Quarter-Comma Meantone (Part 1)

I’ve spent the last few weeks drawing pictures of tuning systems, since I realized this is a good way to show off their mathematical beauty. Now I’ll start deploying them!

I’ve already written about the first two hugely important tuning systems in Western music:

• Pythagorean tuning.

• Just intonation.

It’s time to introduce the third: ‘quarter-comma meantone’.

But first, remember the story so far!

Pythagorean tuning may go back to Mesopotamia, but it was widely discussed by Greek mathematician...