In my sound therapy practice I work with frequency, amplitude, intensity, harmonics, overtones, timbre, pitch, vibration and resonance.
The number of times per second that a sound pressure wave repeats itself is called frequency. Frequency is measured in hertz (Hz). Humans with normal hearing can hear sounds between 20 Hz and 20,000 Hz. Frequencies above 20,000 Hz are known as ultrasound.
The lowest resonant frequency of a vibrating object is called its fundamental frequency. Most vibrating objects have more than one resonant frequency and those used in musical instruments typically vibrate at harmonics of the fundamental.
The fundamental frequency provides the sound with its strongest audible pitch reference – it is the predominant frequency in any complex waveform.
If we could watch a vibrating object in slow motion, you could see movements in different directions. A vibrating object moves back and forth from its normal stationary position. A complete cycle of vibration occurs when the object moves from one extreme position to the other extreme, and back again. When we think about sound, we often think about how loud it is (amplitude, or intensity) and its pitch (frequency).
AMPLITUDE AND INTENSITY
A vibrating object moves to a certain maximum distance on either side of its stationary position.Amplitude is the distance from the stationary position to the extreme position on either side and is measured in metres (m).The intensity of vibration depends on amplitude. Acceleration is a measure of vibration intensity.
Envelope or Change in Volume over Time. In sound and music, an envelope describes how a sound changes over time. It may relate to elements such as amplitude (volume), filters (frequencies) or pitch. An ADSR envelope determines how sound unfolds over time. It can be defined by four numbers, representing attack time, decay time, sustain level (the amplitude to which the sound decays and is then sustained constant by the player), and release time.
FREQUENCY AND NOTES
The frequencies 440Hz and 880Hz both correspond to the musical note A, but one octave apart. The next higher A in the musical scale would have the frequency 1760Hz, twice 880Hz. In the western musical scale, there are 12 notes in every octave. Notes correspond to frequencies:
B flat 466Hz
C sharp 554Hz D 587Hz
D sharp 622Hz E 659Hz
F sharp 740Hz G 784Hz
A flat 831Hz
The frequency of a sound wave is what your ear understands as pitch. A higher frequency sound has a higher pitch, and a lower frequency sound has a lower pitch.
A harmonic is defined as an integer (whole number) multiple of the fundamental frequency. Frequencies produce harmonics. A harmonic is a multiple of a fundamental frequency. For example a fundamental frequency of 500 Hz has a first harmonic frequency of 1000 Hz (2f), double the fundamental frequency. Its second harmonic is 1500 Hz (3f), the third harmonic is 2000 Hz (4f), and so on.
The frequencies of the harmonics are integer multiples of the fundamental frequency. This mathematical connection is called a “harmonic series”. The frequency difference between two harmonics is always identical to the basic frequency, accordingly.
Dissonance (or disharmony) is defined as the perceived stability or instability of two or more sounds. Whereas consonance (or harmony) is perceptually defined as the stability of two or more sounds. The opposite of resonance is dissonance. Dissonance happens when energy moves back and forth between two or more bodies without merging into unified pulsation. Even harmonics are the “musical” or “pretty” harmonics, while the odd harmonics can be interpreted to sound negative, rough or noisy sounding.
Partials are made up of a series of notes in the harmonic series. Odd and even refers to the numbering of the harmonic partials.
2nd, 4th, 6th, 8th… are even partials 3rd, 5th 7th, 9th… are odd partials
An overtone is a part of the harmonic series above a fundamental note. The lowest frequency is called the fundamental and the higher frequencies are referred to as overtones and harmonics.
THE HARMONIC SERIES
When you play a note on a particular instrument, say middle C on a piano, the resulting sound is a complex wave. That piano string vibrates as a whole but it also vibrates in halves and in thirds and in fourths and so on when it does this it produces notes above the note that was played which we call harmonics.
In this series which we call the harmonic series or overtones series we call that bottom note the fundamental (also called the first partial). That fundamental will have a particular frequency for example this A note has a frequency of 55 Hz, we find each additional partial by adding the fundamental frequency. In many cases we cannot individually distinguish the different overtones which are sounded, these overtones contribute to the overall sound colour or timbre of an instrument.
