Usually, you think of a scale as an ordered sequence of single notes. Chapter 4 was all about identifying melodic intervals, scale degrees, and the organization of melodic scales.

Does the same apply to harmony? That is, having identified the various harmonic degrees (chords) and harmonic intervals (chord changes, also called chord progressions), can they be organized into harmonic scales—harmonic equivalents of melodic scales?

And if so, does that mean there’s a guaranteed way to write a chord progression that holds together? Sounds like it “knows where it’s going”?

The answer is yes.

Few songwriters know about it, though.

The harmonic equivalent of a melodic scale is called a harmonic scale, or scale of harmonic degrees. It’s a powerful musical phenomenon. You’re about to learn to make creative use of it.

There are 12 such harmonic scales, one for each pair of relative keys—major and relative minor (or vice versa).

In the following sections, you’ll learn how easy it is to create chord progressions that sound “different” from your run-of-the-mill “three-chord wonders.” And yet natural and attractive to the ear.

True, many great songs have only three basic chords. But the same three basic chords also show up in zillions more awful songs.

Tune and lyrics notwithstanding, most songwriters simply don’t know how to create beautiful chord progressions because they have zero knowledge of harmonic scales and how to use them. Once you understand how easy it is to use harmonic scales, you won’t ever have to worry about writing lame chord progressions again.

6.6.2

UNREST AND DIRECTION: THE MAGIC OF V – I

Recall from Chapter 4 that, in melodic scales, two scale degrees (notes of the scale) “point” strongly towards scale degree 1, namely, its two neighbors, scale degree 2 (from above) and scale degree 7 (from below). Scale degrees 2 and 7 have both unrest and direction.

For example, in this scale:

C – D – E – F – G – A – B – C

the note D strongly seeks resolution (unrest) down (direction) to C, and B strongly seeks resolution (unrest) up (direction) to C.

Unrest and direction.

In harmony a parallel situation obtains. But in harmony, only one harmonic degree, or chord, “points” strongly towards harmonic degree I, not two chords.

The only chord in harmony that has both unrest and direction is harmonic degree V (“the five chord”).

1. As Table 43 below shows, the notes comprising harmonic degree V include scale degree 7 and scale degree 2. Both of these notes point strongly to the tonic note of the key, scale degree 1.

TABLE 43 Notes Comprising Harmonic Degree V (“The Five Chord,” As They Say In Nashville)

5th Note Up From Root

(Interval of a third)

3rd Note Up From Root

(Interval of a third)

Root of Triad

(Scale Degree)

2. Recall from Chapter 5 that the more scale notes two keys have in common, the more closely they’re related. And keys having tonic notes a fifth apart have six out of seven scale notes in common. (For example, the key of C major and the key of G major have 6 of 7 scale notes in common.)

3. The simplest frequency ratio after the octave (1:2) is the ratio that corresponds to the fifth (2:3).

For all of these reasons, the harmonic interval (chord change or chord progression) V – I plays the same role in harmony as do melodic intervals 7 – 1 and 2 – 1 in melody.

The V – I chord change is the strongest, most natural chord progression in harmony.

Just as melodic intervals 7 – 1 and 2 – 1 impart both unrest and direction with respect to the tonic note, so the harmonic interval V – I imparts both unrest and direction with respect to the tonic chord—the chord built on scale degree 1.

6.6.3

HARMONIC “SCALE NEIGHBOURS”

Just as scale degrees 7 and 2 are scale neighbours of the tonic note in melody, so in harmony the V chord is the scale neighbour of the tonic chord.

And that means the chord change V – I is the smallest scale move you can make in harmony. The V chord and the I chord are, therefore, harmonic scale neighbours.

This is precisely the opposite of the situation in melody.

For example, in the key of C major:

• Melodically, the notes B and C are close together. They’re melodic scale neighbours. The notes C and G are as far apart as you can get—definitely not melodic scale neighbors.

