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PAGE
INDEX
5.5.1 The Keys, They Are A-changin’ (Good Thing,
Too)
5.5.2 A Brief, Star Spangled Modulation
5.5.3 Signalling a Shift In Tonal Centre
5.5.4 “The Centre Cannot Hold” (Or Can It?)
5.5.5 Keys in Cozy Relationships
5.5.6 Octaves and Fifths: Simple Frequency Ratios, Close
Relatives
5.5.7 Why
Heinichen’s Circle of Fifths, While Somewhat Useful, Is Often Misunderstood and
Misused
5.5.8 Tonality and Tonal Music
5.5.9 Distinguishing Tonal Music from Modal Music and Atonal
Music
5.5.10 Emotional Effects of Tonality
~ • ~ • ~ • ~
5.5.1
THE
KEYS,
THEY
ARE
A-CHANGIN’
(GOOD
THING,
TOO)
Why in blazes did so many people struggle for so long to come up
with a musical system of 12 major keys, 12 minor keys, and equal
temperament?
To
open and explore new frontiers of brain-friendly musical variety without
sacrificing musical unity.
As
will become clearer in later chapters, with too little variety, listeners get
bored. With too little unity, they get confused. The equally-tempered 24-key
system enables composers and songwriters to move around melodically and
harmonically from key to key, while maintaining a cohesive musical narrative.
Changing keys within a piece of music is called modulation.
Modulation enables a songwriter to slip through tonal doorways
into the parallel universes of other keys. It's one of the most
powerful ways to create interesting, evocative music. Most
songwriters don't use modulation simply because they don't know
how. It's not difficult to learn, and you certainly don't need to know
anything about music notation to make full use of modulation.
Each of the 12 major and minor keys has a unique set of notes.
Think of each key as its own musical universe. If you write a song
that stays in one key throughout the song, you effectively stay within
one musical universe—even though there's nothing stopping you
from travelling to any of 23 other musical universes using
modulation.
For example, you could start off in the key of C Major. You
compose a tune using the notes C, D, E, F, G, A, and B. Then, you
could switch to the key of E♭ major, and continue the tune using the
notes E♭, F, G, A♭, B♭, C, and D (see Table 24 above). When you
do this (modulate), the tune suddenly takes on new life, because the
key of E♭ introduces a parallel universe of notes.
• It's a parallel musical universe because, as you can see in
Table 24, the E♭ major scale uses the same interval order as
the C major scale:
● tone ● tone ● semitone ● tone ● tone ● tone ● semitone ●
• But it's a different musical universe, because every note of
the E♭ major scale is pitched three semitones away from its
counterpart in the C major scale.
It's as though you're playing your guitar without a capo and singin' a tune in the key of C major, and then, part way through the
tune, exactly when you want it to happen, a capo magically clamps
down on the third fret (while you continue playing chords in the key
of C), changing the key to E♭ major.
Parallel Universes on a Somewhat Grander Scale
Speaking of parallel universes, you might be living in one
universe and
copies of you in other universes.
Physicists have hypothesized that the existence of parallel
universes would explain a number of observed phenomena in
quantum mechanics and cosmology that otherwise don't make
horse sense.
One of the best known and respected hypotheses is that of the
American physicist Hugh Everett. According to his “many-worlds”
or “multiverse” interpretation of quantum mechanics, there are
many copies of you, each existing in a separate parallel universe.
However, a phenomenon known as “quantum decoherence”
prevents you from communicating with your other selves. (Dang!)
Mathematically, Everett's theory respects scientific determinism
(important in formulating theories in physics), and also does not
require the acceptance of hidden variables, a weakness of other
interpretations of observed phenomena in quantum mechanics.
Some evidence indicating the existence of parallel universes:
• Physicists have conducted many successful
demonstrations of teleportation, from data-encoded laser
beams to calcium and beryllium atoms. (Alas, they have
not yet succeeded in teleporting Captain Kirk...)
• A number of investigators have successfully demonstrated
quantum computing on a small scale. A quantum computer
could theoretically handle huge numbers of complex
calculations millions of times faster than conventional
computers because the computations would take place
simultaneously in parallel universes.
