Q factor filter bandwidth in octaves conversion and converter octave bandwidth - sengpielaudio Checker
 
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Relation between Q factor and bandwidth BW

Conversion: 'bandwidth in octaves' N to quality factor  Q

Q factor to 'bandwidth in octaves' N (octave bandwidth)
Also called bandwidth per octave. Bandwidth BW = f2 − f1= f0 / Q

 Bandwidth BW   in octaves N   |   Quality factor Q 
      |      
   ↓   |      ↓
      |      
Quality factor Q                |    Bandwidth BW   in octaves N 

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Filter resonance

Conversion formula: 'octave bandwidth' N to quality factor Q:

Q factor N to Q - sengpielaudio

Conversion formula: Quality factor Q to 'octave bandwidth' N:

Q factor Q to N log - sengpielaudio

Also known is this longer formula with 4 Qs; see its development at:
Bandwidth in octaves versus Q in bandpass filters − RaneNote 170

Q factor Q to N log - sengpielaudio

Frequency ratio of an octave:

Ratio Formula - sengpielaudio

Formula to convert quality factor Q to 'bandwidth in octaves' N,
but with logarithmus naturalis:

Q factor Q to N log - sengpielaudio

And the very short formula to convert quality factor Q
to 'bandwidth in octaves' N, but with sinh-1 :

Q factor Q to N - sengpielaudio

The Q Factor - Sengpielaudio

Conversion chart or table of 'bandwidth in octaves' N to quality factor Q:

BW in
octaves		  Filter 
Q		      BW in
octaves		  Filter 
Q		      BW in
octaves		  Filter 
Q		      BW in
octaves		  Filter 
Q
1/80 115.4   1 1.41   4 0.267   7 0.089
1/60 86.6   1 1/4 1.12   4 1/4 0.242   7 1/4 0.082
1/50 72.1   1 1/3 1.04   4 1/3 0.234   7 1/3 0.079
1/40 57.7   1 1/2 0.92   4 1/2 0.220   7 1/2 0.075
1/30 43.3   1 2/3 0.82   4 2/3 0.207   7 2/3 0.071
1/25 36.1   1 3/4 0.78   4 3/4 0.200   7 3/4 0.068
1/20 28.9   2 0.67   5 0.182   8 0.063
1/16 23.1   2 1/4 0.58   5 1/4 0.166   8 1/4 0.058
1/12 17.3   2 1/3 0.56   5 1/3 0.161   8 1/3 0.056
1/10 14.4   2 1/2 0.51   5 1/2 0.152   8 1/2 0.053
1/8 11.5   2 2/3 0.47   5 2/3 0.143   8 2/3 0.050
1/6     8.65   2 3/4 0.45   5 3/4 0.139   8 3/4 0.048
1/5     7.20   3 0.40   6 0.127   9 0.044
1/4     5.76   3 1/4 0.36   6 1/4 0.116   9 1/4 0.041
1/3     4.32   3 1/3 0.35   6 1/3 0.113   9 1/3 0.039
1/2     2.87   3 1/2 0.33   6 1/2 0.106   9 1/2 0.037
2/3     2.14   3 2/3 0.30   6 2/3 0.100   9 2/3 0.035
3/4     1.90   3 3/4 0.29   6 3/4 0.097   9 3/4 0.034
                  10 0.031

Q factor as a function of the bandwidth in octaves N

Bandwidth in
octaves N		 Q factor
3.0 0.404
2.0 0.667
1.5 0.920
1.0 1.414
2/3 2.145
1/2 2.871
1/3 4.318
1/6 8.651
1/12 17.310   
 
 
 Notice:
 A low Q factor gives a broad band (wide) bandwidth or 
 a high Q factor gives a narrow band (small) bandwidth. 
  
 
 A high filter quality means narrow-band filtering (notch), with a large Q factor.
 This results in steep filter flanks with a small bandwidth.
 
 A low filter quality means broad-band filtering, with a small Q factor.
 This results in flat filter flanks with a large bandwidth.

Slope in dB/oct = steepness of the filter flanks
• Only with high pass and low pass filters − not with bell curves •
Note: The Q factor (quality factor) or the bandwidth is not convertable to the "slope" as dB / Oct.
converted. There are mastering equalizer with false information regarding the filter setting as
"Slope in dB / octave" or Q factor (width), see: Flankensteilheit (Slope in dB/Oct) ist nicht
Bandbreite = Slope in dB / Oct or steepness of filter flanks is not bandwidth.

Calculating the 3 dB cut-off frequencies; given center frequency f0 and the Q factor
Interrelationship of 'octave bandwidth' N and the quality factor Q
Formulas for conversion of bandwidth in octaves to quality factor
Questions on "Parametric filter adjustment"
Conversion table Q to N and N to Q for parametric filters
Excel conversion - quality factor Q to bandwidth in octaves N
Filter Slope (dB/oct) is not Bandwidth

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