• Harmonically, the chords C major and G major are close together. They’re harmonic scale neighbours. But the chords C major and B major are far apart—definitely not harmonic scale neighbours.

Wanted: Musical Marriage Counsellor

Think of harmony and melody as opposite sexes.

In melody, the fifth is the furthest note from the tonic. But in harmony, the fifth is the closest chord to the tonic.

Opposites in a fundamental way.

When they’re together, harmony and melody usually get along. Sometimes they fight. Paradoxically, such fighting often sounds delightful.

When they divorce, melody functions fairly well on its own. But harmony does not. By itself, poor harmony flounders, and must find a way to reconcile with melody.

6.6.4

THE HARMONIC SCALE: WILL THE CIRCLE BE UNBROKEN?

To construct a harmonic scale (scale of chords), here are the chords to start with, the basic chords for any given key (in Nashville Number notation):

I IIm IIIm IV V VIm VIIº

The next step is to arrange these chords with each chord the smallest distance apart harmonically (just as, in a melodic scale, the notes are the smallest distance apart as you go up or down the scale stepwise, from note to note). That means the root of each chord would be a fifth apart, since, in harmony, a fifth progression is the smallest harmonic distance.

A major difference between a melodic scale and a harmonic scale would be this:

• A melodic scale begins with scale degree 1 and ends with scale degree 1 (8)—two different notes. That’s because, in melody, the octave matters.

• In harmony, the octave does not matter. Therefore, a harmonic scale would need to begin with harmonic degree I and also end with harmonic degree I—the same chord. As pointed out above, a chord is a chord is a chord. No distinction is made between a chord played in one octave and the same chord played in a different octave.

Since the first and last chords in the harmonic scale are the same chord (the tonic chord, I), what shape, then, must a harmonic scale take?

If a harmonic scale must begin and end with the same chord ...

The harmonic scale must necessarily

take the shape of a circle.

That’s the only way the harmonic scale could begin and end with the same chord.

Figure 47 shows how the chords of a harmonic scale are arranged in fifth progressions, and in the shape of a circle.

FIGURE 47 The Harmonic Scale: Basic Structure

6.6.5

FAMILIES WITHIN THE CIRCLE

The first thing you notice about the chords in Figure 47 above is that they clump together. The major chords form a little family of three on the right side of the harmonic scale. The minor chords form another little family of three on the left side. (Isn’t that sweet?)

The diminished chord (VIIº)—no doubt trained as an expert in family group dynamics and conflict resolution—appears to bridge the two families.

The next thing you might notice is that all but one of the intervals between the roots of the chords is five semitones apart (a fifth progression down, going clockwise; a fifth progression up, going counterclockwise). The exception is the interval between the root of the IV chord and the root of the VIIº chord (six semitones).

Later in this chapter, you’ll see how this little anomaly helps explain why composers have a hard time working with the Church modes (Dorian, Phrygian, Lydian, Mixolydian, Locrian) when it comes to constructing palatable-sounding chord progressions.

6.6.6

WHICH DIRECTION HOME?

How does it feel

How does it feel

To be on your own

With no direction home

—BOB DYLAN (“Like A Rolling Stone”)

Next, try an example. Replace the Nashville Numbers with the chords of a representative key—actually a pair of relative keys— and try out the harmonic scale. Use the keys of C major and A minor (Figure 48):

FIGURE 48 Harmonic Scale, Key of C Major / A Minor

So far, so good. But this harmonic scale needs some tweaking.

If you play the harmonic scale clockwise, starting from C major and ending with C major, your brain senses natural, directed harmonic motion. The progression is definitely “going somewhere.”

It pulls out of Dodge City (the C major chord) and moves smoothly to Fowler (the F major chord). It feels like you’re on your way to somewhere. The sense of motion continues as the harmonic train moves from town to town on a grand circle tour. Tyrone, Richfield, Johnson City, Garden City, Cimarron. Finally, it pulls into Dodge City once more. With that last harmonic interval (G – C), there’s no mistaking the feeling of arriving back home.

