I would like to ask about something like theoretical foundations or fundamentals of an 88 piano keyboard. My thinking is
a) there is a range of pitch a human can hear (lets assume that there is no interpersonal differences)
b) there is a number of tones (not sure if this is a right name) a human can differentiate (out of this range in #a); lets just assume this. My question is - what is or could be the number of these "tones" and what is the best of objectively measuring them (is it in Hertz)?
c) as far as my knowledge goes (but it is not complete yet, as I have asked the above questions) this is laid out on a piano keyboard (and lets assume that we are talking only about the main 7 octaves (like there is these two white keys and the beginning and one white at the end, lets exclude these; unless you could explain why they are there). Now every octave is 12 keys - wbwbwwbwbwbw (as colors) - Do we have exactly the same distance between these as far as the number of units that we would use to measure these sounds or tones (as in the question #b)? I am talking about laying it out one after another - lowest tone to the highers, so the black ones would also be in the mix (like the first black one after the first one). Basically kind of going in the direction how this range of pitch "a human can hear and differentitate" translates onto this keyboard and why.
d) Is the above, how this translates onto a keyboard arbitrary or not? What are the reasons for doing it this particular way (I know that this could be a lenghty disuccion, but maybe... :) )?
e) Looking at these 88 keys they are different but have something in common (in this "music theory system" that I dont yet understand, I will add) as we have (as an example) C1, C, c, c1, c2, c3, c4 - and these applies to all the other ones white, we can make sets of this. So my question is - what is this "occurence", how this can be explained? Like a range of pitch a human can hear and differentiate and then there is tones or pitches in the mix that are different (in these units that we would measure) but also have something in common too? What is the nature of this relation, how this can be explained?
f) What is the difference between white and black keys? Are the black keys less important (it has always seemed to me this way; if we could pick just one type it would definitely be the white keys)?
g) So we have octaves. Could we have a system where this would be 14 sounds or 16 sounds as a mix (and also with these repetitive tone names, like the C1, C and so on, example above)? (Is this something like, yes, there could be but the sounds would be too similar to each other so more than 12 is not a needed thing - like getting into this aspect of differentiation - like 12 is a good pick, more would be too close to each other in how they sound to a human and it would sound [closer to] the same [than not, lets say, to a human]).
Thanks a lot for the reading.