#1
Why do we use sharps and flats to represent some notes? My friend raised the point and was wondering why don't we just use separate letters to represent sharp / flat letters? For example, instead of A, Bb and B, we could use A, B and C (B representing the Bb, and C representing the B).

This may be a retarded question but I can't think of a specific reason... >_>
#2
it would complicate things way too much, and an Ab is still an A, just lowered a half step,

rearranging the entire music theory structure at this point would be stupid
#4
It's all to do with the history of western music. iirc , the first only had the white notes on a normal piano, ABCDEFG, because these were the only notes they could make with the string lenghts they knew. Therefore, they did name all the notes after letters because those were all the notes they used. Later on when they found out how to make all eleven semitones (because before the intervals between each note were not the same), they decided not to rename everything but just to put flats and sharps in.
This is also why medieval (right time period?) music was very modal, because they could only play in c major so they used different modes a lot more.

I hope this helps, please correct me if i have got anything wrong or just swear at me if it's all wrong.

12345abcd3
#5
All western music is based around tonalities. Accidentals, keys, sharps, flats, whatever...are there so that we can see what tonality a piece is in.

Example: say we are in what looks like C#maj. But then we see a peculiar thing, an E#/Gdouble#/B# chord. Gdouble sharp is the same as A!! BUT...now a musician can tell from that chord, oh, this piece is most likely centered around the tonality of a#minor and NOT C#Major (because in tonal music the 7th of a#minor(G#) is raised another half-step) It's a rather loose explanation, but I think it shows how if we had separate letters for every tone, we'd be very lost in figuring out what tonality we are in.

In ancient music(or at least up to the 11th century) - before our notation was invented, there was a system called neumes where there was a seperate symbol for each pitch. If you see an example of it, it's incredibly freakin' complicated. Other similar systems like you're describing(a different symbol/letter/number for each pitch) was also common around the world. So...in the end, musicians found that our current system was(though it's still complicated) the easiest to understand when reading.

But...there's always room for more improvement. Maybe you'll come up with a better system, who knows?

EDIT: Damnit! I knew someone would post a similar explanation while I was typing my wall post.
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#8
western music uses 7 tones.

A B C D E F G

thats 7.

this is the reason for it, it is much more obvious on some other instruments. a harp for example has 7 strings in each octave, with a pedal to sharp or flat them. it couldn't really work any other way could it?
#10
I always thought it was just to make it easier to organise - a bit like 12345 and KryptNet have already said.
In traditional Western theory, we've got 7 pitches in a scale, for whatever reason (we had to settle somewhere) and therefore seven pitches in any given key. Although we sometimes use others, they wouldn't really be in key.
So, if we want to be able to make different scales, we need a few more notes, but we still only use 7 notes per scale. The other 5 notes, therefore, are given names such as Ab or G#, and we make the rule that we can't have A and Ab in the same key. This helps us make sense of things by key and we base all our theory on it. Until you get to 12-tone music and serialism, then you're ****ed.
Any help at all, or just ramblings?