Yo! I see you guys have been studying hard. You've been learning. You've built a machine of theory, which crushes and destroys musical confusion and ignorance. But sometimes, there's itty-bitty trivial matters that will utterly stop the gears of this engine, and you'll feel like crying for your mommy.
So sit up, pay attention, and get ready to learn about these bits 'n pieces. Loose ends always bothered Lieutenant Columbo in the hit TV series, and they're certainly not going to be the undoing of The Crusade!
Well, sir, there's just a few more things...
Loose End #1: The Non-Functioning Dominant Chord
Would this be a dysfunctional chord that lords over everyone with it's twisted and entrenched issues?
Ha ha, good thing chords aren't like certain members of my extended family!
No, this chord is not like your crazy uncle Zeke. It's actually a lot like me. It sits there, makes a lot of noise, and does...nothing.
Dominant chords (G7, G9, etc) by their very nature pull to other chords. The movers and shakers of the chordal world, they are effectively magnetized to resolve to chords, usually a fifth below. (In the case of tritone substitution, they will also pull to a chord a half step away. Check out The Crusade - Part Nine for more details.)
In certain compositions, there will be dominant chords that don't resolve to the expected chord. They'll be there, just because. This doesn't have anything to do with the dominant chord itself. It's actually the chord after it that makes the dominant chord functioning or non-functioning.
Here's what I'm talkin' about:
Functioning: G7 to Cmaj7
Non-functioning: G7 to Em7
It's just there, and not resolving to a chord. (G7 does not pull to Em7) G7 is not serving any particular purpose in the second example.
Sometimes they'll be the foundation of a static groove, such as in a funky vamp. In other settings, you'll find one buried in the middle of a swiftly moving river of chord changes, sitting like an unexpected boulder in that sonic flow.
The hallmark of the non-functioning dominant chord is that it does not resolve to another chord
And sometimes, they won't even be in the same key!
If the composer thinks it sounds good, it is good. Our job as theoreticians is to realize what's going on, and roll with the punches. Namely, seeing how it fits in to the big picture, and choosing a scale to play over it. More on that later. Hang with this for now.
Here's a few examples, with the Non-functioning dominant chord in boldface type. These examples use a non-functioning dominant chord that's not in the same key as the rest of the chords.
Ex. 1: Em7 Am7 Dm7 G7 Cmaj7 C7 Cmaj7
Ex 2: A7 | G7 | A7 | G7
Example 1 is an illustration of a non-functioning dominant chord in a progression, while Example 2 is more along the lines of a funky vamp. Of course, these are just two of an endless array of possibilities.
Realizing that these creatures exist can be of great help, especially if it's not in the same key! Sometimes a chord is not supposed to fit in a simple key structure. A chord plopped in the middle of a song like this may be best treated as it's on island key, and dealt with specifically. What am I babbling about? We'll check this out more in the future, but simply put, sometimes a song is ideally viewed as several keys, instead of one. Hang tough, and just realize that there are oddball chords in certain songs. Knowing this can save a lot of wear and tear on your mullet when you're pulling your hair out 'cause you can't cram that pesky chord into a key...Or to figure out why it's there in the first place!
Loose End #2: Relative Minor Scales
Knowingly or not, you've played relative minor scales before. A Relative Minor scale is a minor scale that is built from the sixth degree of the Major scale it's related to
. When built when Mercury is in conjunction with Jupiter, the flatted 13th note acts on the tangent on which I've gone. Does that make sense? Liar! Wake up, and pay attention!
It's called a relative minor because it contains exactly the same notes as the Major scale a minor third above it. Put simply, A minor is the relative minor of C major. They've both got the same notes, but one is a minor scale, and one's a major.
But - it sounds slightly different. Remember the WWHWWWH construction of the Major scale? (Whole steps and Half steps.) Since those steps are in a particular order, it gives the scale a certain sound. For the Major scale, the half steps are found between the 3rd and 4th degrees, as well as the 7th and root note. To build a relative minor scale, we start on the sixth of our major scale. Our half steps are now between the 2nd and 3rd notes, and the 5th and 6th notes.
Here's what the letters look like, with the half steps in boldface type:
C D E F
G A B C
A B C
D E F
For the C major scale, this translates to the half steps being found between the 3rd and 4th, and 7th and 8th (same as the root note) degrees.
Starting on A, we find that the half steps pop up sooner: A B C
D E F
This results in a slightly different sound. Sure, the notes are still in the same key, but they're cast in a slightly different light. It's the minor sound. So where have you played this? If you've ever played an A minor Pentatonic scale over a progression in the key of C major, you've played a relative minor scale. Applying these scales to the guitar, the relative minor scale is always found three frets down from the major scale which we started on
I have a goofy way to remember this. Minor scales sound sad. When folks get depressed, they feel down in the dumps. To find the relative minor, go down three frets from our major scale, and play a minor scale. Gaaaa!
And it gets even more corny! What if you're in a minor key, and you want to find the major scale it's related to? Well, you've gotta cheer up three frets!
If you're happy and you know it, clap your hands....
Loose End #3: Parallel Minor Scales
A Parallel Minor scale is a minor scale starting on the same root as the major scale we're comparing it to. In this case, C minor is the parallel minor scale of C major. Unlike the relative minor, the parallel minor starts at the same place as our major scale, but contains different notes.