Now, try going the other way around, from the chord C major to G major to D minor, and so on. You’ll soon find that something’s amiss. When you try to take the grand circle tour counterclockwise, your train gets lost and ends up somewhere between Moose Jaw, Saskatchewan, and Dildo, Newfoundland (yes, there is such a town).

Even though you eventually arrive back home, your brain does not sense that your train has arrived home. It’s Dodge, seemingly. But nobody’s around that you’d recognize. Where’s Marshall McDillon? How come Doc Yada-Yadams is sober and hardly ever performs brain surgery? Since when did Ms Puma start playing the flute? How come Sadie and Ellie Sue’s store is full of mules instead of horses?

In a minute, you’ll find out what went wrong in the counter-clockwise trip. But first, a brief revisit to the interval dynamics of the melodic scale.

6.6.7

THE MELODIC SCALE: TWO DIRECTIONS HOME

In melody, as you move up the scale, from scale degree 1 to 2 to 3, and so on, your brain senses a feeling of “going away”—paddling against the current— until you reach scale degree 5.

Then, as you continue in the same direction (away from scale degree 1), you sense that the current reverses itself. And you find yourself somehow paddling with the current, even though you haven’t turned around.

It’s the current that reverses, not you. The current even carries you home. But it’s not the same home you left. Instead of “home” being scale degree 1, it’s scale degree 1 (8). Yet your brain still perceives 1 (8) as “home.” That’s the important thing (Figure 49 below).

Your brain has evolved to expect complex frequency ratios to resolve to simpler frequency ratios. And what’s the simplest? The tonic note of the octave: scale degree 1, or scale degree 1 (8).

FIGURE 49 Melodic Scale: Two Directions Home

This also happens when you move down the melodic scale, from scale degree 1 (8) to 7 to 6. Again, your brain senses that you’re padding against the current. Until you reach scale degree 5. Then you sense reversal of the current and paddle downstream until you get home to scale degree 1.

So, in melody, you can get home by either ascending or descending the melodic scale. The most powerful forces for resolution are the melodic intervals 7 – 1 (8) and 2 – I.

In melody, there are two directions home.

In harmony ... maybe not.

6.6.8

HOW DOES IT FEEL TO MOVE CLOCKWISE ROUND THE HARMONIC SCALE?

Have another look at Figure 48 above, (key of C major/A minor). Suppose you start at the C major chord. To stay within the circle, you have two choices:

1. You can progress clockwise to F major; or

2. You can progress counterclockwise to G major.

Suppose you start by playing four bars of the C major chord on your guitar or piano to establish tonality. Then progress clockwise to the F major chord and play a few bars. How does it feel?

Your brain senses a purposeful, natural harmonic move. A feeling of moving ahead, of going somewhere.

It doesn’t matter if you start by playing the C major chord in a high octave, then move to the F major chord in a lower octave, or vice-versa. Either way, you sense a purposeful, natural, comfortable harmonic progression.

How come?

When you progress from C major to F major, you move from these notes

C – E – G

to these notes:

F – A – C

When you leave the C major chord and move to the F major chord, your brain wonders, “What’s going on? The chord has changed. Looks like the new chord is assuming the role of the tonic chord—at least for the moment.”

Therefore . . .

1. The scale relationship of the note E in the C major chord (the chord being left behind) with respect to the root note F (the foundation note) in the new chord, F major, is 7 – 1 (8).

Your brain feels a strong sense of satisfaction when the note E in the C major chord resolves to the root note F in the new chord, F major.

2. Similarly, the scale relationship of the note G in the C major chord (the chord being left behind) with respect to the root note F in the new chord, F major, is 2 – 1.

Your brain feels a strong sense of satisfaction when the note G in the C major chord resolves to the root note F in the new chord, F major.

