## 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