The Harmonic Series


In the pages on singing bowls we can see how the sounds of singing bowls are composed of separate, different ingredient sounds (partials).

Many musical sounds (and sounds from many other things that were not designed for musical purposes) have their sonic ingredients (partials) arranged in a special way, called a harmonic series. When this is the case the sonic ingredients (partials) are called harmonics.

The idealised form of an harmonic series is associated with a series of frequencies in the ratios 1:2:3:4:5:6;7… and so on. An harmonic series in audible sound will generally be some kind of approximation to the ideal.

Many musical instruments produce sounds that are rich in harmonic series. The tone of a single string on a piano, guitar, violin, and other stringed instruments, is composed of an harmonic series (approximating to the ideal).

A notable feature of the harmonic series is that in the first part of the series there are recognisable musical intervals (as associated with Western music) between the harmonics. So the first 8 harmonics, for example, constitute a major seventh chord. The first 6 constitute a root-position major chord.

Here are some examples of the harmonic series.

Harmonics 1

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Illustration of the harmonic series.

In these examples the first harmonic we hear is harmonic number 1, the second is harmonic number 2, and so on. As the harmonic number gets higher, so the "musical distance" between the adjacent harmonics gets smaller. A theoretical harmonic series is infinite. Notice the characteristic combined tone of the higher harmonics.
Another example of the first 22 harmonics:

Harmonics 2

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This is an example of the characteristic musical harmony of the first 7 harmonics, which make a major seventh chord:
And here is the first 8 harmonics, also a major seventh chord:


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This is an example of the harmonic series from a piano note. First, the note itself:
Here are the first 17 harmonics in order. You will probably need headphones or earbuds to hear the 1st harmonic which is low frequency:
And here are harmonics 18 to 23 all played together:


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The guitar note itself:
The harmonics 1 to 7:
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All seven "strummed":

Harmonic Bowls 1

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A first set of "harmonic singing bowls", whose voices are arranged as an ensemble, as the harmonic series. Such bowls are referred to in Ekanta, and are fictional.

Harmonic Bowls 2

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A second set of "harmonic singing bowls", whose voices are arranged as an ensemble, as the harmonic series. Such bowls are referred to in Ekanta, and are fictional.

Coffee Machine

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Even an ordinary coffee machine can produce the harmonic series.

For the purposes of this demonstration, the harmonics (under the coloured spheres) have been amplified, except from the first one. The 11th harmonic is absent from the series.
The coffee machine itself:


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