Chapter 1
All sounds are caused by vibrations. To make music you have to control vibrations.
Before we discuss notes, scales and more, let’s look at sound.
Understanding the structure of sounds is fundamental to all music creation. Sounds occur naturally in nature. Wind, rain, thunder, waves in the sea and lakes, rivers flowing, and tree branches shaking all create sound waves.
Animals and humans make unique sounds that are immediately recognisable as being a friend or foe. The human voice is a complex instrument. In simple terms, human sounds are made by air being pressed through a series of vocal cords, which vibrate similarly to string vibrations.
Every sound originates from a disturbance of some form. Disturbances create vibrations, which in turn create waves in a medium. String vibrations and the movement of air in wind instruments creates wave movements of air, which in turn reach our ear as sound waves.
Every sound originates from a disturbance of some form. Disturbances create vibrations, which in turn create waves in a medium. String vibrations and the movement of air in wind instruments creates wave movements of air, which in turn reach our ear as sound waves.
Wave theory involves some complex physics. We will not be visiting the maths behind waves in this section.
For those who wish to get a fuller understanding of the maths behind wave theory, the following link is to a video lecture produced by Prof. Walter Lewin of MIT on the subject.
Resonant Frequency
When an object is stimulated it will vibrate at its natural frequency and will emit a sound.
This natural frequency is called its resonant frequency.
If you wet one of your fingers and rub it along the circumference of the top of a wine glass, the glass will vibrate at its fundamental frequency. The fundamental is the lowest frequency at which the glass vibrates. This vibration will in turn produces a loud vibrating sound.
An object can also be stimulated into resonance by an external source. The breaking glass experiment is where a sound at the resonant frequency of a wine glass is played through a loudspeaker beside the glass.
The wine glass is seen to oscillate (move) at its resonant frequency. As the volume is increased through the loudspeaker, the glass will eventually break due to the increased amplitude of the vibrations occurring in the glass.
A tragic example of resonance is the collapse of the Tocamo bridge in 1940. Over that fateful day, wind gusts were increasing. These gusts created waves across a whole spectrum of frequencies. At some point, the bridge was stimulated to vibrate at its resonant frequency. The continuing gusts supported the resonant frequency vibrations until tragically, the bridge destroyed itself. Note the similarities between a suspended bridge where the middle spans are contained between two fixed pillars and a tensioned instrument string fixed at both ends.
We will now examine how waves behave in a string medium and how this behaviour is fundamental to understanding melody and harmony in music.
Note: Some of this information may seem technical and overwhelming. Don’t worry, it will make sense as we move through the lessons.
Let’s take a string fixed at two points:
When we pluck the string near the left fixing, waves travels down the string:
When the wave travelling down the string from left to right hits the barrier on the right it flips over and reflects back. The reflected wave will now travel to the left fixing, flip over and reflect again and travel over to towards the right fixing. This back and forth travelling action continues. We now have two travelling waves moving in opposite directions on the string.
If conditions for these waves are just right, the waves support each other and generate a large-amplitude wave.
Their superposition results in what is known as a standing wave.
Standing waves are produced whenever two waves of identical frequency and amplitude interfere with one another while travelling in opposite directions along the same medium. In any situation where two waves meet while moving along the same medium, interference occurs.
A standing wave pattern is not actually a wave; rather, it is the pattern resulting from the presence of two waves (sometimes more) of the same frequency and amplitude with different directions of travel within the same medium.
We will now look more closely at the tensioned string fixed at both ends like those fitted in a piano or any stringed instrument. The string is tensioned and fixed at position A at the left-hand end and position B at the right-hand end.
If the fixing “B” were not present, a wave would just keep travelling along the string until it came to an end somewhere or hit a barrier. The length of a wave is the distance between any two corresponding points on an adjacent wave.
A full wave, called a wavelength, is from position A to position C, in the image below.
A full wavelength has both a peak and a trough.
The travelling waves are shown at the top of the image above. The standing waves are shown in black, below the travelling waves. In the image above, the red arrows show that the standing wave does not travel but moves up and down, in a stationary position, between two zero positions (nodes).
To better understand how the travelling wave superimposes, a simulation of two travelling waves creating standing waves can be seen in this animation.
With a musical instrument, a string is fixed at both ends as shown below. The wave does not travel forward but is reflected at barrier B as shown below. The length of the travelling waves in an instrument string is half a full wavelength which equals the length of the string.
Earlier, we learned that the natural frequency of vibration of an object is its resonant frequency. The lowest resonance frequency is generated when the complete string goes up and down in a single wave between its fixings (nodes) to generates a single standing wave that goes up and down.
The standing wave produced by the single vibration of the whole string develops the maximum amplitude vibration possible for the string.
This single standing wave at the resonant frequency is called the fundamental frequency.
The harmonics produced by a single vibrating string follow a mathematical formula known as the harmonic series. The harmonic series is fundamental to any understanding of melody and harmony in music and we will examine it in detail.
Now, for the really interesting and most important information on string vibrations.
When a string is plucked, a whole spectrum of frequencies are thrown at the string and a whole series of travelling waves are produced.
We saw above, that only at very specific frequencies, called resonant frequencies does the string go up and down, generating standing waves that go up and down.
Now for the important piece, there are other specific frequencies that also simultaneously produce standing waves on a string.
A tensioned string that is fixed at both ends will simultaneously oscillate at specific frequencies that are multiples of the fundamental frequency. (All other frequencies that are not multiples of the fundamental are ignored).
These multiple simultaneous vibrations are called harmonics of the fundamental frequency (often called overtones).
The harmonic series is very appropriately named as consonant notes fit together in a mathematical form disclosed by the harmonic series.
Below we show the standing waves developed for the first six harmonics of a string vibration.
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Helpful Videos:
Before you proceed to the next section, and you have some free time, it might be beneficial to view a video on the structure of musical instruments and how they work in practice (by Prof. Walter Lewin of MIT).