If there is any moment to discover I know nothing about music theory, it is when I read the booklet of this giant boxed set. That never stopped me in the past, so I’m going to try this anyway.
I will try this in the most limited form that I’ve found: the piano is out of tune. It has been since around the time of this work. Before that, it was also out of tune, but in a way that supported the compositions that were made until then.
The reason for this is that there is a difference between what feels right, and what is the physical, classical model of music. Every musical theory book starts with the theory that if you have a string of length x, and you hit it, sound of a certain frequency will come out. If you use the same string, apply the same strength for the tension, but you use half the length, you will get double the frequency. Music theory then says that note is one octave higher.
The problem starts when you divide it in different intervals. Then it runs out that if you add these intervals together, they don’t make the exact octave. So a third and a fifth do not complete the whole octave. It might be a bit more here and there, a bit less in other places.
This problem is the worst with a piano, but it exists in all instruments. For the piano, It was common to at least make sure the most used intervals were correct. So thirds were exactly right, but most certainly fourths were not: they were not supposed to be used.
As music changed however, demands on this system also changed. As a result, and probably also as a sign of the times, in the eighteenth century a more “equally” distributed system was invented. For some pieces it sounded vastly different.
Interestingly though, Bach never made clear what his “Wohl temperierte Klavier” was using. It is generally assumed however that he was referring to the newly invented system.
Is there anyone out there that can give me a better explanation about this?
Bachs handwriting looks to me like what I used to do at school.