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CHAPTER 3:
How Tones and Overtones REALLY
Work
  
3.2  Overtones: The Harmonic Series

 
PAGE INDEX
  

3.2.1 The Tone Path To Your Brain

3.2.2 A House Is Not a Home, and a Tone Is Not a Tone

3.2.3 So, What Exactly Are Harmonics/Overtones?

3.2.4 Not Just One Overtone—A Bunch of ‘Em

3.2.5 The Harmonic Series (Overtone Series)

3.2.6 Your Brain’s Automatic Tone-processing Skill

3.2.7 Bring Out Those Overtones!

3.2.8 Overtones Identify Musical Instruments and Voices

 

~ • ~ • ~ • ~


3.2.1

THE TONE PATH TO YOUR BRAIN


Acoustics is the study of sound and its transmission.


     When you pluck a string of an acoustic guitar to initiate a tone, here’s what happens:

 

        The string vibrates really fast. Hundreds of times per second. So fast that your eye can’t follow the movement.

 

        The vibrating string connects to the body of the guitar via the bridge. This enables the vibrating string to set the body of the guitar flexing back and forth at the same frequency (number of vibrations per second) as the vibrating string.

 

        When the guitar body flexes one way, it compresses the air molecules that surround it (compression). When it flexes the other way, the air pressure drops (rarefaction). As the guitar body flexes back and forth, the compression and rarefaction of the surrounding air particles repeats itself over and over. And over and over. Really fast.

 

        As a result, spherical pulses—pressure waves—of air particles radiate outward in all directions from the flexing guitar body. Really fast. These pulses—not the air itself!—move through the atmosphere at 743 miles an hour, the speed of sound. (In Canada, that’s 1,188 km per hour, which seems faster than in America, probably because of the cold, crisp Canadian air.)

 

        The tone travels as a pressure wave through the air until it hits your ear drum. At that point, it transmogrifies into mechanical motion, setting your ear drum vibrating, just like the diaphragm inside a microphone.

 

        And then those three teeny bones in your middle ear get into the act. Remember the “hammer, anvil, and stirrup” from elementary or middle school? Smallest bones in your body.

 

        Finally, your inner ear transduces the vibrations into nerve impulses. The nerve impulses then travel to a number of different parts of the brain, each specialized to analyse a specific element of the sound, some related to pitch (tones, intervals, chords), some to time (beat, pulse, tempo meter, rhythm).


     At this point, your brain interprets your original plucking of the guitar string as a tone. Or, if you’re British, a note.


     The whole process happens so fast it seems instantaneous. You pluck the guitar string, you hear the corresponding tone or note instantly.


     If you’re listening to a song, depending on how well crafted the tune is, you may then experience an emotional reaction as your brain processes the music.


     Being a parallel processor, your brain easily and automatically handles all the different sound processing tasks simultaneously.


     Your brain may look up tones in a neural dictionary. The cortex of marmoset monkeys contains pitch-sensitive neurons, that is, neurons that actually code for pitch. These nerve cells respond to specific frequencies, which means that if the same holds true for humans (it’s likely), then the human brain stores a vocabulary or dictionary of different pitches, the way the brain stores a vocabulary of words.



3.2.2

A HOUSE IS NOT A HOME, AND A TONE IS NOT A TONE


So, that’s what happens when you hear a tone (or note).


     Or is it?


     Music—as distinct from sound—begins, not with tones, but with something called harmonics or overtones (these two terms mean the same thing) and their role in the construction of scales (the subject of Chapter 4).


     When you play the note “Middle C” on the guitar (B string, first fret), the string vibrates 261.6 times per second (assuming you’ve tuned your guitar), or 261.6 cycles per second. Also called 261.6 Hertz, after physicist and wave theory pioneer Heinrich Rudolf Hertz. Also abbreviated 261.6 Hz.


     The vibrating string sets the body of the guitar pulsing at the same frequency, 261.6 Hz.


     When you play the same note, Middle C, on the piano, a hammer hits some strings attached to the sound board inside the piano, which starts vibrating at the same frequency, 261.6 Hz.


     You hear the same note, Middle C, on each instrument. Yet, you can easily tell the sound of the guitar from the sound of the piano.