Overtones are also present in our voices and, in fact, they are responsible for our own unique speaking and singing qualities.
DIFFERENCE BETWEEN HARMONICS AND OVERTONES
Harmonics and overtones are often used interchangeably. Harmonic series is sometimes used interchangeably with overtone series but it is not the same. There is a mathematical difference between harmonics and overtones. While it is possible for harmonics to be overtones and for overtones to be harmonics, it is also possible to have harmonics that are not overtones, and overtones that are not harmonics. To make things simple without having to get into too much math all you have to remember is this:
Harmonic: resonant frequency that is an integer multiple of the fundamental frequency.
Overtone: any resonant frequency above the fundamental frequency.
The term overtone does not imply harmonicity or inharmonicity and has no other special meaning other than to exclude the fundamental.
A Pure Sound generates no or few overtones, a pure tone is a sound with a sinusoidal waveform; that is, a sine wave of any frequency, phase, and amplitude. Single-frequency sound waves are sinusoidal waves. Although pure single- frequency can be created artificially by means of a computer. Naturally occurring sound waves are mostly combinations of frequency components.
The musical term for frequency is pitch. Though they both describe the same thing, they aren’t quite synonymous. Frequency and pitch describe the same thing, but from different viewpoints. While frequency measures the cycle rate of the physical waveform, pitch is how high or low it sounds when you hear it. This is directly related to frequency: the higher the frequency of a waveform, the higher the pitch of the sound you hear. Though pitch and frequency are not equivalent, they are correlated. This means that as one goes up, the other does as well. A higher frequency produces a higher pitch, and a lower frequency produces a lower pitch. In music, the pitch of a note means how high or low the note is. In physics, it is measured in a unit called Hertz (Hz).
Frequencies are labeled with numbers, and pitches are labeled with letters. Pitches also repeat themselves, so you can have the same pitch at different octaves. Frequencies are more specific than pitches. A particular pitch can have many different frequencies. For example, the note A could be any frequency from 425 hertz all the way up to 455 hertz.
Resonance was discovered by Galileo Galilei with his investigations of pendulums beginning in 1602. The word resonance comes from Latin and means to “resound” – to sound out together with a loud sound. When the forced vibration frequency is the same as the natural frequency, the amplitude of vibration can increase tremendously. We know from study of simple pendulums that without being pushed, the person in the swing rocks back and forth with a frequency that depends on gravity and the length of the chain. This is one example of a natural frequency – the frequency at which a system vibrates normally when given energy without outside interference.
Pushing on the person in the swing will affect the amplitude of the swinging. This is called forced vibration – when a periodic force from one object (the person pushing) affects the vibration of another object (the person swinging).
To get the most effect, the person pushing will start just at the very back of the swing. In other words, the frequency of how often they push is exactly the same as the frequency of the swing. Suppose they don’t push at the right time, but instead push at some other frequency. That would mean that sometimes they are pushing forward when the swing is still going backward. In that case, the swing would slow down – i.e. the amplitude of the swing will be reduced.
Timing the pushes of a swing to be the same as the natural frequency is called resonance. For this reason, the natural frequency is also known as the resonant frequency. If the pushes are timed just right, then even if each individual push is small, the vibration will get larger with each push.
Every substance has a natural, or resonant, frequency — the frequency at which its own atoms vibrate. The object’s natural, or resonant, frequency depends on the size, shape, and composition of the object. An object will vibrate strongly when it is subjected to vibrations or regular impulses at a frequency equal to or very close to its natural frequency. When one object vibrates at the same natural frequency of a second object it forces that second object into vibrational motion.
Sometimes this resonance is good—for example, when producing music with a stringed instrument. At other times, the effects can be devastating, such as the collapse of a building during an earthquake. Mechanical resonance can produce vibrations strong enough to destroy the object in which they occur. For example, soldiers marching over a bridge can set up extreme vibrations at the bridge’s natural frequency and shake it apart. For this reason soldiers break step to cross a bridge. In 1940 wind gusts at Puget Sound Narrows, Tacoma, Washington, caused a suspension bridge to vibrate at its natural frequency and the bridge collapsed.
Sound is powerful it can be destructive and it can also promote wellbeing.