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!
Cheers!

Best answer:

Answer by YahooUser
I’ll just answer one, see if you can figure out the rest.
One octave=doubling of frequency
There are 12 notes in one octave (never mind what they are called, 12 is the relevant number).

Each note differs from the previous ( and consequently the next one) by the 12th root of 2 which is about 1.0596. So the frequency of D is 1.0596x frequency of the (preceding) C and so on.

Note that this spacing makes the notes belong to a geometric, rather than arithmetic, progression.

Now, let’s introduce the notes’ names: A, B, C etc. We stop at G: that is seven names and we have 12 notes, so we add # (or ♭if you go backward … :-)) to each name. Problem: we now have 14 names for 12 notes! 2 have to go and you know which ones went.

Now,why 12 notes, why flats and sharps and so on: search the net, it is a long story. You may want to read why Bach composed the Preludes for the Well Tempered Clavier.

Know better? Leave your own answer in the comments!

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