FYI for anybody. Your A440 is not the only frequency. There’s every integer multiple (880, 1320, etc) as well. Different coefficients of those overtones are why you can sing “ahhh” and “eeee” at the same note but they sound different.
Polyphonic overtone singing is a technique where one or more overtones are heavily emphasized in the timbre.
This is also why major 3rds on pianos are noisy. A has a C# as it’s 5th harmonic at 2200Hz (5*440). But C#7 on piano is slightly higher at 2217.48.
That’s why if you listen close there will be a ~17Hz oscillation around C#7 when you play A4 and C#5.
Other than that, I also think you may want to hear a different polyphonic singer.
It's the same thing we do when we shape our mouths to make different vowel sounds, only much more precise. The physical thing that underlies what we perceive as "vowel quality" is the frequency of spectral peaks ("formant" is the linguistics terminology). When we shape our mouths (more generally our vocal tracts) to say "aaa" versus "iii" we are creating resonances at certain frequencies.
Admittedly when creating vowel sounds the bandwidth of the resonator is pretty wide, and when we hear vowels we can still perceive "a" quality vs "i" quality with even a wide bandwidth.
What Anna-Maria Hefele and other overtone singers do is much more precise. They can get a very narrow bandwidth by controlling their vocal tracts more precisely.
Some of what singer from Laybach does sound 2 voice as well. In some cultures this style is a natural.