     How come?


     The answer has to do with tone color. The technical term for tone color is timbre (pronounced, TAM-ber, unless you know proper French). It’s a function of harmonics, or overtones.



3.2.3
S
O, WHAT EXACTLY ARE HARMONICS/OVERTONES?


Try this little experiment:


     Grab your guitar again. Acoustic or electric, it doesn’t matter. If it’s electric, plug it into an amp and crank it a bit. If you’re a keyboard player, borrow a guitar.


     If you don’t know how to play guitar, that’s okay—you don’t have to know how to play to do this:

 

        Tune the high “E” string down to “C” (Middle C). (Never mind why Middle C is called Middle C. Or why it vibrates at 261.6 Hz instead of some nice round number like 250. That’s coming up in a bit.)

 

        Now pluck the string. When you do this, you set the whole string vibrating at 261.6 Hz.

 

        If you look closely, you can observe the string blur, immediately after you pluck it. The blurring becomes less intense as the note dies away.


     Whether you realize it or not, when you pluck the string, at the same time as the string vibrates at 261.6 Hz, the string also automatically divides itself in half. The two halves vibrate at exactly twice the frequency, 523.2 Hz. You can’t see this—the string vibrates way, way too fast for the naked eye to see. You observe only a blur.


     This secondary high-speed vibration, at a frequency of 523.2 Hz, also produces a tone, of course. But that tone has a considerably higher pitch than Middle C. The secondary tone is called a harmonic or overtone.


A harmonic or overtone has two properties:

 

     1.  It’s higher in pitch than the original (261.6 Hz) tone, and

 

     2.  It’s way softer in volume than the original (261.6 Hz) tone.


     Now, with overtones in the picture, the original tone needs a name to distinguish it from the overtones. That name is the fundamental. You can think of the fundamental as the primary tone, and the overtone as secondary, because it’s softer.


     The overtone is so soft that the much louder sound of the full-length string vibrating at 261.6 Hz, the fundamental, drowns out the overtone. (In a few situations—when playing an electric bass, for example—an overtone can sound louder than the fundamental. But that’s the exception to the rule.)



3.2.4

NOT JUST ONE OVERTONE—A BUNCH OF 'EM


Now things finally start to get interesting from a musical perspective. That vibrating string, at the same time it divides itself in half, also divides itself into thirds. And quarters. And fifths. And sixths. And so on, and so on, and so on. All at the same time.


     In other words, the string vibrates in a complex way. The secondary vibrations happen much too fast for the eye to see.


     Each of the string-subdivisions produces a different, soft, high-pitched overtone. The comparatively loud fundamental drowns out all of them. So it seems that you don’t even hear the overtones. But you do. Your brain does process them (coming up in just a moment).


     To summarize: a single vibrating string (or other vibrating thing—such as a pair of vocal folds) simultaneously divides itself many times and produces a whole series of soft, high-pitched overtones. Dozens.



3.2.5

THE HARMONIC SERIES (OVERTONE SERIES)


If you have the right equipment, you can identify and measure all the overtones present when you pluck a single guitar string and produce Middle C. The frequencies of all the dozens of overtones turn out to be simple whole-number multiples of the fundamental.


     Taken together, the fundamental and all the overtones are called the harmonic series or the overtone series (these two terms mean the same thing).


     Table 4 below shows the frequencies of the first 15 overtones of Middle C. It’s important that you sit down right now and memorize every single number in the “Frequency” column.


     (No, wait! It’s not important.)

   



TABLE 4  Fundamental and First 15 Overtones of the “Middle C” Overtone Series


  Tone /

 Overtone

Multiple of

Fundamental

Frequency

(Hz)

Fundamental

1st Overtone

2nd Overtone

3rd Overtone

4th Overtone

5th Overtone

6th Overtone

7th Overtone

8th Overtone

9th Overtone

10th Overtone

11th Overtone

12th Overtone

13th Overtone

14th Overtone

15th Overtone

1 (f)

f x 2

f x 3

f x 4

f x 5

f x 6

f x 7

f x 8

f x 9

f x 10

f x 11

f x 12

f x 13

f x 14

f x 15

f x 16

261.6

523.2

784.8

1,046.5

1,308.0

1,569.6

1,831.2

2,093.0

2,354.4

2,616.0

2,877.6

3,139.2

3,400.8

3,662.4

3,924.0

4,186.0





     These are just the first 15 overtones—they continue on and on, ever higher in pitch, ever softer. The next overtone in the series above would be the 16th overtone, with a frequency 17 times that of the fundamental, or 4,447.2 Hz.



