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6.7.1
THE
PROBLEM
OF HARMONIC
AMBIGUITY
When you play two major chords a fifth
progression apart, an ambiguity arises. Here’s a little experiment to try. Play
this progression of major chords:
C – G – C – pause – G – C – G – pause – G – C – G
You’re
playing exactly the same two chords. But which key are you in, C major or G
major?
The
progression appears to start out in the key of C major, then seems to change to
G major. Or does it? You can’t really be sure.
The problem is that all major triads are consonances. So your
poor brain has trouble identifying which of the two chords is the tonic
chord.
Music depends for its vitality on establishing tonality, then
disturbing it, then recovering it. Just like drama. If it’s done right,
music is drama. You start out in some sort of “normal” situation. Then
someone or something comes along to upset things—which makes the situation
dramatically interesting.
As every dramatist knows, you cannot wreak delicious havoc
upon an established order unless you first establish the order upon
which you can wreak the delicious havoc.
In
music, you first have to establish order—tonality—unambiguously before
you can disturb it. If you don’t establish tonality, your brain has no context
in which to process subsequent sonic information.
If you
just play random chords, the music sounds just as unpalatable as a tune sounds
if it’s based on a random scale. (Recall the imaginary chalk marks on the cello
fingerboard.)
Chords
and scales only sound coherent if they’re organized in accordance with the
simple frequency ratios that your brain has evolved to comprehend.
In the
above example, C – G – C – pause – etc., tonality is not established. The C
major chord could be the I chord if the key is C. Or it could be the IV chord if
the key is G. And the G major chord could be the I chord if the key is G. Or it
could be the V chord if the key is C.
Ambiguity prevails.
6.7.2
DISSONANCE
TO
THE RESCUE!
Good music works like good story-telling. There’s
conflict, suspense, intrigue. That’s the function of dissonant harmony.
As long as there’s dissonance, you don’t feel a sense of finality or resolution.
So the brain expects more musical story-telling and an eventual release from
suspense.
Resolution only comes with a return to scale degree 1, the tonic
note (the centre of gravity) and the simple non-dissonant major triad.
This usually happens periodically throughout the song, not only once
at the end.
But if it happens too much and too often, the chord progression
gets boring. Like leaving home but never venturing more than a few
hundred metres before returning home.
The other extreme is going away for too long a time, getting lost
and never finding your way back home.
So, in
good songwriting, you have to know how much consonant harmony to balance with
dissonant harmony. You want to make things interesting, but not so “interesting”
that following the music gets so difficult and confusing that the listener zones
out.
Getting
back to the problem of ambiguity inherent in the progression...
C – G – C – pause – G – C – G – pause – G – C – G
...fortunately, there’s an easy fix. Just turn the V
chord into a dissonant
chord.
In the
above example, if the G major chord were converted into a dissonant chord, your
brain would know for sure that the key could not possibly be G major. That’s
because the I chord is always a
consonant triad.
Recall that there are only two basic types of chords, namely,
triads and sevenths. All triads (except diminished and augmented)
are consonant. All seventh chords are dissonant because they all
contain at least one interval that arises from a complex frequency
ratio.
So, to
convert that consonant V chord to a dissonant chord, the simplest thing to do is
to add another note, converting it into a dissonant V7 chord (“five-seventh,” in
Nashville Number parlance).
6.7.3
THE
DOMINATOR: WHY
THE V7
CHORD
CONTROLS
HARMONY
Figure 54 below shows the four notes that comprise the V7 chord.
This chord has three internal intervals:
1. Major
third (5 – 7, four semitones)
2. Minor
third (7 – 2, three semitones)
3. Minor
third (2 – 4, three semitones)
FIGURE 54
Notes of the V7 Chord: Scale Degrees 5,
7, 2, and 4
The V7 chord has some remarkable properties. Compare Figure
54 above with Figure 55 below:
FIGURE 55
Interval Dynamics
• The
V7 chord contains the first note of all three of the most highly unbalanced
intervals—scale degrees 2, 4, and 7; and
• The I chord contains the second note
of all three of these intervals—scale degrees 1, 3, and 1 (8).