These two simultaneous moves—E moving up to F (7 – 1) and G moving down to F (2 – 1) combine to provide your brain with a feeling of assured, inevitable harmonic motion.

Resolution from complex to simple frequency ratios has taken place.

6.6.9

HOW DOES IT FEEL TO MOVE COUNTERCLOCKWISE? (HINT: THE CAT WANTS BACK IN)

What happens when you go the other way around the circle?

Again, start by playing four bars of the C major chord to establish tonality. Then progress counterclockwise to the G major chord and play a few bars. How does it feel?

Your brain senses a desire to get right back to C major. It’s like opening the door to let Tritone the cat outside. A minute later, the cat wants back in.

What’s going on?

When you progress from C major to G major, you move from these notes (the notes that comprise the C major chord):

C – E – G

to these notes:

G – B – D

When you leave the chord C major and move to the chord G major, your brain at first tries to accept the G major chord as assuming the role of the tonic chord.

But it doesn’t work out. Your brain feels no sense of purposeful, forward motion.

When you leave the C major chord and move to the G major chord, your brain senses that:

1. The scale relationship of the note E in the C major chord (the chord being left behind) with respect to the root note G in the new chord, G major, is 6 – 1.

This does not in any way reinforce G as a potential new tonal centre.

2. Similarly, the scale relationship of the note C in the C major chord (the chord being left behind) with respect to the root note G in the new chord, G major, is 4 – 1.

With this interval move, your brain senses no reinforcement of G as a potential new tonal centre.

If the new chord, G major, is supposed to be the new tonic, how did the old chord, C major, yield its power as tonal centre?

The answer is, C major did not yield its power.

The notes C and E in the C major chord do not provide any significant propulsion to resolve to the root note G in the new chord, G major.

In fact, when you progress from C major to G major, your brain senses exactly the opposite of “harmonic resolution.” It correctly senses that the chord change from C major to G major has created harmonic tension—not resolved it.

How does it feel? It feels unstable, restless. Your brain expects resolution back to the C major chord. (The cat wants back in.)

If you then do exactly that, progress from the G major chord back to the C major chord, the same interval dynamics apply as if you were progressing from C major to F major. When you move from G major to C major ...

1. The scale relationship of the note B in the G major chord (the chord being left behind) with respect to the root note C (the foundation note) in the new chord, C major, is 7 – 1 (8).

So, your brain feels a strong sense of satisfaction when the note B in the G major chord resolves to the root note C in the new chord, C major.

2. Similarly, the scale relationship of the note D in the G major chord (the chord being left behind) with respect to the root note C in the new chord, C major, is 2 – 1.

Your brain feels a strong sense of satisfaction when the note D in the G major chord resolves to the root note C in the new chord, C major.

These two simultaneous moves—B moving up to C (7 – 1) and D moving down to C (2 – 1) combine to provide your brain with a feeling of assured, inevitable harmonic motion. Just like moving from the C major chord to the F major chord. Again, resolution from complex to simple frequency ratios has taken place.

6.6.10

THE HARMONIC SCALE: ONE DIRECTION HOME

In melody, you have two directions home—by ascending through 7 to 1 (8), or by descending through 2 to 1.

But in harmony, as you’ve just seen, you have only one direction home—by descending the circular harmonic scale (moving clockwise).

In harmony, your brain senses the descending fifth progression of V – I as “coming home.” Just as, in melody, it senses scale movements of 7 – I (8) and 2 – 1 as “coming home.”

So, it’s necessary to tweak the harmonic scale by adding arrows to show clockwise (descending fifth) natural direction of motion (Figure 50 below).

FIGURE 50 Harmonic Scale: One Direction Home

In harmony, when you paddle clockwise, you paddle with the current. When you paddle counterclockwise, you paddle against the current (with one small exception—third progressions—coming up in a while).

