If you had separate B#, C and E#, F then you would have 14 semitones between octaves (instead of 12).
That would sound radically different (and dissonant) from what we're used to.
Since you'd be squishing 14 (instead of 12) notes between a doubling of frequency (next octave up), the adjacent semitones would be closer to one another in frequency. Frequency-wise, you wouldn't get the pleasing sounding intervals that we get in our 3rds, 5ths, etc. in the 12 semitone system. You'd get something very different.
Aside from the total unfamiliarity factor and cultural conditioning, I'm not sure how well those frequencies would mesh together.
This is a bit mathematical but I believe our ("well tempered") 12 semitone system with equal 2^1/12 factors separating adjacent frequencies (as you go up) was developed for good reason. Overall, it probably offers the most pleasing system for harmony. I don't think it's random.
Or ... maybe it's all a conspiracy to save money on fret wire!
That would sound radically different (and dissonant) from what we're used to.
Since you'd be squishing 14 (instead of 12) notes between a doubling of frequency (next octave up), the adjacent semitones would be closer to one another in frequency. Frequency-wise, you wouldn't get the pleasing sounding intervals that we get in our 3rds, 5ths, etc. in the 12 semitone system. You'd get something very different.
Aside from the total unfamiliarity factor and cultural conditioning, I'm not sure how well those frequencies would mesh together.
This is a bit mathematical but I believe our ("well tempered") 12 semitone system with equal 2^1/12 factors separating adjacent frequencies (as you go up) was developed for good reason. Overall, it probably offers the most pleasing system for harmony. I don't think it's random.
Or ... maybe it's all a conspiracy to save money on fret wire!
I was wondering this too. Why isn't it just A A# B B# C C# D D# E E# F# ?