3.2.6

YOUR BRAIN’S AUTOMATIC TONE-PROCESSING SKILL

 

Although you think you only hear Middle C, (the fundamental, at 261.6 Hz), your brain sort outs all the overtones. Automatically. Without the slightest conscious effort on your part. A miraculous feat of naturally-selected engineering.


     Any note you play on any musical instrument is named for the fundamental, even though each note comes with a bunch of overtones.


     Your brain has evolved mechanisms to identify harmonic relations. It breaks a tone into its various harmonics or overtones, analyses them, then puts them back together to identify the sound as a specific tone (as opposed to random noise).


     Because the separate harmonics are related to each other in simple frequency multiples (Table 4 above), the brain understands that a single soundmaker must be producing them. The necessity of identifying soundmakers probably drove the evolution of the brain’s naturally-selected ability to parse a tone into its overtones. In Palaeolithic times, having the capacity to tell the difference between an owl’s hoot and a lethal predator’s growl would have saved you from getting eaten.


     The harmonic series is sometimes known as the chord of nature, because it’s not cultural in origin; it’s a phenomenon of nature. Any tone, whether coming from a musical instrument or not (e.g., pinging a wine glass), consists of a fundamental plus a batch of overtones that are always related to the frequency of the fundamental as integer multiples of the fundamental.

 

 

Homing in on the Human Hearing Range

 

The range of human hearing spans roughly 20 Hz at the low end to 20,000 Hz at the high end. That means your brain does not respond to tones or overtones with frequencies lower than 20 Hz or higher than 20,000 Hz.

 

Of all the common acoustic musical instruments in the world, the piano has the widest frequency range. Its 88 keys span a range of 27.5 Hz to 4,186.0 Hz.

 

What do you hear when you plink that last, highest key of the piano? You hear the fundamental tone at 4,186 Hz, and your brain also picks up and processes the first few overtones. But only the first few.

 

Recall that overtone frequencies are always whole-number multiples of the fundamental. So the first overtone of the highest note on the piano has a frequency of 8,372 Hz. The second overtone, 12,558 Hz. The third overtone, 16,744. Your brain probably does not process the fourth overtone—it’s too high.

 

The highest key of the piano actually produces dozens of overtones, but your brain does not react to any of the ones with pitches higher than about 20,000 Hz.

 

Suppose, by accident or disease, your hearing became restricted to, say, 5,000 Hz at the high end. Would you still be able to hear every note on the piano? Yes, you would. But the instrument would sound muffled, lacking in treble. That’s because your brain would not be able to process the rich array of overtones in the 5,000 to 20,000 Hz range.

 

Roedy Black’s Musical Instruments Poster, available at www.CompleteChords.com, shows the pitch ranges of more than 70 musical instruments and six vocal ranges. The Musical Instruments Poster organizes the information by note and by frequency, including the frequencies of each of the 88 notes of the piano.


 

3.2.7

BRING OUT THOSE OVERTONES!


Normally, you do not hear overtones directly, the way you hear fundamentals. But you can hear for yourself what overtones sound like.


     Try this (if you’re a guitar player, you probably know how to do this):

 

        If you’re right-handed, pluck the guitar string—the one you tuned to Middle C a few minutes ago—with your right hand. At the same time, with any finger of your left hand, lightly touch the vibrating string just over the 12th fret (over the metal fret itself, not the space between frets).

 

        What you now hear is a high-pitched note. You have “exposed” the sound of the first overtone by damping (“killing”) the sound of the fundamental. You have effectively cut the string in half, and you can hear both halves vibrating at the same frequency. What you’re hearing is the first overtone of Middle C, vibrating at double the frequency of Middle C.

 

        The point at which you damped (muffled) the fundamental using your finger is called a node. You can clearly hear the overtone, even though it sounds softer than the fundamental was before you damped it.