• Solitary particles passing through a “double slit” apparatus
at random intervals of time create interference pattens that
could only be made by groups of particles. Copies of
particles from parallel universes passing through the
double slits at the same time as the solitary particles would
explain the collective characteristics of the interference
patterns.
David Deutsch and Michio Kaku (see the
References section),
among others, have written good, readable books on parallel
universes, in case you're interested in what your other selves
might be up to.
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5.5.2
A
BRIEF,
STAR
SPANGLED
MODULATION
Modulation is both melodic and harmonic in nature. What follows is
an example of a brief modulation. Chapter 6 goes into more depth
about the various types of modulation and the kinds of chord
progressions you can use to modulate.
How exactly do you modulate? One way is to exploit the brain's
recognition of the semitone move from 7 to 1 (8), from the leading
tone to the key note of the scale. For example, stick a semitone
move in an unexpected place and use it to signal a modulation—a
change to a new key with a different tonal centre.
This is what happens near the beginning of “The Star Spangled
Banner,” on the notes to the words, “early light.” The tune does not
proceed along the scale like this (the numbers represent scale
degrees):
3 4 5
ear - ly light
Instead, the tune has a sharpened scale degree 4, creating a
semitone between 4 and 5:
3 ♯4 5
ear - ly light
Suppose you're singing
“The Star Spangled Banner” in the key
of C major. If the tune had been composed without using any
chromatic notes (notes outside the notes of the C major scale), then
you would sing these notes:
E F G
ear - ly light
and the tune would sound completely different from the tune you
know. Instead, songwriter John Stafford Smith did this:
E F♯ G
ear - ly light
That's the sequence of notes you actually sing.
A sharp (♯) or flat (♭) symbol that designates a chromatic note
that a composer adds into a tune is called an accidental. So, in the
above example, the “♯” sign in “F♯” is an accidental.
Purposeful Accidentals
You could run across any of five kinds of accidentals:
|
Notice that move from F♯ to G. A chromatic note causes a
semitone move. That's the important thing here. Did songwriter
Smith make this move to signal a change to another key (a
modulation)? If so, which key is the music moving to?
First, have a look at the interval order of the major scale (for the
umpteenth time):
● tone ● tone ● semitone ● tone ● tone ● tone ● semitone ●
There are two semitones in this interval order. One is between scale
degrees 3 and 4. The other is between scale degrees 7 and 1 (8).
Next, have a look at Table 30 below (an excerpt of Table 24). It
shows that only two keys have the specific interval, F♯ to G. One
occurrence, in the key of D major, corresponds to the move from 3
to 4. The other, in the key of G major, from 7 to 1 (8).
TABLE 3O
Major Keys with Occurrences of F♯-to-G
Interval
So, if that F♯ is signalling a modulation, it could be to one of two
keys. It could be to the key of D via 3 to 4. Or it could be to the key
of G, via 7 to 1 (8).
Which is it?
One way to signal a new tonal centre is to hold a note a bit
longer after making a move from VII to I (8). In this example, the
word “light” gets held for a couple of beats.
So, it would appear, the modulation is to the key of G, because
the note G is held for a couple of beats. This is what songwriter
Smith has done.
But the modulation does not last very long. Hardly long enough
to consider it a bona fide modulation. Within a couple of notes, the
tune goes back into the key of C.
The modulation is just long enough to accomplish the
songwriter's aim: to infuse the tune with some variety without
sacrificing unity.
A limited modulation of this nature, a modulation that does not
completely establish another tonal centre, is usually called a
tonicization. In this example, the F♯ “tonicized” G—made G the tonic
note—although only briefly. No clear-cut boundary exists between
tonicization and full-blown modulation. Think of tonicization as a mild
modulation. Modulation lite. It adds color, variety, interest.
In an inspired stroke of modulatory repetition, the songwriter
duplicates this tonicization later in the tune, on the words “was still
there” (i. e., in the phrase, “our flag was still there”). This reinforces
unity (repetition) plus variety (modulation).
5.5.3
SIGNALLING
A SHIFT
IN TONAL
CENTRE
Another way to strongly signal a shift in tonal centre is to exploit the
other semitone interval in the major diatonic scale, the interval from
3 to 4.
