# How wide are critical bands?

I hope this is the most appropriate SE site to ask a question about psychoacoustics.

I don't quite understand critical bands. As far as I know, if two pure tones which frequencies are inside the same critical band are heard, a single tone is perceived. But what would be that tone's frequency?

According to the classical rule of thumb, the bandwidth would be the following:

• 100 Hz if f<500 Hz
• 20% of the tone frequency if f>500 Hz

But I really don't know how to apply this. If I have two tones with f1=800Hz and f2=950 Hz, what would be perceived?

Would the critical band be 800-0.2*800=640 Hz to 800+0.2*800=960 Hz and therefore a single tone would be perceived? Or is 0.2*800=160 the real bandwidth (so the band would be from 720 to 880 Hz)? And, if a single tone is perceived, what frequency would it be?

I'm not an expert in psychoacoustics, but in trying out examples such as an 800Hz tone and another (which I varied from 802Hz to 1khz) they were all distinguishable instantly, with no effort. At very close frequencies (ie 0 to about 2 Hz difference) beats were the major audible component, but above that, two pure tones are heard.

The only combinations which caused more interesting results were when one tone was a harmonic of the other - it was possible to 'lose' one in the other tone...

I have been lucky enough to find a whole chapter about critical bands and masking in An Introduction to the Psychology of Hearing by Brian C.J. Moore in college library. The phenomenon I asked about in my question seems to be just one of the many aspects of critical bands. In fact, this is a way to experimentally find out the critical bandwith for each frequency.

Given two complex periodic sounds containing 12 sinusoidal components (partials), which are:

1. fundamental frequency f0 and its harmonics: f2 = 2 ⋅ f0, f3 = 3 ⋅ f0, ..., f11 = 11 ⋅ f0.
2. fundamental frequency f0 and out-of-tune harmonics (i.e. not multiples of the fundamental frequency).

Subjects were requested to listen the following pure tones:

• a tone whose frequency was contained in the previously heard complex sound.
• a tone whose frequency was half-way between two of the harmonics contained in the previously heard complex sound (e.g. 3/2 ⋅ f0)

Assuming that a partial is only heard when its nearest neighbour is at least a bandwidth away, the stated results for the bandwidth were found:

• 100 Hz if f < 500 Hz
• 20% of the tone frequency if f > 500 Hz

The bold sentence being the one that really answers my question.