That’s
why the V7 chord desperately seeks to resolve to the I chord. It’s down on its
knees in the dirt, its horse having bolted, weeping and pleading, "Resolve me, resolve me.”
(The
V7 chord also seeks to resolve to the Im chord, but not quite as strongly. The
Im chord has that ♭3 note, so the distance from the 4 note to the ♭3 is a whole
tone instead of a semitone.)
When you progress from G7 to C major, you move from these
notes:
G – B – D – F
to these notes:
C – E – G
1. The
scale relationship of the note B in the G7 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).
Your brain feels a strong sense of satisfaction when the note
B in the G7 chord resolves to the root note C in the new
chord, C major.
2. Similarly,
the scale relationship of the note D in the G7 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 G7 chord resolves to the root note C in the new
chord, C major.
3. Finally,
the scale relationship of the note F in the G7 chord (the chord being left
behind) with respect to the middle note E in the new triad, C major, is 4 – 3.
Your brain feels a strong sense of satisfaction when the note
F in the G7 chord resolves to the middle note E in the new
triad, C major.
No wonder, then, that these three simultaneous moves:
• B
moving up to C (7 – 1),
• D
moving down to C (2 – 1), and
• F
moving down to E (4 – 3),
combine to provide your brain with a feeling of
“perfect” cadence.
The V7
chord also contains that most unstable of all intervals, the pitchfork-toting
tritone. It’s the interval formed by the fourth and seventh notes of the scale.
As if
that weren’t enough, the V7 chord subsumes the entire unstable diminished triad
(VIIº)—scale degrees 7, 2, and 4.
All of this makes the V7 chord ...
• Highly unbalanced and dissonant, and at the same time
• Strongly focussed, directed at the tonic centre, the I chord.
The V7 chord is the only chord in harmony
capable of establishing tonality all by itself. It doesn’t even need the I chord
to do it!
The
moment your brain hears a single V7 chord, without any other musical reference,
without any reference whatsoever to the tonic chord or even the tonic note—the
instant that V7 chord sounds, your brain knows where the dynamic centre is. It knows
what the key is.
When
the seventh is added to the V chord, the chord’s name changes from the dominant chord to the dominant seventh chord.
Try that little experiment with the C and G chords again, but this
time, substitute G7 for G, like this:
C – G7 – C – pause – G7 – C – G7 – pause – G7 – C
– G7
Adding
that seventh makes all the difference in the world. There’s no ambiguity
whatsoever. The key can only be C major.
The
dominant seventh chord (V7) assumes its “dominant seventh” powers only if it’s
a major V chord with the seventh note
added. If you add the seventh note to a minor V chord (such as Gm,
changing it to Gm7), the minor seventh chord does not become a dominant
seventh, thanks to the ♭3 note in the Gm7 chord. That ♭3 does a couple of things
to sabotage the dominant seventh quality:
• It
changes 7 – 1 (8) to ♭7 – 1 (8) with respect to the tonic note, C. The leading
tone disappears, removing directionality.
• It removes the tritone, making the chord much more stable-sounding.
That’s
why the dominant seventh chord of a minor key is a major
V chord with the seventh note added. Just like the dominant seventh
chord of a major key.
If you
were to hear only the single dominant seventh chord G7, without reference to any
other chord (unlike the above “C – G7 – C” example), the key could be either C
major or C minor, because G7 is the dominant seventh of both keys. These are
called parallel keys. (More on this later in the chapter, in the discussion of
various types of modulation.)
6.7.4
LAST
TWEAKS
OF THE HARMONIC
SCALE
In light of all this, it’s now possible to make
three more adjustments to the harmonic scale, finalizing it.
1. The V chord must be changed to V7, the dominant seventh,
so that it points unambiguously to I, the tonic chord of the
major key.
2. Similarly, the III chord must be changed to III7, the dominant
seventh, so that it points unambiguously to VIm, the tonic
chord of the relative minor key.
