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 0.2667
3.8333 0.2848
3.6667 0.3046
3.5 0.3261
3.3333 0.3497
3.1667 0.3755
3 0.4041
2.8333 0.4357
2.6667 0.4710
2.5 0.5107
2.3333 0.5557
2.1667 0.6072
2 0.6667
1.8333 0.7364
1.6667 0.8193
1.5 0.9198
1.3333 1.0445
1.1667 1.2035
1 1.4142
0.9167 1.5477
0.8333 1.7074
0.75 1.9021
0.6667 2.1449
0.5833 2.4564
0.5 2.8710
0.4167 3.4505
0.3333 4.3185
0.25 5.7636
0.1667 8.6514
0.0833 17.3099

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