thirds and sixths

[martin store]

what is the relationship between thirds and sixths?

for inctance: 

f3 - a3  if this one beats 6,9 bps what is the
f3 - d4 sixth suppose to beat?

and what should these intervalls beat if they are correctly tuned?

f3 - d4 sixth
a#- d4 third 



how do this really work?