Suppose, for example, your tune starts by running up the scale
from 1 to 3 and back a few times. Then it moves from 7 to 1 (8) to
establish 1 as the tonal centre.
Then suppose the tune repeats a move from 3 to 4 several
times, then continues up the scale to 5, then 6, touching on ♭7, then
back down to 6 and up to ♭7 and back once or twice. Then back
down to 5, then 4.
For example, starting in the key of C major, the tune would run
up and down the scale from C to D to E and back a few times. And
also from B to C to establish the initial tonal centre.
Then it would go from E to F several times. Then it would
proceed up to G, A, and touch on B♭, back and forth once or twice.
Then back down to G, then F.
It's that B♭ that sends a signal to your listener's brain that
something has changed. The note B♭ is not a note in the C major
scale. It's a foreign, chromatic note. This heightens musical interest.
By introducing that B♭ note, you have signalled that the tonal
centre has shifted.
• The notes E and F have become the new scale degrees 7
and 1 (8).
• The notes G, A, and B♭ have become the new scale degrees
2, 3, and 4.
• That means you have modulated from the key of C major to
the key of F major.
Look it up. Table 24 above. Try it out to get the drift of it.
The thing is, you have control over these musical variables. If you
want to, you can pick a couple of keys, decide you're going to write
a tune that modulates from one key to the other and back again,
then write a tune and a set of chord changes that does exactly that.
If you know what you're doing, the tune is likely to be a lot more
musically interesting than it would have been had you stayed in one
key throughout.
5.5.4
“THE
CENTRE
CANNOT
HOLD”
(OR
CAN
IT?)
Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned
— W. B. YEATS (“The Second Coming”)
Yikes! Mr. Yeats, it couldn't be that bad, could it?
Well, actually, it could. Modulation means changing the tonal
centre within a song or other composition. And when you change the
tonal centre, mere anarchy just might be loosed upon the world if
you aren't careful.
Some songwriters modulate skilfully. Most are afraid to even try.
Some modulate clumsily, throwing in melodic twists and chord
changes without the slightest idea of what they're doing musically.
This has nothing to do with ability or inability to read or write music.
If you move the melody at random to some chromatic note or
other, or throw in an out-of-context chord, thinking you're introducing
musical variety, chances are, you'll screw things up. You will muddy
the waters. Mere anarchy will be loosed upon the world. The
blood-dimmed tide will be loosed. And, yes, everywhere the
ceremony of innocence will be done drowned. And maybe your
horse, too.
When you're experimenting with new tunes and chord changes,
you need to have an awareness in the back of your mind of the
musical implications of introducing chromatic notes into a tune.
Particularly when you also accompany chromatic notes with
chromatic chords (chords comprised of notes that are outside the
key you're playing in). You might actually be signalling a
modulation. Whether you know it or not. Whether you mean to or
not.
When you do this, the brains of your listeners will be searching
for a new tonal centre—even though they aren't conscious of it.
So if you don't understand how to handle switching tonal centres,
you're likely to confuse (and alienate) your audience.
As you'll see in Chapter 6, it's a lot easier and faster to switch
tonal centres—to modulate—when you use chord changes to
accompany melodic moves, because chords wield multi-tonal power.
Try out these examples of modulation:
1. Play the chord C major on your guitar or piano for a few bars,
while humming the note G.
Now change to the chord E major while simultaneously
changing your humming-note to G♯.
2. Play the chord C♯ minor while simultaneously humming the
note sequence:
E,
then down to C♯,
then down to G♯,
then back up to C♯,
then back to E.
Repeat this E – C♯ – G♯ – C♯ – E tune a few times.
Now change
the chord to C major, while simultaneously changing
the tune to E – C – G – C – E.
5.5.5
KEYS
IN COZY
RELATIONSHIPS
The more notes two keys have in common, the more closely they're
related. Coziness of relationship between keys plays a big role in
modulation. Keys that share the identical set of notes have the
coziest relationship—the majors and their relative minors.
For example, the key of C major and A (natural) minor use
exactly the same seven notes. The two keys are simply organized
around two different tonal centres.
