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When two musical notes are an octave apart, one has double the frequency of the other yet we hear them as the 鈥渟ame鈥� note 鈥� a 鈥淐鈥� for example. Why is this?

Perry Bebbington

Kimberley, Nottinghamshire, UK

This question has a false premise. I hear two notes an octave apart as different notes.

I have no musical training or skill, and accept that someone who does will label them as the same note, but that is a matter of nomenclature, not an indication that they are the same note.

Damian Pang

Discovery Bay, Lantau Island, Hong Kong

Our sensory organs pick up a range of stimuli from the environment around us, but what we actually perceive is our brain鈥檚 interpretation rather than an exact representation of what surrounds us.

鈥淭he sounds we perceive are our brain鈥檚 interpretation rather than an exact representation of the sounds around us鈥�

Sound exists only as a wave with an amplitude and frequency. We perceive sound as coming from a specific direction, which is the result of complex neural computations rather than what the cochlea in our ear directly picks up. Pitch 鈥� how high or low a note sounds 鈥� is also the result of our brain鈥檚 analysis, but unlike directionality, pitch doesn鈥檛 exist in the environment.

We perceive some sounds as having no pitch 鈥� a knock on a door, for example. We can distinguish if this sound is high or low, but we can鈥檛 assign it a musical note. Pitch is only perceived when a sound has a single frequency or evenly spaced frequency bands and periodic waves. In essence, pitch is the brain鈥檚 way of grouping harmonically related sounds. This helps us make sense of the flood of sounds around us, because many natural objects create sounds that are harmonically related.

This grouping helps the brain to solve the 鈥渂inding鈥� problem: the challenge to put deconstructed sensory pieces back together. Pitch perception allows us to focus on a conversation in a noisy environment, for example.

The same notes in different octaves are harmonically related: a harmonic series based on a low 鈥淐鈥� note contains the frequencies of every higher C. As such, these notes share a unique mathematical relationship with each other that they don鈥檛 share with other notes.

Since the brain creates pitch perception based on grouping harmonically related sounds, it isn鈥檛 surprising that we perceive related notes similarly.

There are some exceptions to this. The Tsiman茅 people in Bolivia, for example, don鈥檛 perceive a similarity between the same notes in different octaves. Traditional Tsiman茅 music usually only involves the playing of a single note at a time.

It could be that grouping pitch cyclically into octaves isn鈥檛 innate, but is culturally learned through the kinds of music we hear.

Ian Gammie

St Albans, Hertfordshire, UK

Take the note played by the bottom string of the cello. We hear this low C note as the strongest note, but it has a series of harmonic overtones.

The sound also contains a C one octave higher, a G a fifth higher than that, a C two octaves higher and many more overtones and dissonances reaching eventually beyond the range of the human ear. These overtones become progressively weaker as they go higher.

So we hear the cello鈥檚 bass C and can tell that it is a cello. The same note played on a bassoon or piano, say, will provide different qualities and volumes of overtones, depending on the characteristics of the instrument, what it is made of and the technique of the player. This enables us to differentiate which instruments are playing the same note.

Alan Harding

London, UK

Many aspects of human sensory perception are logarithmic, enabling us to perceive stimuli over a very wide range. With sound, each doubling of the frequency seems like the addition of an equal interval.

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