3. And finally, since the harmonic scale subsumes the basic
chords of two keys, a major key and its relative minor, it
would help to identify the two tonic chords.
As for
the VIIº chord, it’s always acutely dissonant, unbalanced. It can either be left
it as it is or changed to a diminished seventh chord (VIIº7). It doesn’t really
matter. Either way, the chord remains eminently unstable.
One
interesting thing about the VIIº chord. Because the four-note dominant seventh
(V7) contains all three notes of the VIIº chord (and three out of four notes of
the VIIº7 chord), you can often substitute the VIIº or VIIº7 chord in place of
the V7 chord to create a striking harmonic effect.
By the way, the IV chord is called the subdominant chord
of the major key because, even though it only contains notes from the major
scale and forms the only other major triad (besides the I and V triads), the IV
chord does not have “dominant” power to focus harmonic traffic towards the
tonic, the way the V7 chord does.
As a
major triad containing two notes not found in the other major triads, the IV
chord belongs with I and V7 as one of the three basic chords of the major key.
But, since it doesn’t have dominant power, it’s necessarily “subdominant,” like
Deputy Fester.
The IIm chord serves as the subdominant of the relative minor
key and belongs with VIm and III7 as one of the three basic chords
of the minor key.
6.7.5
THE
HARMONIC
SCALE:
FINAL
(“DEFAULT”)
VERSION
At last, with the final revisions in place, it’s
show time for the harmonic scale (Figure 56).
FIGURE 56
Harmonic Scale (“Default” Version)
In a
little while, you’ll learn how to creatively mess with the “default” version of
the harmonic scale—customize it to create strong, interesting chord progressions.
To try out the default version of the harmonic scale, once again
swap the Nashville Numbers for the chords of the keys of C major
and A minor (Figure 57):
FIGURE 57
Harmonic Scale (“Default” Version): Key of C Major / A Minor
In the sections ahead, you will learn how to use harmonic scales
the way you use melodic scales (major or minor).
When
you write a tune, do you simply go up and down the scale without skipping any
notes? Without repeating notes? Without doubling back? Without reaching outside
the scale to grab chromatic notes? Of course not! You’d never dream of limiting
your melodic creativity that way.
Similarly, when you use a harmonic scale, you will not simply go
round the circle clockwise, without skipping any chords, without
doubling back, without grabbing chords from outside the harmonic
scale.
A harmonic scale is not some formula that you have to adhere to
rigidly, any more than a major scale is a rigid formula. A harmonic
scale is just a scale, like a melodic scale. If you use harmonic scales
intelligently, your music will just get better and better.
Both
melodic and harmonic scales provide coherent frameworks that enable you to write
music of infinite variety without sacrificing unity. Ultimately, that’s why
songwriters and composers use scales of any description, melodic or harmonic.
Your
brain—and the collective brain of your audience—has evolved to reject tonal
confusion and accept the tonal order (founded on simple frequency ratios)
inherent in the octave, diatonic scales, the triad, and the harmonic scales.
6.7.6
TWO
DIFFERENT
ANIMALS:
COMPARING THE
CIRCLE
OF FIFTHS
WITH THE HARMONIC
SCALE
You might have noticed a vague resemblance between the Circle of
Fifths and the circular harmonic scale. Except for their shape, the
two are totally different. Different in structure, different in function.
Table 44 summarizes the differences.
