Musical Half and Whole Steps with Respect to Frequency (Hz) [10 points!]?

Question by Sketchy Skeptic: Musical Half and Whole Steps with Respect to Frequency (Hz) [10 points!]?
I’m somewhat new to music theory and would like to truly understand it, not just memorize, so I can use it properly. I’m looking for a little more of an explanation that “because that’s the way Western music is”.

I would like to know why in a major scale we call E->F a half step and B->C a half step. An octave is a doubling of the frequency of a note, and I assume the notes A->G are spaced by some relationship of frequency (I would appreciate this relationship if you know). What I really want to know is, does this relationship of frequency actually change between E->F relative to D->E (i.e. is the expected jump in frequency between notes halved or something?) and if so, why does it sound good (do they sound like a half an interval the trained ear?), and why would they bother giving them major letter names- just laziness when making major scales?

I know that’s a lot of questions, but if you can answer them, you will have probably changed my entire outlook on music. Thanks in advance!

Best answer:

I don’t know music theory either, but I do know that Hz increases exponentially. Therefore, the jump from F3 to G3 is not as big number-wise as the jump from F4 to G4.

If you graph (easiest with a graphing calculator) the function y equals 2 to the x power,or y=2^x, you’ll notice that the interval from x=1 to x=2 is not as big as the jump from x=2 to x=3, which is not as big as the jump from x=3 to x=4, etc.
Here’s a picture of the function y=2^x

I think you may get more (and better, and more useful) responses if you ask again somewhere else entirely (not Y! Answers). Good luck, and sorry if I couldn’t help

Know better? Leave your own answer in the comments!

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