For example, why are a C6 and a C4 both considered to be the note of C? They sound different, so why the repeated naming convention? Can people (without extensive musical training) hear some similarity between the two that indicates they are the same note?
In: Mathematics
It is down to physics. The frequency of a given note doubles each time you go up an octave. Picking the note A because the maths is easy, the frequencies in hertz of the A keys of a piano are:
27.5, 55, 110, 220, 440, 880, 1760, 3520
We perceive this array of frequencies as the same note because they stimulate our senses in very similar ways. Unless listening to a pure tone, instruments will generate different harmonics as well as the fundamental frequency. It is the strength of these harmonics that we perceive as tone.
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