Equally important are keys that have all but one note in
common—six out of seven notes. For example, the key of C major
has these seven notes:
C D E F G A B
The key of G major has these seven notes:
G A B C D E F♯
Six out of seven notes belong to both keys. So the keys of C major
and G major have a cozy relationship.
Similarly, the key of F major has these seven notes:
F G A B♭ C D E
Six out of seven notes belong to both the key of C major and the
key of F major. So the keys of C major and F major also have a cozy
relationship.
Every key (major or minor) has a close relationship with five other
keys (out of a total of 24 keys). Specifically, every key has a cozy
relationship with:
1. Its relative minor or major key. The scales of both keys use
the same seven notes (e.g., key of C major and key of A
minor);
2. The key whose tonic note is scale degree 5. The scales of
both keys have six out of seven of the same notes in
common (e.g., key of C major and key of G major);
3. The relative minor or major of the key whose tonic note is
scale degree 5. The scales of both keys have six out of seven
of the same notes in common (e.g., key of C major and key
of E minor);
4. The key whose tonic note is scale degree 4. The scales of
both keys have six out of seven of the same notes in
common (e.g., key of C major and key of F major);
5. The relative minor or major of the key whose tonic note is
scale degree 4. The scales of both keys have six out of seven
of the same notes (e.g., key of C major and key of D minor).
5.5.6
OCTAVES
AND FIFTHS:
SIMPLE
FREQUENCY
RATIOS,
CLOSE
RELATIVES
Overtones and their frequency ratios (yet again) underlie close key
relationships. The frequency ratios of the first few overtones of any
fundamental tone correspond mostly with scale degrees 1 and 5,
which have the two simplest frequency ratios, 2:1 and 3:2,
respectively (Table 31 below).
Consider, for example, three fundamental tones, C, G, and F,
and their overtones. The note G appears as two of the first five
overtones of the fundamental tone C. The note G also appears as
two of the first five overtones of the fundamental tone G itself.
Just as G is scale degree 5 of C, so C is scale degree 5 of F.
Therefore, as expected, The note C appears as two of the first five
overtones of the fundamental tone F. The note C also appears as
two of the first five overtones of the fundamental tone C itself.
To generalize, any two keys (and their relative major or minor
keys) whose tonic notes are an interval of a perfect fifth apart, such
as C and G (G is scale degree 5 of the key of C) or F and C (C is
scale degree 5 of the key of F) have a close and special relationship.
TABLE 31 Overtones and “Fifth” Relationships
Tone /
Overtone
|
Multiple of
Fundamental
|
Freq.
Ratio
|
Assoc-iated
Scale
Degree
|
Examples:
Tones in Key
of . . .
|
C
|
G
|
F
|
Fundamental
1st Overtone
2nd Overtone
3rd Overtone
4th Overtone
5th Overtone
|
1 (f)
f x 2
f x 3
f x 4
f x 5
f x 6
|
1 : 1
2 : 1
3 : 2
2 : 1
5 : 4
3 : 2
|
1
1
5
1
3
5
|
C
C
G
C
E
G
|
G
G
D
G
B
C
|
F
F
C
F
A
C
|
5.5.7
WHY
HEINICHEN’S
CIRCLE
OF FIFTHS,
WHILE
SOMEWHAT
USEFUL,
IS
OFTEN
MISUNDERSTOOD
AND MISUSED
We owe a small debt of gratitude to German music theorist and
prolific but under-appreciated composer, Johann David Heinichen,
who, in 1728, published the Circle of Fifths. This simple “clock face”
shows the special relationships between keys with tonic centres a
fifth apart (Figure 40 below).
If Mr. Heinichen were to rise from his grave today, who knows
how many thousands (or, perhaps dozens) of songwriters and composers would show up and form a queue leading to his tombstone
to shake his hand and thank him for his somewhat useful musical
clock face.
And also to ask him, by the way, if there's life after death, what
it's like if there is, why did he rise from his grave, and would he like
to stay or go back.
FIGURE 40 Heinichen's Circle of Fifths
The bottom three elements of the Circle of Fifths show
enharmonic keys. For example, F♯ major is the enharmonic
equivalent of G♭ major.