TABLE 44
Summary of Differences Between the
Circle of Fifths and the Harmonic Scale
|
Circle of Fifths
|
Harmonic Scale
|
Shape
|
Circular
arrangement of
Key signatures.
|
Circular arrangement of
chords.
|
Other Names
for the Same
Thing
|
• Heinichen’s Circle of Fifths
• Modulatory
Circle of Fifths
• Real Circle of Fifths
|
• Key-specific Circle of Fifths
• Virtual Circle of Fifths
NOTE: Do not use these
names. They do not reflect
reality, and will only confuse
you.
|
Constituent
Elements
|
Key signatures and
letter names of
keys.
|
Chords.
|
Number of
Constituent
Elements
|
12 key signatures
representing 2
keys each.
|
7 chords.
|
Number of
Keys
Represented
|
24 keys—12 major keys and 12 relative minor keys.
|
2 keys—1 major and 1 relative minor key. (There are 12 different circular
harmonic scales, one for each pair of keys—major and relative minor.)
|
Natural
Direction of
Motion
|
Clockwise or
counterclockwise.
|
Clockwise is the “natural” direction.
|
Visual
Representation
of Major and
Minor Keys
|
Represented in
parallel. Major and
minor keys form
concentric circles.
|
Represented in series.
Chords of one major key and
one minor key form part of the
same circle.
|
Main Purposes
|
• To show key signature formation. Proceeding clockwise, sharps increase by one.
Proceeding counterclockwise, flats increase by one.
• To show degree of relatedness of keys to each
other. Keys adjacent to each other share all the same scale notes but one, so
are musically closely related. Keys across the circle from each other share few
of the same scale notes, so are musically remote.
|
• To show the natural direction of harmonic scale neighbours within a single pair
of “relative” keys. Proceeding clockwise resolves harmonic imbalance and
tension. Proceeding counterclockwise creates harmonic imbalance and tension.
• To provide an easy way to identify third and
second progressions. Second progressions are separated by one position on the
circular scale. Third progressions are separated by two positions.
• To show how dominant and subdominant chords
relate to tonic chords.
• To show secondary dominant chords.
• To show how the chords of major and relative
minor keys relate to each other.
• To provide an easy visual means to spot pivot
chords for purposes of modulation. Any two harmonic scales, no matter how
musically distant their constituent keys, will always have at least two chord
roots in common. These chords can be used to pivot smoothly between keys without
losing tonal unity.
|
6.7.7
CIRCLE
OF FIFTHS:
THE
MISTAKE
OF TREATING
KEYS
AS “CHORDS”
For generations, students, songwriters, and even music teachers,
unaware of the harmonic scale and how it works, have used the Circle of Fifths as a
crude harmony- organizing tool.
Big mistake.
If you treat the key names in the Circle of Fifths as chord names
and proceed around the Circle of Fifths counterclockwise, you get
descending fifth progressions. (Such progressions even have a
name: Circle-of-Fifth progressions.)
This
is counter-intuitive, because the “natural” direction of the hands of a clock is
obviously “clockwise” (the 12 positions of the Circle of Fifths are arranged to
resemble a clock face). But apart from that, the Circle of Fifths has several
major disadvantages as a harmonic scale stand-in:
1. No key-specific organizing framework. As you progress
around the Circle of Fifths, you exit the key after the second
chord! And you don’t return unless you go all the way round the circle.
(More on this in a moment.)
2. No
connection between the chords of a major key and the chords of its relative
minor. Not only is the bridging diminished chord missing, but the 12 minor
chords are visually organized in their own separate circle. Again, if you start
a chord progression in any given minor key, you exit the key after two chords
and don’t return until you go all the way round the circle.
3. No identification of dominant sevenths or subdominant
chords for any given key.
4. No way to identify third and second progressions.
5. No way to identify pivot chords for purposes of modulation.
The Circle of Fifths has its uses, but not for showing pathways to
meaningful, coherent chord progressions and harmonic movement.
Many musicians mistakenly think that the Circle of Fifths actually
has something to do with chord progressions. Even authors of books
on songwriting and music theory make this mistake, propagating
rubbish and confusing their readers to no end.
To be
clear: the Circle of Fifths shows key signatures and key relations—but not chord relations.
