Hacker News new | ask | show | jobs
by euroderf 1883 days ago
As a kid I dismissed the piano because nobody explained to me why the keyboard was so stupid looking, laid out so irregularly. WbWbWWbWbWW. Wot? Only some self-education (much later) revealed that 12 tones per octave deliver some excellent harmonies, not 11 or 13 or 20 or 36 or whatever. Twelve. But the harmonies come only on odd steps. So we have 5 semitones to a perfect fourth (4:3 harmony), then two semitones to a perfect fifth (3:2 harmony), then 5 semitones to the octave. And then - just to keep it confusing - we have to split both of those groups of five semitones, so... we arbitrarily split them as 2-2-1 (i.e. WbWbWW keys). Thus the white/black keyboard pattern, starting at C, of WbWbWWbWbWW. If only someone had explained all this in grade school.
1 comments

I didn't really understand your explanation so I might be restating your ideas, but just in case:

> And then - just to keep it confusing - we have to split both of those groups of five semitones, so... we arbitrarily split them as 2-2-1 (i.e. WbWbWW keys). Thus the white/black keyboard pattern, starting at C, of WbWbWWbWbWW. If only someone had explained all this in grade school.

We don't arbitrarily split them! It was very much made on purpose to match the diatonic scales, which are very natural due to being a chain of fifths. E.g. from F ascending 5ths: F-C-G-D-A-E-B-¡F!

It's not arbitrary that we based modern keyboards around heptatonic scales! Then we added some black notes so we can transpose, which is pretty convenient on 12-TET.

I'm not sure what you're saying. B to F is not a fifth. A fifth up from B is F#.
Huh, I copypasted that from wikipedia but botched the text when trying to highlight the part where sharps start and left it half-written.

I'll just link the relevant wikipedia article:

https://en.m.wikipedia.org/wiki/Pythagorean_tuning

B to F is a fifth; that interval is called a diminished fifth (one semitone less than a perfect fifth like B to F#).
Yes, this is true, but it's not how the circle of fifths works (which is what the comment I was responding to seemed to be alluding to).
He's right though, that's not what I was trying to write (not a 3:2 ratio).