The Circle of Fifths shows the
key signature for each key—the
sharps or flats that belong to the key. The key signature shows you
which notes to sharpen or flatten when you play in a key, so that you
maintain the diatonic interval order for the key (e.g., tone, tone,
semitone, tone, tone, tone, semitone—the diatonic order for all
major keys).
Looking at the top of the Circle of Fifths, you can see that the
keys of C major and A minor have no sharps or flats, so there's just
a treble clef with no sharps or flats. As you move down each side of
the Circle of Fifths, the number of sharps and flats increases by one,
for each successive key.
For any key in the circle, the adjacent keys (major or minor
modes) are the keys most closely related. For example, look at the
key of A major on the right side of the Circle of Fifths. The adjacent
keys, D major and E major, are the keys most closely related to A
major. That means D major and E major share six out of seven of
the same notes as A major. To confirm this, have another look at
Table 24.
Is the Circle of Fifths useful if you don't read music?
In a word, yes.
For example, you can use the Circle of Fifths to find out the key
of a song when you use a book of lead sheets that show the song's
basics— chords, lead vocal melody line, and words. Suppose the
lead sheet of a song has a key signature with four sharps. The Circle
of Fifths tells you that the song must be in the key of either E major
or C♯ minor. The chords will make it pretty obvious which of these
two keys prevails.
It's easy to overestimate the usefulness of the Circle of Fifths. It
has its place as a device for identifying keys, but it's not something
you need to regard as an essential tool.
A lot of musicians mistakenly think the Circle of Fifths has
something to do with chords and chord progressions. Sadly, they
labour for weeks, months, and yea, even years of their lives, 16
hours a day, miserably attempting to reconcile the data in the Circle
of Fifths with odd notions of chord construction and progressive
harmonic intervals. Or something.
In Chapter 6, you will get to know another circular device that
looks a bit like the Circle of Fifths but is much, much more useful. It's
called the harmonic scale.
5.5.8
TONALITY
AND TONAL
MUSIC
Also in Chapter 6, you'll learn that, when you modulate, you don't
have to stick to closely-related keys, such as adjacent keys in the
Circle of Fifths. In fact, it's often harder to move the tonal centre (i.e.,
modulate) to a closely-related key because the two keys have so
many notes in common. This sometimes makes it difficult for your
listeners to figure out which key you're in. For this reason, a
successful modulation usually takes several measures.
Have another look at the Circle of Fifths (Figure 40 above). The
further apart the keys are on the circle, the less closely they're
related. For example, the key of C major is more closely related to
the key of G major than to the key of E♭ major.
Modulation to a distant or unrelated key often enlivens a piece of
music very substantially—if done skilfully. Modulation introduces the
element of surprise.
It's Not Only NBA Players Who Pivot
As you'll discover in Chapter 6, more often than not, a modulation
requires something called a pivot chord. A pivot chord is a chord
that has one role in the original key, but a different role in the new
key.
The melody usually moves chromatically in conjunction with a
chord change to the pivot chord. This enables the tune and its
harmony to magically pivot like an NBA player out of the original
key and into one of 23 other possible keys.
Sometimes a series of chord changes and melodic moves will
pivot the tune quickly through a series of keys: a modulation
chain. These are called transient modulations, and normally result
in the tune finally setting up shop in a new tonal centre.
|
Before you can modulate, you first have to establish a tonal
centre. There's a term that encompasses everything that goes into
establishing a tonal centre. That term is tonality.
Music based on 24 keys, equal temperament, and tonality is
usually referred to as tonal music, or sometimes Western tonal
music.
The great majority of the popular music of the West is tonal
music, including nearly all 5,000 songs on the GSSL. (And the music
of composers such as Bach, Handel, Mozart, Beethoven, Chopin,
and Tchaikovsky.)
Tonality refers to all of the organized relationships of pitches
around a key note or tonic centre, including:
• The tonic note or key note itself
• The scale named for, and related to, the tonic note
• The chords related to the tonic note
Just think of “tonality” as meaning the same thing as “key.”
For instance, if you pick up your guitar or sit down at your piano
and
• Play the chord C major for a few bars, while you
• Hum or sing a tune comprised of notes from the C major
scale (C D E F G A B),
• Including the tonic note, C,
then you're playing and singing in the tonality of C or the key of C.
