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
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