Well Temperaments (Part 2)

Last time I ended with a question: why are certain numbers close to 1 so important in tuning systems? It helps to understand a bit about this before we plunge into the study of well temperaments. It turns out that in some sense western harmony evolved one prime at a time, so let’s look at the subject that way.

The prime 2

If all the frequency ratios in our tuning system were powers of 2:

2i

life would be very simple. Multiplying a frequency by 2 raises its pitch by an octave, so the only ...