Using the F2 Check Note to Get Better Accuracy
We can use F2 to measure the relative sharpness of A4 and the fork.
We can do this if we "set" F2 flat so that it produces beats with
both A4 and the fork.
If F2A4 and F2Fork both beat at the same speed, then A4 and the Fork are both "sharp" the same amount, i.e. they are the same pitch.
Using F2 as a check note allows us to know if A4 is sharp or flat when A4 is very close to the fork.
This diagrams below shows the fifth partial of F2 as being close to A4 but flat of A4. A4 and the fork produce different beat speeds with the 5th partial of F2, and we can use those different speeds to measure the relative pitches of A4 and the fork.
A4 and the Fork are very close but not equal. There is a slow beat at the fundamental of 440Hz,
but it is so slow, we do not know whether A4 is sharp or flat of the Fork.
Using F2 as a check note, we can tell that A4 is sharp of the fork.
The 5th partial of F2 shares the fundamental of A4 and the Fork.
But F2 is tuned flat so that its 5th partial beats with A4 and the Fork.
The sharper A4 and the Fork are, the faster the beating.
F2-A4, the black arrow, is beating faster.
F2-Fork, the green arrow, is beating slower.
“Slower means Lower”
The Fork is lower than A4.
A4 is sharp of the Fork.