What does “well-tempered” mean, such as in music – Bachs Well Tempered Klavier?
I don’t know how much you know about physics and music, but let’s have a go: You know that the pitch of a vibrating string is a function of how fast it vibrates (and also its length, but that doens’t count here). The A above middle C is generated by the string vibrating at a speed of 440 per second. (Middle C is 256 and you may be more familiar with that, but it makes the illustrative maths even more painful). An octave above, the string vibrates twice as fast – e.g. 880 in the case of A in alt. And the ratio for a fifth is 2: 1, so the E above the first A is 660; the ratio for a fourth is 3:2. When you’re tuning a keyboard instrument, the further away you get from those ‘pure’ ratios, the more horrible the sound becomes – so if you start with A, then tune E, then F, then the A above … by the time you’ve reached a key like F sharp you’ve strayed so far from the pure ratios that the result is quite exceptionally nasty. (Note that this doesn’t apply to an instrument like a violin, wher
