Whether an interval sounds smooth can actually be calculated! Little Pi introduces the sensory dissonance curve: two close frequencies create beats, and faster beats turn into roughness, which Helmholtz proposed in 1863 as the main source of dissonance. In 1965, Plomp and Levelt's listening experiments found that two pure tones sound roughest at about a quarter of a critical band. Add up the roughness between all the overtones of two notes, and the curve's valleys land on the octave, fifth, fourth and major third. William Sethares (1993 paper; 1998 book Tuning, Timbre, Spectrum, Scale) showed that for sounds with uneven overtones, like xylophones, bells and gamelan, the valleys move: timbre and scale are partners, so you can design the timbre first and then the scale.
References:
William Sethares - Relating Tuning and Timbre: https://sethares.engr.wisc.edu/consemi.html
Consonance and dissonance - Wikipedia: https://en.wikipedia.org/wiki/Consonance_and_dissonance
Beat (acoustics) - Wikipedia: https://en.wikipedia.org/wiki/Beat_(acoustics)
Critical band - Wikipedia: https://en.wikipedia.org/wiki/Critical_band
Hermann von Helmholtz - Wikipedia: https://en.wikipedia.org/wiki/Hermann_von_Helmholtz