Harmonics, overtones and timbre

Harmonics, overtones and timbre


6 minute read

Sonic Environment 

We are constantly surrounded by sound. The sound of a car, the sound of people talking, the sound of cow bells, the sound of a dog barking, the sound of the wind in the trees and on and on. In these examples, harmony is not the goal, the sound is either the unintended consequence of a deployment of energy or the sound serves a utilitarian purpose- to warn or to locate for example. 

Conversely, we humans will frequently deploy sound with the intention of creating harmony. We delight in specific tonal relationships and combining tones and timbre in pleasing, delightful or interesting ways is considered an important aspect of what makes us human. What distinguishes arbitrary noises from sound arranged in a way that is considered musical is primarily the harmonious relationships between the frequencies, the judicious application of volume and the evocative power of timber.

One single sound can contain great beauty. A single note on a piano, a cleanly struck Tibetan bowl or even the rumble of thunder. Such sounds, however, will generally be complex in nature, not simple. that is to say that, while they may resonate in the key of a fundamental tone, the sound will also contain a series of other tones harmonically related to the fundamental, also known as overtones. This can be visualised if we imagine a guitar string. When it is picked, the dominant sound will be the pitch of the entire string vibrating. So, if we pluck the A string on a guitar, it will- if tuned to a standard tuning- oscillate 440 times per second. It is the tension of the string that determines how many times per second the string vibrates and this will be experienced as its particular pitch or tone- in this case middle A.  

However, the sound of the note will also contain a series of overtones, because it is not just the entirety of the string that vibrates, but also fractions of the length of the string. There is a separate, though less pronounced, vibration starting at the halfway point of the string. The halves of the string vibrate with a higher frequency than the fundamental. So, while the entire string is vibrating at 440hz, the first harmonic, the two halves of the string will be vibrating at 880Hz. The third harmonic, where the string divides into three equal parts, will vibrate at 1,320Hz. This sequence continues with harmonics at multiples of the fundamental, that is to say x2, x3, x4, x5 etc... These points of oscillation are functions of the fact that they interfere only minimally with the oscillation of the fundamental. 

These harmonic frequencies can sometimes be isolated from the complex wave form, either electronically or through certain vocal techniques, and heard individually as overtones. The particular combination of the fundamental and the overtones, which ones are emphasised and which ones are not, in combination with the elements of frequency and amplitude, creates what is known as timbre. Timbre is the unique signature of a particular sound when all of these elements are combined.

As Above so Below

As I mentioned earlier, a single sound can contain great beauty, in part because it contains all these elements. And a part of what distinguishes sound therapy from music is that the focus is on the beauty and complexity of sound per-se and not necessarily on the relationship between sounds. That said, we will soon become habituated to a repeated single sound and the combination of harmonious sounds, especially where the intention is on the creation of coherence, will have a calming and possibly therapeutic effect. 

It thus becomes important to follow a sequence that embodies a harmonic coherence as this is most likely to resonate with a person in such a way as to bring them into a resonant alignment. It would seem that our body responds at the level of our cellular tissue to the creation of certain harmonic relationships.

For example, if we hear a middle c note played on the piano and then hear the c note played one octave higher, we will intuitively recognise the close relationship between the two sounds and the arrangement will be pleasing to us. Similarly, other notes played along harmonic intervals of the fundamental will be pleasing. What is more, such arrangements seem to encode a narrative element. Every melody is organised around a fundamental tone. More often than not it commences with the fundamental tone, explores a range of harmonic possibilities before returning finally to the fundamental tone from which it started.

There is an irresistible parallel here between the narrative progression of a melody and the narrative progression of so many of our most ancient and oft-repeated stories. Consider the Hero's Journey, an archetypal tale that appears in many different cultures at many different times. The hero starts from the comfort and harmony of his or her home, is then compelled to undertake a journey during which he or she is confronted with challenges, or disharmonious situations which must be resolved. 

The hero embraces these challenges, perhaps relishing the opportunity to take the full measure of his or her strength and resourcefulness, before inevitably completing the journey with a return to the harmony of home. This basic progression can be found across the arts. Consider the lines from the poem Four Quartets by T.S.Elliot;

We shall not cease from exploration

And the end of all our exploring

Will be to arrive where we started

And to know the place for the first time. Or listen to Chopin's prelude in E minor and the way it meanders, almost seeming to dawdle as it reluctantly returns to the final harmonic resolution (beautifully described in this Ted talk by Benjamin Zander).

It is tempting to speculate whether the explanation for this tantalising symmetry, and the powerful emotional response that it can evoke in us, may be that it mirrors some more basic pattern that informs the coming into being and passing out of being of things. Perhaps the structure of our lives, perhaps all life, follows something like a harmonic progression of departing from an initial state of harmony, an exploration of the harmonic possibilities available to us, and the particular timbre of our voice, before resolving back into the initial harmony. And if something like that is the case, it may shed some light on the healing properties of music in general and sound therapy in particular.

Author: Oliver Sutton Owen

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