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.

N (bandwidth in octaves) Q
4 0.267
3.830 0.285
3.667 0.305
3.5 0.326
3.333 0.350
3.167 0.376
3 0.404
2.833 0.436
2.6667 0.471
2.5 0.511
2.333 0.556
2.167 0.607
2 0.667
1.833 0.736
1.667 0.819
1.5 0.920
1.333 1.044
1.167 1.204
1 1.414
0.917 1.548
0.833 1.707
0.75 1.902
0.667 2.145
0.583 2.456
0.5 2.871
0.417 3.450
0.333 4.318
0.25 5.764
0.167 8.651
0.083 17.31

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