Why was the well tempered clavier so important to other composers?

Answer 1

The Well Tempered Clavier was written so people, such as students, could have a cycle of pieces, one each, in every major and minor key. This was something that was not possible in earlier times. Prior to the time of Bach, Musical Instruments were tuned with what were called just tempered systems. The intervals between notes were based on the overtone series, which give precise relationships based on ratios of integers; for example the relationship between the lengths of pipes in an organ that gave a C and the G above it were 2:3, between C and E was 4:5, and so on. The problem with this is that there are notes that cannot be tuned in this way, because no ration of integers is right. Ultimately, such notes had to be approximated, and were quite out of tune with certain other notes. The effect of this was that an instrument was tuned to be played in one key, and playing on it in other keys often sounded horrible. Also harmony was very restricted, because certain combinations of notes did not work together.

Well temperment was based on a very different approach to tuning. Instead of ratio of integers, the relationships between notes were irrational, in the mathematical sense of the word. The ratio of the C-sharp to C was the same as the twelfth root of two to one. The ratio of E to C was the same as the twelfth root of two raised to the fourth power, or the cube root of two, to one; this is very close to 5:4. So, relative to the overtone series, all the notes are almost inaudibly out of tune, but they are uniformly so, for all keys.

Answer 2

Because It's important to other composers to know about music