The Chord of Nature (harmonic series) (2) 

All physical sound is wave motion or vibration. 

A vibration or a wave motion may be simple in form, it may perhaps be very complex in form. Whether simple or complex, if it keeps repeating itself exactly, is of a special kind. It is called periodic.

As long as a vibration or wave is periodic, the form of its motion, however complex, can be shown to be consist of a special set of very simple elemental motions, all added together, each of which is called a simple harmonic motion. An audible sound produced by a simple harmonic motion is a 'pure tone', rather like the sound of a tuning fork. The complex tone produced by a complex vibration or wave that is periodic, therefore consists of a special set of 'pure tones'. These 'pure tones' are called harmonics and are arranged in the so-called Chord of Nature. Their frequencies are arranged in a harmonic series, which means from the lowest frequency upwards, they are arranged in the ratios

1 : 2 : 3 : 4 : 5 : 6 : 7 . . . etc.

Notice that the ratio between the 2nd and 1st harmonic is 2:1 - so they are an octave apart. (See Background to the Musical Scale). Similarly, the 3rd and 2nd have the frequency ratio 3:2, so they are a perfect fifth apart, and the 4th and 3rd are a perfect fourth apart.

For a note C, an octave below middle C, the first 10 harmonics in the chord of nature would be:  

The accidental on the note B is a contemporary '3/4 flat' sign. This is included because the 7th harmonic is rather flat, making the chord of the first 8 harmonics a dominant seventh with an 'out of tune' seventh. 

When sound comes from a source that is not perfectly periodic, the chord of nature may still be inherent in the sound, but the chord will be slightly 'imperfect'. Musical strings are sources whose motion is generally very close to being periodic, so the chord of nature is clearly recognisable as inherent in their tone. If a sound source is not perfectly periodic, the 'pure tones' are then not true harmonics with frequencies arranged in the harmonic series, but may nevertheless be very close to this. Rather than 'harmonics', they are properly called partials.

Any musical tone with a definite pitch can be 'diffracted' into partials, usually arranged in the Chord of Nature, much as white light can be diffracted into colours of the rainbow. The component simple tones within the Chord are beautiful to behold, and stand at the threshold of the inner world of sound. 

Although the 7th harmonic or 7th partial is 'out of tune' by the standards of Western tonality, there is nothing 'wrong' with it. It is, in fact, absolutely perfect in its relationship to the other partial or harmonic tones - but to hear this one has to be free of the expectations brought about by Western musical conditioning.

Many sounds do not have a definite musical pitch. Such sounds are usually generated from aperiodic sources. Sounds from aperiodic vibrations and waves are still generally composed of 'pure tones' or partials, but not necessarily arranged in the 'chord of nature'.

When was this discovered . . . ?

How does this affect consonance . . . ?

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