Quote:
Originally Posted by David Powell
I've been really curious about how this harmonics / resonance phenomenon works with 5th tuning, so I am doing some ****ysis on the frequencies in the circle of fifths vs. those in the reciprocal circle of fourths. So far it appears that there may indeed be a difference. I'll let you know when I have something more definite. It's all math the way I see it, but how it it heard is more important.
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I agree that the perceived effect is more important, but moreso I too am into the math of it all. The tricky part is when you start mixing temperament systems which is inevitable since you choose the intonation based on what you hear. I think that's why some people look at the claims made by fifths players and think "no, that's all wrong because a fifth is just a fourth upside down" - well that's only so if you temper your intervals that way. This is also why I think practicing with a tuner to work on intonation is the worst idea ever - you end up with a 12ET sense of intonation which is useless unless you're playing with other 12ET instruments. Even though we often play with pianos, usually the strings grossly outweigh the piano in both numbers and sound, so you end up with a sort of mixed temperament where the pitch center is defined by the piano in whatever range it's playing, but all the interval relationships are locally tempered according to something more like just temperament. This is the reason I don't get too much into the actual math of trying to prove this or that about a given tuning for the bass - it all comes down to subjective factors which are simply the result of our subjective sense of intonation, even though each temperament can be explained easily with math when taken on its own.