May I add a perspective to this subject, I tuned and repaired many pipe organs before retirement, and I remember whilst tuning, hearing many undesirable beats, and modulations (Acoustic) effects, that to me were not always musical, and those beats that have Always Been Utilized by all Tuners to tune musical instruments, and also used to test the accuracy of a prior tuning. (re:) Thirds and Sixths, The Tuner gets most accustomed to hearing these beats and warbles, and knows which are correct and which not ! Tuning is done by listening carefully to the slow beats produced by playing the, Fourth's and Fifth's of each tonic note !
I hope that this helps us to hear a few of these not so nice sounds, that are usually Masked by the music !
A past musician quoted this to me, If you over analyze "each" and every sound that you hear from an instrument, you may need a padded room in the future ! "Enjoy the music ! ----, Mel