摘要：When two musical notes are an octave apart, one has double the frequency of the other yet we hear them as the “same” note – a “C” for example. Why is this?
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.
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’s interpretation rather than an exact representation of what surrounds us.
“The sounds we perceive are our brain’s interpretation rather than an exact representation of the sounds around us”
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 – how high or low a note sounds – is also the result of our brain’s analysis, but unlike directionality, pitch doesn’t exist in the environment.
We perceive some sounds as having no pitch – a knock on a door, for example. We can distinguish if this sound is high or low, but we can’t 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’s 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 “binding” 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 “C” note contains the frequencies of every higher C. As such, these notes share a unique mathematical relationship with each other that they don’t share with other notes.
Since the brain creates pitch perception based on grouping harmonically related sounds, it isn’t surprising that we perceive related notes similarly.
There are some exceptions to this. The Tsimané people in Bolivia, for example, don’t perceive a similarity between the same notes in different octaves. Traditional Tsimané music usually only involves the playing of a single note at a time.
It could be that grouping pitch cyclically into octaves isn’t innate, but is culturally learned through the kinds of music we hear.
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’s 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.
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.