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.

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:

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 . . .

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

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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You are reading the FREE SAMPLE Chapters 1 through 6 of the acclaimed 12-Chapter book, How Music REALLY Works!, 2nd Edition. Here's what's in Chapters 7 through 12.

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TABLE OF
CONTENTS

PART I

The Big Picture Introduction

   1. W-5 of Music
   2. Pop Music
      Industry

PART II
Essential
Building Blocks
of Music
   3. Tones/Overtones
   4. Scales/Intervals
   5. Keys/Modes

PART III
How to Create
Emotionally
Powerful Music
and Lyrics
   6. Chords/
      Progressions