Greetings, I'd like to comment on the use of ratios here. A third which has a 5:4 ratio is a Just third and doesn't beat at all. In contrast to this, a "Pythagorean" third is what you end up with if you tune Just fifths, (C-G-D-A-E), its ratio is 81:64. Our ET third is appoximately halfway between these two. The reason I point this out is that there are temperaments that use a variety of sizes of thirds, i.e. the Kirnberger III tuning DOES have a 5:4 third for the C-E. This purity in the key of C is a hallmark of his tuning. REgards, Ed Foote
This PTG archive page provided courtesy of Moy Piano Service, LLC