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.
I don’t know if you’re tone deaf, but all C notes sound similar, despite being different pitches. In fact, C5 sounds much more like C4 than B5 does, despite B5 being closer in pitch to C4. To normal, non-tone deaf people, they can hear the consonance between all the Cs and the strong dissonance between all Cs and Bs.
The phenomenon is due to the cyclic nature of pitches: the sound pressure waves move back and forth more synchronously for consonant pitches, and more every-which-way for dissonant pitches.
One way to visualize why C4 and C6 should be similar is to imagine the notes being positions on a clock, and the increasing octaves being the passing of one day to the next. 12 a.m. on Tuesday is similar to 12 a.m. on Wednesday, but unlike 9 a.m. on Tuesday, despite being on the same day.
There is a huge spectrum of sound frequencies we can hear but they all fall under a handful of notes to put it simply. Notes in music are represented by the letters A through G. If you start with A and increase the pitch all the way to G, it will sound much higher than A. But what if you want to go higher than that? Well if you did that you would hit A again, which would be the same note as that A played in the beginning but with a higher pitch than any of the notes mentioned in this example so far.
As a dude, if I wanted to casually sing along with a song that featured particularly high pitched vocals, I would probably take it down an octave in most settings to not sound ridiculous. I would still be hitting the correct notes, just on a different frequency.
The frequences of all sounds denoted by the same note relate to each other as 1:2:4:8:16:32:64:128:256. Yes, those same numbers from computer science.
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