Or, you could say that, clockwise, you sail with the wind; counterclockwise, you sail against the wind. You have to mind your sheets, too. In sailing, sheets are lines attached to sail corners that control sail positions relative to the wind. So if three of them are blowin’ in the wind, your boat will not be terribly manoeuvrable. That’s what you get when you knock back too many margaritas ... you sail three sheets to the wind.

6.6.11

FIXING ANOTHER “MINOR” PROBLEM

So, the natural direction of motion as you progress from chord to chord through the harmonic scale has been nailed down. It’s clockwise.

Still, the harmonic scale needs more work. Some of the harmonic intervals have less directional strength than others.

As always, an example reveals the problem. Once again, swap the Nashville Numbers of Figure 50 above for the chords of a pair of relative keys—C major and A minor, this time with the directional arrows added (Figure 51 below):

FIGURE 51 Harmonic Scale: Key of C Major / A Minor

You’ve probably noticed that the progression Em – Am does not quite measure up to the confident, resolved sound of, say, G – C.

When you progress from E minor to A minor, you move from these notes:

E – G – B

to these notes:

A – C – E

As usual, your brain checks out the new chord against the one left behind for signs that the new chord is assuming the role of the new tonic chord—at least for the moment. And here’s what it finds:

1. The scale relationship of the note G in the E minor chord (the chord being left behind) with respect to the root note A (the foundation note) in the new chord, A minor, is ♭7 – 1 (8), not 7 – 1 (8).

Your brain senses only a moderate sense of satisfaction when the note G in the E minor chord resolves to the root note A in the new chord, A minor.

2. The scale relationship of the note B in the E minor chord (the chord being left behind) with respect to the root note A in the new chord, A minor, is 2 – 1.

Your brain feels a strong sense of satisfaction when the note B in the E minor chord resolves down to the root note A in the new chord, A minor.

Together, these two simultaneous moves—G moving up to A (♭7 – 1) and B moving down to A (2 – 1) combine to provide your brain with only a moderate feeling of harmonic motion.

Why isn’t it a strong feeling of harmonic motion? Because the G – A move is ♭7 – I (8), not 7 – 1 (8).

Recall from Chapter 5 that a semitone interval has considerably more inherent tension than a whole tone interval, because a semitone is derived from a more complex frequency ratio (16:15), compared with a whole tone (9:8).

In the major diatonic scale, a semitone between 7 and 1 (8) points strongly at 1 (8). That’s why the note occupying scale degree 7 is called the leading tone, but only if it’s a semitone from 1 (8).

So, it’s necessary to provide that Em chord with a leading tone, to make it strongly directional with respect to the Am chord. The way to do this is to sharpen the G in the Em chord, converting it into an E major chord.

When you do that, and progress from E major to A minor, you move from these notes:

E – G♯ – B

to these notes:

A – C – E

Now the relationship of the note G♯ in the E major chord (the chord being left behind) with respect to the root note A (the foundation note) in the new chord, A minor, is 7 – 1 (8), a semitone.

The chord progression in the harmonic scale therefore becomes III – VIm (instead of IIIm – VIm). Now the chord change has a strong directional quality (Figure 52).

FIGURE 52 Harmonic Scale with III In Place of IIIm

In the key of C major / A minor, when you play the chord changes, you can easily sense that the chord progression E – Am has much stronger directed quality than Em – Am.

To generalize, any descending fifth progression of two chords must have a major triad as its first chord in order to impart strong directed motion that terminates in a feeling of resolution. The second chord may be either a major or minor triad.

For instance, if you want to convey a feeling of strong directed motion to the chord progression IIm – V (e.g., Dm – G), you have to change the IIm to II, converting the progression to II – V (e.g., D – G).

Voice Leading, Counterpoint, and All That

Voice leading refers to continuity in the way one note moves successively

CHAPTER 6: How Chords and Chord Progressions REALLY Work _______________________________ 6.6 Scales of Chords? Yes!

CHAPTER 6:
How Chords and Chord Progressions
REALLY Work
_______________________________

6.6 Scales of Chords? Yes!