“Roughly, the critical band is the band of audio frequencies within which a second tone will interfere with the perception of the first tone by auditory masking.” – Wikipedia
Depending on where in each others Critical Bandwidth two frequencies lay, one may have consonance, roughness, or beats. is the most imporant result from psychoacoustics as it relates to music. It helps us understand why halfsteps generally sound bad… but so do wholesteps and even minor thirds sometimes! AS well, it helps us differnetiate between the roughness of a tritone, which is not physical, versus the roughness of beats, which is physical.
Frequency envelope
Masking
Linear Distinct: little to no overlap
Non-Linear Rough: distinct overlap
Defines Critical Band: +/- frequency band where second tone will start to sound rough
Non-Linear Beats: strong overlap
The tritone does not beat
Given all that is said above, we examine the tritone and notice that there is no way that straight overlap is responsible for it’s discomforting effect. In fact, there are other reaons for the tritones discomfort which is one of the main motivations to separate it and beats as two distinct “dissonances”.