Hey hey,
I am working on something ina way of vocoding. Quite often I read that the 
bandpass filters have 1/2 octave width or 1 octave width. Searching further I 
see mention of octave bands, which have a more exponential definition:
f_c = sqrt(2) * f_min
f_max = sqrt(2) * f_c

Now with a classic bandpass filter - as I understand it - the slopes are more 
linear.

In my - limited - understanding:
f_min = f_c - 1/2 bandwidth
f_max = f_c + 1/2 bandwidth

How to deal with that conundrum in a practical way? Setting up a pair of 
lowpass and highpass for each band? Approximate by setting a bandwidth of f_c 
for one octave width? Or is the frequency response of a bandpass filter 
"exponential"?

I'd appreciate any practical resource, as long as the math is in pseudo coee 
or some kind of Tex.

Best wishes and TIA,

Jeanette

-- 
  * Website: http://juliencoder.de - for summer is a state of sound
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Hi Oeyvind!
Sep 2 2020, Oeyvind Brandtsegg has written:
...
> https://www.ranecommercial.com/legacy/note170.html
...
This was very concise and clear. Alas, the formulae were either
unreadable or directly included as images. Could you perhaps guide me
just one step further. From the article in the section "Given BW in
octaves, to find Q", I think it is equation 4, which is used to
calculate the reference values in table 1. Could you mail that to me in
some pseudo c-family-memeber or Csound or pseudo Tex...

Best wishes and many thanks,

Jeanette
>
> A bandwidth of one octave means that the higher cutoff frequency is exactly
> twice the lower cutoff frequency.
> The center frequency is then not linearly the midpoint between those two,
> but rather it follows the normal logarithmic of frequency representation.
> Details in the link :-)
>
> all best
> Øyvind
>
> ons. 2. sep. 2020 kl. 11:59 skrev Jeanette C. :
>
>> Hey hey,
>> I am working on something ina way of vocoding. Quite often I read that the
>> bandpass filters have 1/2 octave width or 1 octave width. Searching
>> further I
>> see mention of octave bands, which have a more exponential definition:
>> f_c = sqrt(2) * f_min
>> f_max = sqrt(2) * f_c
>>
>> Now with a classic bandpass filter - as I understand it - the slopes are
>> more
>> linear.
>>
>> In my - limited - understanding:
>> f_min = f_c - 1/2 bandwidth
>> f_max = f_c + 1/2 bandwidth
>>
>> How to deal with that conundrum in a practical way? Setting up a pair of
>> lowpass and highpass for each band? Approximate by setting a bandwidth of
>> f_c
>> for one octave width? Or is the frequency response of a bandpass filter
>> "exponential"?
>>
>> I'd appreciate any practical resource, as long as the math is in pseudo
>> coee
>> or some kind of Tex.
>>
>> Best wishes and TIA,
>>
>> Jeanette
>>
>> --
>>   * Website: http://juliencoder.de - for summer is a state of sound
>>   * Youtube: https://www.youtube.com/channel/UCMS4rfGrTwz8W7jhC1Jnv7g
>>   * Audiobombs: https://www.audiobombs.com/users/jeanette_c
>>   * GitHub: https://github.com/jeanette-c
>>
>> I know you're out there and I know that you still care <3
>> (Britney Spears)
>>
>> Csound mailing list
>> Csound@listserv.heanet.ie
>> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
>> Send bugs reports to
>>         https://github.com/csound/csound/issues
>> Discussions of bugs and features can be posted here
>>
>
> Csound mailing list
> Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
> Send bugs reports to
>        https://github.com/csound/csound/issues
> Discussions of bugs and features can be posted here
>

-- 
  * Website: http://juliencoder.de - for summer is a state of sound
  * Youtube: https://www.youtube.com/channel/UCMS4rfGrTwz8W7jhC1Jnv7g
  * Audiobombs: https://www.audiobombs.com/users/jeanette_c
  * GitHub: https://github.com/jeanette-c

I know you're out there and I know that you still care <3
(Britney Spears)

Csound mailing list
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By any means, I'm not an expert myself either. But this is what I remembered having seen in Dodge & Jerse: "In digital filters of the type implemented in most computer music programs, the center frequency is the arith­metic mean (average) of the upper and lower cutoff frequencies."

The center frequency is then not linearly the midpoint between those two,
but rather it follows the normal logarithmic of frequency representation.