Here's
an example of what happens when you treat the elements around the clock face of
the Circle of Fifths as chords instead of keys. Presumably, you would want to
progress around the Circle of Fifths as though it's a big circular chord
progression. To simplify matters, consider the outer circle only, the elements
that would be the major “chords” if the Circle of Fifths had anything to do with
chords (Figure 58):
FIGURE 58 Circle of Fifths: Outer Circle Only
Start
at the top of the Circle of Fifths with the first chord, which is C, the tonic
chord in the key of C. Then, moving counter-clockwise around the circle,
progress to the next “chord,” which is F. Now you have a perfectly good
two-chord progression in the key of C, namely C progressing to F.
So far, so good.
However
(continuing counter-clockwise), the next “chord” you progress to is B♭. Now
you’ve got a problem. The chord B♭ is not a chord in the key of C. Therefore, at
this point you've actually exited the key of C.
As you
progress the rest of the way round the Circle of Fifths, you do not re-enter the
key of C until you get to the “chord” G.
Clearly, then, any notion that the elements of the Circle of Fifths
having anything to do with chord progressions is wrong. The Circle
of Fifths shows relationships among and between keys, not
relationships among and between chords within a given key.
To
summarize, the Circle of Fifths does not work as a chord progression device.
That’s the job of the harmonic scale—which also happens to be circular in shape,
but has no functional relationship with the Circle of Fifths.
6.7.8
COMPARING
MELODIC
SCALES
WITH HARMONIC
SCALES
Before discussing how to make practical use of
harmonic scales for fun and profit, here’s a summary of the differences between
melodic scales and harmonic scales (Table 45):
TABLE 45
Summary of Differences Between
Melodic Scales and Harmonic Scales
|
Melodic Scales
|
Harmonic Scales
|
Scale Units
|
Notes (pitches).
|
Chords (triads, sevenths,
etc.).
|
Number of
Units in Scale
|
Normally 5 to 7
notes, not including
repetition of the
octave note.
|
Always 7 chords.
However, each harmonic
scale position may be
occupied by one of
numerous variants of the “default” chord.
|
Number of
Scale Types
|
Many types,
including major and
minor diatonic,
pentatonic, modal,
Indian, Arabic, etc.
|
Only one type: the
harmonic scale.
|
Number of
Scales in
Western Tonal
System
|
24 in total: one
melodic scale for
each major key and
one for each minor
key. (Note: there
are several minor
scale variants:
natural minor,
melodic minor,
harmonic minor.)
|
12 in total: one harmonic scale for each pair of relative keys—major and
relative minor.
|
Scale Degree
Numerical
Labels
|
Arabic numbers
represent scale-
degree notes. For
example, the notes
of the diatonic
scale are
represented as 1,
2, 3, 4, 5, 6, 7, 1(8).
|
Nashville Number
System: Roman numerals
represent chords named
for their scale-degree
roots. Alphabetic letters,
Arabic numbers and other
symbols represent chord
functions. For example:
I Major triad with root
of scale degree 1
IIm Minor triad with root of
scale degree 2
V7 Dominant seventh
chord with root of
scale degree 5
VIIº Diminished
chord with “root” of scale degree 7 (in reality, diminished chords are rootless)
|
Scale Degree
Alphabetical
Labels
|
Alphabetic letters
represent the notes
of a specific
melodic scale.
Accidentals follow
the letter-names of
the notes where
applicable.
For example, the D major scale is: D, E, F♯, G,
A, B, C♯, D.
|
Alphabetic letters
represent the chords of a
specific harmonic scale.
Accidentals follow
letter-names of chords
where applicable.
Alphabetic letters, Arabic
numbers and other
symbols are then added,
representing chord
functions.
For example, the harmonic scale for the key of
D major and its relative minor is: D, G, C♯º, F♯7, Bm, Em, A7, D.
|
Normal Interval
Movement
Between
Adjacent Scale
Degrees
|
Melodic interval of
a semitone or a
tone.
|
Harmonic interval of a fifth
progression.
|
Natural
Direction of
Movement
|
Ascending or
descending are
equally natural.
|
Descending only
(clockwise) is natural.
|
Visual
Representation
|
Vertical curve:
|
One-way circle:
|
~ • ~ • ~ • ~
~ • ~ •
~ • ~
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