 

        Pluck the string again, but this time, lightly stop the string over the seventh fret. Now you hear a completely different overtone. It’s even higher-pitched than the first one. And it’s softer. It’s the second overtone.

 

        Pluck the string again. This time, lightly stop the string over the fifth fret. Yet another, even softer overtone. So soft, you can barely hear it. The third overtone.

 

You can keep doing this, teasing out even higher, fainter overtones.

 

 

Another Way of Exposing Overtones

 

Next time you have access to an ordinary acoustic piano (upright or grand), try this:

  • Lightly press down on Middle C, and also on the E and G immediately above Middle C—so lightly that the hammers do not hit the strings.
     

  • Hold down the three keys. The strings associated with Middle C, E, and G are now undamped and free to vibrate.
      

  • With your left hand, hit the note C below Middle C. Give that key a short, hard, quick, unsustained “bonk.”

The vibrating strings of C below Middle C cause the sound board to vibrate only for the brief duration of the “bonk.” However, the C-below-Middle-C bonk sets the open strings of the three keys you are holding down into sympathetic vibration. This causes the soundboard to vibrate and produce sound waves at the same frequencies as some of the overtones of C below Middle C. So that’s what you hear—a series of faint harmonics of C below Middle C.


    

3.2.8

OVERTONES IDENTIFY MUSICAL INSTRUMENTS AND VOICES


When you play a single note on any musical instrument, the note consists of a fundamental tone plus a whole series of simultaneous overtones. No matter what the instrument is. Not only that, it’s the same group of simultaneous overtones, regardless of the musical instrument.


     So, if it’s the same group of overtones, why does a guitar sound different from a piano when you play Middle C on each instrument?


     Because the loudness (volume) of each individual overtone is different for each type of instrument, depending on the instrument’s shape, size, construction, etc.


     Your brain’s evolved music-processing modules instantaneously analyse the varying loudness levels of the overtones and accurately sort out which overtone series belongs to which instrument.


     Each instrument produces its own “overtone signature”—its own characteristic array of relative loudness levels of each overtone. That’s what gives rise to an instrument’s unique tone color or timbre. And that’s why you can instantly differentiate the sounds of numerous musical instruments.


     Your brain can do this for all manner of different sound sources, not just musical instruments. Practically any source of sound. They all produce overtones, each with its own characteristic overtone signature.


     Your voice and all other human voices have unique overtone signatures. You can easily tell different human voices apart, even when you can’t see who’s talking or singing. This capability of the human brain makes possible industries such as radio broadcasting and sound recording.


~ • ~ • ~ • ~

 

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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

   7. Pulse/Meter/
  
      Tempo/Rhythm

   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
     
  Performance

  

 PART IV
 Making a
 Living In Music
 12.
Business of
   
     Music

 
 Appendixes

   

 Notes

   

 References

  

 Index
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   Top

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 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

   7. Pulse/Meter/
  
      Tempo/Rhythm

   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
     
  Performance

  

 PART IV
 Making a
 Living In Music
 12.
Business of
   
     Music

 
 Appendixes

   

 Notes

   

 References

  

 Index
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   Top

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 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

   7. Pulse/Meter/
  
      Tempo/Rhythm

   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
     
  Performance

  

 PART IV
 Making a
 Living In Music
 12.
Business of
   
     Music

 
 Appendixes

   

 Notes

   

 References

  

 Index
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   Top

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 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

   7. Pulse/Meter/
  
      Tempo/Rhythm

   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
     
  Performance

  

 PART IV
 Making a
 Living In Music
 12.
Business of
   
     Music

 
 Appendixes

   

 Notes

   

 References

  

 Index
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   Top

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 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

   7. Pulse/Meter/
  
      Tempo/Rhythm

   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
     
  Performance

  

 PART IV
 Making a
 Living In Music
 12.
Business of
   
     Music

 
 Appendixes

   

 Notes

   

 References

  

 Index
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   Top

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 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

   7. Pulse/Meter/
  
      Tempo/Rhythm

   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
     
  Performance

  

 PART IV
 Making a
 Living In Music
 12.
Business of
   
     Music

 
 Appendixes

   

 Notes

   

 References

  

 Index
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   Top

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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