Everything about Harmonics totally explained
In
acoustics and
telecommunication, the
harmonic of a
wave is a component
frequency of the
signal that's an
integer multiple of the
fundamental frequency. For example, if the frequency is
f, the harmonics have frequency 2
f, 3
f, 4
f, etc, as well as
f itself. The harmonics have the property that they're all
periodic at the signal frequency. Also, due to the properties of
Fourier series, the sum of the signal and its harmonics is also periodic at that frequency.
Many
oscillators, including the
human voice, a
bowed violin string, or a
Cepheid variable star, are more or less periodic, and thus can be decomposed into harmonics.
Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at several frequencies known as
overtones. When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the overtones are still integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Overtones whose frequency isn't an integer multiple of the fundamental are called
inharmonic and are sometimes perceived as unpleasant.
The untrained human ear typically doesn't perceive harmonics as separate notes. Instead, they're perceived as the
timbre of the tone. In a musical context, overtones that are not exactly integer multiples of the fundamental are known as
inharmonics. Inharmonics that are not close to harmonics are known as partials.
Bells have more clearly perceptible partials than most instruments. Antique
singing bowls are well known for their unique quality of producing multiple harmonic overtones or
multiphonics.
The tight relation between overtones and harmonics in
music often leads to their being used synonymously in a strictly musical context, but they're counted differently leading to some possible confusion. This chart demonstrates how they're counted:
| 1f | 440 Hz |
fundamental frequency |
first harmonic
|
| 2f | 880 Hz |
first overtone |
second harmonic
|
| 3f | 1320 Hz |
second overtone |
third harmonic
|
| 4f | 1760 Hz |
third overtone |
fourth harmonic
|
In many
musical instruments, it's possible to play the upper harmonics without the fundamental note being present. In a simple case (for example
recorder) this has the effect of making the note go up in pitch by an
octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the
timbre of the note. This is part of the normal method of obtaining higher notes in
wind instruments, where it's called
overblowing. The
extended technique of playing
multiphonics also produces harmonics. On
string instruments it's possible to produce very pure sounding notes, called harmonics by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a
unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found half way down the highest string of a
cello produces the same pitch as lightly fingering the node 1/3 of the way down the second highest string. For the human voice see
Overtone singing, which uses harmonics.
Harmonics may be either used or considered as the basis of
just intonation systems. Composer
Arnold Dreyblatt is able to bring out different harmonics on the single string of his modified
double bass by slightly altering his unique
bowing technique halfway between hitting and bowing the strings. Composer
Lawrence Ball uses harmonics to generate music electronically.
The
fundamental frequency is the
reciprocal of the
period of the periodic phenomenon.
Harmonics on stringed instruments
The following table displays the stop points on a stringed instrument, such as the
guitar, at which gentle touching of a string will force it into a harmonic mode when vibrated.
Table of harmonics
Audio Samples
Further Information
Get more info on 'Harmonics'.
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