This concept is vital with respect to modulation because, to
modulate successfully, you have to first establish one tonality, then
move tonality to a different tonal centre (change keys),
then—usually—return to the original tonality.
If you don't know what you're doing, this process can get dicey
because:
• There are 24 possible keys (12 major, 12 minor), and your
listener's brain can only make sense of the tonal relationships
of one key at a time—one tonality. (Well, usually. In Chapter
6, a brief analysis of the song “Gimme Shelter” illustrates how
two tonalities can coexist simultaneously.)
• Those 24 keys are all based on a selection of the same 12
pitches only (the individual notes of the chromatic scale), so
if you're playing in a given key and you introduce chords and
notes from other keys without knowing what you're doing, you
can easily muddy the tonality and confuse the listener's
music processing modules.
When your melody emphasizes certain notes of the scale, such
as 1, 3, and 5, and when you play certain chords, such as the chord
built on the key note (the chord C major in the key of C major),
you're establishing tonality in the collective mind of your audience.
(They don't know consciously that you're doing this, of course.)
Once you've established tonality, your listeners expect that the
notes to follow will be related to the tonal centre in simple frequency
ratios—the notes of the diatonic scale for the key you're in.
When you're composing a tune, with the intention of modulating,
you have to firmly establish tonality early. A song runs only three or
four minutes. You can't successfully move to a different key until
your listener's brain has first locked into the identity of the original
tonality.
Most songs have an instrumental introduction of four, eight, or
sixteen bars. One of the main reasons for having that instrumental
introduction is to establish tonality.
5.5.9
DISTINGUISHING
TONAL
MUSIC
FROM MODAL
MUSIC
AND ATONAL
MUSIC
You might consider modal music as a kind of tonal music, but only
in a decidedly restricted sense. Each of the modes has a tonic note
and a scale based on small integer frequency ratios.
But ...
• For reasons discussed earlier, the true sense of a tonal
centre doesn't materialize in modal scales;
• True modal chords and chord progressions are seriously
problematic. This is explored towards the end of Chapter 6.
Nevertheless, modal scales can be put to good use in Western
tonal music, as you'll see in later chapters.
Then there's atonal music. No diatonic order, no tonal centre, no
tonality.
Atonality refers to music composed deliberately without a tonal
centre. It's usually associated with, among others, Arnold
Schoenberg and his serial system. Serial composers seek to
compose music with every note having the same importance,
avoiding the likelihood of the listener recognizing a tonal centre. The
result, atonal music, is practically unlistenable except by a hardy
minority of masochists. But Schoenberg and the atonalists deserve
credit for bravery, attempting as they did (unwittingly) to modify
preferences in the human brain that evolved over millions of years.
Hardly anybody actually listens to atonal music because of the
near exclusion of small-integer ratio intervals in melody and
harmony. The brain hears atonal “music” as chaotic, irritating static.
The brain responds to small-integer-ratio tunes. That's biological
reality. It's inborn, true of infants, true of adults, and applies cross-culturally.
Brain recognition of organized relationships of tones is not a
science or technology. It does not become obsolete with the
invention of “upgraded tonal technology” such as atonal
composition. Tonality is linked in the brain directly with human
emotions, which have not changed from generation to generation for
many thousands of generations.
5.5.10
EMOTIONAL
EFFECTS
OF TONALITY
Table 32 lists a few emotions found to be associated with clear vs
unclear tonality (and atonality).
Even if you're playing in what you think is a major key, and are
deliberately trying to express positive emotions, your music may
unintentionally have negative emotional effects on the audience if
tonality is unclear and you don't realize it.
On the other hand, if you want to express negative emotions
musically, you can certainly put unclear tonality (or atonality) to good
use.
TABLE 32
Emotional Effects of Tonality
Tonality Characteristic
|
Associated Emotions
|
Clear tonality (major or
minor mode)
|
Happiness, sadness,
tenderness, joy, peace
|
Unclear tonality (highly
dissonant)
|
Fear, sadness, anger
|
Atonality
|
Anger
|
~ • ~ • ~ • ~
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