This sounds similar to a book by J. Cree Fischer (I hope I have his name correct) in which a temperament can be set using only fifths. However, the end result is supposed to be the same as with other standard methods. I have tried this method without much success however. Another tuner I know used to set his temperament with just fourths and fifths, not using thirds and other checks at all. He was an excellent tuner but could not explain how he did it, and he didn't even know what I meant when I asked him about the speed of the beats in thirds and such...a technician from Russia taught him. But he sure knew how to make even the worst pianos sound great!
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