Maybe I should just let this go, but here is the science: When you tune with a fork, electronic or otherwise, you are tuning A4 to the fundamental of that fork, i.e., 440 bps. F2 works for the test because the 5th partial of F2 is A4, where it coincides with the fundamental of the fork. B1 works because the 6th partial of B1 is A4, where it likewise coincides with the fundamental of the fork. F3 is a poor choice because it has no partial at A4! It has a 6th partial that coincides with A5 which is, of course the 2nd partial of A4. So if F3 is used, the beats that you are counting are at A440 (the fork) and A880+, i.e., the inharmonic 2nd partial of A4. Therefore, if you very accurately match the beat rates of F3-Fork and F3-A4, you will tune A4 sharp every single time! The Yamaha example doesn't really bear on this discussion because they are talking about an altogether different approach (and shouldn't the #1 example be tuning A49 instead of A47?). F3 is only mentioned in relation to the 3rd-10th test of the octave, which is only to ensure that you have the A3-A4 octave expanded, or at least not contracted, which has nothing to do with the dead-on-ness of A4 at 440 bps. Here is another logical way of seeing this. When we tune an interval 5th, we are comparing a 3rd partial to a 2nd partial. Likewise, when tuning an interval 4th, we are comparing a 4th partial to a 3rd partial. In the case of setting A4 to the fork, we are tuning a UNISON where the interval ration is 1:1 and we must, therefore, compare beat rates arising from the exact same partial. Because the fork is only sounding (for all practical purposes) at its fundamental, we must use comparison intervals that have a coincident partial at A4. Hence B1 or F2. But not F3; it has no coincident partial at A4. We can debate technique, we can debate art and style, we can disagree on temperaments, octave widths, baseball teams, ad infinitum. But, please, let's not debate demonstrable science. Alan Barnard Salem, Missouri
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