The formula for building a minor scale is:
(Much different from the major scale's WWHWWWH. But it's actually the same sequence, just starting off the sixth note of the major scale.)
Hence, plugging the note C into the equation, we end up with the following (Half steps are shown in boldface type):
C major: C D E F
G A B C
(Half steps between 3 and 4, and 7 and 8)
C minor (Parallel minor scale to C major): C D Eb
F G Ab
Bb C (Half steps between 2 and 3, 5 and 6)
A minor (Relative minor scale to C Major): A B C
D E F
G A (Contains the same notes as C major.)
Harmonizing Da' Brew
OK - Wanna try playing the scale to see what it sounds like? Play a C major scale at the 8th fret, and then play a C minor scale (6th, or Aeolian mode) at the 8th fret. For charts of those shapes, check out my article Stretching out - Soloing, part II.
Hmmm...How could this tie in with analyzing a chord progression? Let's take a look.
First, we'll need to harmonize (build chords from) the C minor scale.
The order of chords in a natural minor scale is always:
m7 m7(b5) Maj7 m7 m7 Maj7 7
(Note that this is exactly the same order of the chords as a major key, but it starts on the sixth chord.)
Adding the notes of the C minor scale, we arrive at the following conclusion:
Cm7 Dm7(b5) Ebmaj7 Fm7 Gm7 Abmaj7 Bb7
Suppose we stumble upon this:
Em7 Am7 Dm7 G7 Cmaj7 Cm7 Cmaj7
What key could this belong to?
While there's many ways to look at the puzzle, here's a way using parallel minor
It's (mostly) in C major.
Em7 is the iii chord. Am7 is the vi chord. Dm7 is the ii, G7 is V, Cmaj7 is the I. And Cm7 is still the I, but it's derived from the parallel minor scale. It's sort of an impostor, something that's close enough, but is still different.
All of a sudden, we're presented with chords that, at first glance, are seemingly unrelated to our original key, but do, in fact, share a quasi-bond with our key. We can use these chords to add color, or use them as bridges to change keys.
Take this as an example. C minor is the relative
minor of Eb major, and hence shares the same notes as that scale. If we were to put a key change in a song from C major to Eb major, what would be a slick way to do this?
Well, the un-slick way is to play C major, and then jump up a minor third to Eb major, the I chord of our new key.
Let's look for what these two keys have in common. Remember, Eb Major could also be called C minor. Well, C minor has a C minor
chord in it,and C major contains a C major chord. Hey, they both have a C chord! Sure, one's a C minor chord, but it's a heck of a lot closer to C major than Eb major is! Bingo, we've found a great way to smoothly transition into a new key. By playing the C minor as the transition, we jump into the next key with very little fuss.
Parallel minor scales can provide both variety and prove useful in changing keys. Neat. And furthermore, wrap your brain around this: When we first learned about keys and harmonizing scales, we were presented with only seven different chords to build songs from. Adding secondary dominant chords, tritone substitutions, and chords from the parallel minor scale gives us many new sounds to use. We break the seven link chain, and rock onward toward artistic freedom. Yeah!
Rockers! We've covered three important topics today. Here's the Cliff notes (of dover) version:
Non-Functioning Dominant chords are simply dominant sounding chords that do not resolve to the expected chord. They may be found anywhere, from complex chord progressions to simple funk vamps. The bottom line is that they don't serve the typical dominant chord job of resolving to another chord. Functioning dominant chords are followed by a chord they resolve to, and non-functioning dominant chords are not. Additionally, a non-functioning dominant that's out of key will sometimes appear in a composition.
Non-Functioning Dominant Chords can also add a sense of surprise to the composition, as they don't resolve to the expected chord.
Relative minor scales are minor scales that share the same notes (and key signature) of a certain major scale. A minor is the relative minor of C major. The minor key is found three frets below the major.
Feel down in the dumps (3 frets) to find the relative minor, and cheer up (three frets) to reverse the operation.
Parallel minor scales are minor scales that start on the same root of the major scale we're using as comparison. C minor is the parallel minor of C major. They do not, however, share the same key signature, and hence contain slightly different notes.
Parallel minor scales and their related chords can be borrowed for use in a composition to add additional color and variety.
The chords found in the parallel minor key can also serve as a pivot chord for a key change. C minor would be an ideal pivot chord to change from the key of C major to Eb major, as the C minor chord contained in the relative minor key is very similar to C major chord.
Instead of being limited to the original seven diatonic chords that define a key, we now have a much wider range of chords to use. Secondary dominant chords, tritone substitutions, and now, chords from the parallel minor key offer a colorful palette, indeed.
Have fun learning, and I'll see you next time! And for more music ideas and entertainment, please check out my blog! I think you'll like it.
Don't forget to check out my blog.
Copyright 2008 Josh Urban - All Rights Reserved
Josh Urban (photo) is a musician with a unique perspective on music. Always a thinker, he gains insight wherever he can find it, be it in the clubs as a working musician, busking on the city streets, or teaching in the classroom. A naturally enthusiastic fellow, Josh is always fired up about bringing the lessons he's learned to his readers. Maintaining a website, a blog, and a monthly newsletter, he aims to make musicians stop, think, and play with a little more intensity, integrity, and inspiration. You never know who's listening.