Consonance and dissonance
Joe Monzo considers consonance and dissonance to be opposite poles of a continuum of sensation, which he calls "sonance". However he was not the first who used the term sonance: also Wilhelm Keller distinguishes between sonanzmodal and distanzmodal aspects when analysing sounds, see his Handbuch der Tonsatzlehre from 1957.
The term sonance goes back to Giovanni Battista Benedetti [1]
Going back to Giovanni Battista Benedetti, an Italian Renaissance mathematician and physicist, sonance can be best described as relative consonance and/or dissonance of a musical interval – a continuum of pitches encompassing consonance on one end, and dissonance on the other (Palisca, 1973). [2]
Musical vs. sensory dissonance
Musical dissonance is a complex phenomenon depending on not only the fundamental frequency ratio but also the register, timbres, volume, spatialization, and the listener's conditioning and cultural background. Sensory dissonance or roughness, however, is a psychoacoustic effect that is much more consistent among most human listeners except for those with conditions like congenital amusia (tone deafness). In its most basic form, sensory dissonance occurs when two sine wave tones in the audible frequency range are played simultaneously, within about a critical band of each other but far apart enough that beating is not audible.
A study by Kameoka & Kuriyagawa in 1969 had listeners grade the roughness of two sine waves played simultaneously at equal intensity. They computed that if the lower sine wave has frequency f1 Hz, then the upper frequency that maximizes roughness is about [math]\displaystyle{ f_2 = f_1 + 2.27 f_1^{0.477}\ \text{Hz} }[/math]. This assumes that each sine wave has intensity 57 dB SPL; the formula changes slightly depending on volume. The interval [math]\displaystyle{ f_2/f_1 }[/math] is about 1.56 semitones at 440 Hz, and narrows as frequency increases.
To address some possible misconceptions, sensory dissonance is not musical dissonance, and it has nothing to do with approximation to e.g. JI intervals. It's specifically about the basilar membrane's ability to separate nearby partials. Sensory dissonance only happens when the constituent tones are played simultaneously, not necessarily in succession. Also, it's important that the partials have comparable volumes; if one is much quieter than the other than it may be masked.