so notes that are dissonant on piano are not necessarily dissonant with human voices.
a big reason for that is apparently overtone matching (and i guess that because of formants/resonant cavities of the human vocal tract, there must be a lot of matching overtones in more cases, maybe? i wonder if there is a youtube vid about that, there must be...)
big chances it does not make dissonance "smoother", but that the sound is less dissonant in the first place.
For example, if you are on the fifth in the chord, you adjust the tone slightly up. If you are on the major third, slightly down. Minor third, slightly up. These rules are consciously applied by choral singers, and are even genre-defining for things like barbershop.
apparently it's often done in pro recorded music.
my peterson tuner actually has these tunings embedded inside.
on a more fundamental level our perception of pitch (the musical psychoacoustic thing) also vary with loudness and frequency (physical reality)...
add to that, that at low frequencies we have difficulties tracking the pitch in the first place (so we rely on overtones/harmonics) -- which makes it even more important to tune on evertone (because our heads can recreate/track the note through psychoacoustic effects... so we will ear it "nice" when without the overtones we would be lost)
funny extra fact, our ears are cavities with resonances and distortions... (some musicians exploit that https://en.wikipedia.org/wiki/Maryanne_Amacher )
i might be wrong on some points since i starting learning about music 2 years ago as a hobby but i think it is mostly correct. the whole thing is fascinating.
That's the comprise you get from trying to play with fixed notes even though you actually care about ratios.
Smoothing out the dissonance may be a bug, not a feature. I live for timbre and new sounds. Choral music can have the feel of overly polished rocks.
And funnily enough, as I wrote this, music of Bernard Parmegiani started playing. This gave me a (mostly) good jolt, following the more atmospheric music of Alan Hovhaness.
As an addendum, for anyone interested in choral music I highly recommend listening to Caroline Shaw. She is among the most interesting new voices in the genre. Her piece Partita for 8 Voices [1] won the Pulitzer Prize a few years back. For a somewhat more accessible piece I also really like Its Motion Keeps [2].
[1]: https://www.youtube.com/watch?v=NDVMtnaB28E
[2]: https://www.youtube.com/watch?v=oT1PqR97urc