I have noticed that a sixth, particularly a harmonic sixth, sounds very harsh when the lowest note is below C3 and especially harsh if the sixth is minor. In fact, a minor sixth below C3 sounds to my ears, more like an augmented fifth than a minor sixth. Below C2, the sixth might as well be as harsh as the tritone. But why? Why is it that a very consonant interval becomes harsh below C3? Thirds become muddier, but they don't become more harsh. Fourths and fifths also don't become more harsh. And of course the octave isn't going to become harsh unless that octave turns into a false relation.
Now, if that sixth is part of a consonant triad, it doesn't become harsh, just muddy. But by itself, the sixth becomes harsh below C3. Even if upper voices in the treble clef add harmony, if the sixth is below C3, it still sounds harsh, though not as much as it does unharmonized. It is only when the harmony is added within the same register that I don't hear a harshness from the sixth. But why is the sixth so harsh in the low register? Here is the harmonic series:
And here is where the consonant intervals show up in the harmonic series:
As you can see, in the harmonic series, both the major and minor thirds and the major and minor sixths overlap at the fifth harmonic. The major sixth is between the third and fifth harmonics and the minor sixth is between the fifth and eighth harmonics. So, this might explain why the minor sixth sounds like an augmented fifth in the low register. But, according to this, the major sixth should be more consonant than the major third because the major third uses the fourth harmonic whereas the major sixth uses the third harmonic. But in the low register, even this major sixth sounds harsh, whereas the thirds just sound muddy.
So what gives? Why is it that below C3, all sixths sound harsh whereas thirds just sound muddy in that register and all sixths above C3 sound like a very consonant sixth? Harmonics alone doesn't seem sufficient to explain this harsh sixth in the low register.