor third on the pile?
Yup, we’re back at the root again! The interval of a minor third is equal to three half steps, and twelve divided by three is four. So depending on what note you choose as your root, you actually have FOUR different diminished seventh chords here at your disposal:
And now you’re probably jumping ahead of the game and you’ve already guessed the next big secret of life: There are only three different diminished seventh chords! We’ll use flats instead of sharps this time but be sure to check and see if I’ve missed any, will you?
So, knowing this, how easy is it to figure out your moveable diminished seventh chords? Pretty easy, I suspect. Just find one note of the diminished seventh chord on any of the first four strings and use this pattern:
As you can see, this repeats itself every third fret up the neck. Not a bad thing to know!
Remember when I gave you a list of possible resolutions for the Cdim7? Well, that was a pretty good clue for what you were getting yourself into, no? And again, for a songwriter, this is like having a passkey (no pun intended) to get free access from one key to the next with a minimum of trouble. C to Db? They said it couldn’t be done! “Ha!” I say. Just use the Cdim7 chord and you’ll be there long before anyone knows you’re gone!
This, sincerely, is one crazy subject that tends to confuse the daylights out of people. So please take the time to read it all over as many times as you need to. I hate telling people this, but it is all numbers and nothing more. Okay, it is more – it’s also a lot of fun! A warning, though… Augmented diminished dementia is fairly contagious. Please do try not to overdo!
Until next time…