Years ago I was messing around with an electric guitar and a distortion / wah pedal. With distortion, one can play only two simultaneous notes and get a pretty “thick” sound. Under the right circumstances, I could hear very strong difference (sub) tones. It only took a mild amount of distortion to make it happen, but the strength of the difference tones relied on the wah pedal being in a particular position. Moving the wah to a certain position allows the amplitude of the two vibrating strings to be matched. The resonance peak of the movable-band-pass-filter (wah) is placed at a frequency between the frequencies of the two strings, allowing the attenuation on either side of the peak to match the amplitudes of the two tones. Duh, sorry for my not-totally scientific explanation. Without matching amplitudes, the difference tones will not happen, or they will be weak.
Once I got the strong difference tone, I could bend one of the strings and listen to the resulting change in the difference tone. In the process of bending a string, the difference tone could be brought from an audible range all the way down to a sub-audible bunch of beats. Needless to say, this was pretty cool! It became very clear when I was playing in tune, because the difference tone formed “root” of the chord formed by the two strings. I used to occasionally hear, in orchestra, difference tones produced by two clarinets playing in tune. Over time, however, I heard it less and less. This is because, on average, orchestral clarinetists nowadays play with “darker” sounds, sounds lacking higher overtones. Adding harmonic distortion to my guitar sound strengthened the difference tones. I surmised that a superior method of tuning was to listen for these difference tones (which in an acoustic situation are pretty weak and mostly create a subtle change in the texture of the sound). Not sure if this relates to your own experience singing in tune.
Regarding the “veil” comment, I was not very clear. My professor felt that some musicians threw a veil over the music, obscuring it. In fact, we call a “dark” sound “covered”, which is the meaning of obscure. Taking the veil off the music is the opposite of obscuring it. There are all kinds of examples of music being obscured. Auditorium acoustics, for example. People start associating classical music with reverb, but that starts to obscure a lot of the detail of the music. They don’t know what they’re missing, but that’s okay because reverb is so ingrained into their classical music aesthetic. Reverb also hides inaccuracies in the ensemble. So, my professor was saying we should keep things as real as possible.
Thread-jacking complete!!!