EQ bandpass filter: Q factor and bandwidth

When using the bandpass (or peak) filters of a parametric equalizer, you might be asking what is exactly the effect of the quality factor Q. You have probably noticed that a high Q curve is narrow, a low Q curve is wider and that the bandwidth is not linearly related to Q.
Here are some bandwidths in octaves and the corresponding Q.

Q N (bandwidth in octaves)
0.267 4
0.326 3.5
0.404 3
0.511 2.5
0.667 2
0.920 1.5
1.414 1
1.707 5/6
2.145 2/3
2.871 1/2
4.318 1/3
8.651 1/6

N = LOG(SQRT((((2+(1/Q^2))^2)/4)-1)+(1/(2*Q^2))+1)/LOG(2)
Q = SQRT(POWER(2;N))/(POWER(2;N)-1)

Thanks to SengpielAudio explanations and useful calculators:
Bandwidth in octaves to Q factor (filter) conversion and vice versa
Q Factor and filter center frequency - Find -3 dB cutoff frequencies

See also RaneNote 170 (2008) by Dennis Bohn:
Bandwidth in Octaves Versus Q in Bandpass Filters


November 2016