[sdiy] Filter bank design

[Ian Fritz]

JB --

At 10:43 AM 12/15/2002, jbv wrote:

>As for "frequencies spaced at a ratio of 2.1^(1/5)", how many bands per
>octave does that mean ? Three ? Five ?
>And what are the practical frequency limits (both high & low ends) for
>such a module ? 100 Hz to 10 KHz ?

If you used 2.0^(1/5) there would be 5 bands per octave, an octave being a 
factor of 2.0 in frequency and the exponent of 1/5 representing five 
subdivisions.  So 2.1^(1/5) represents five divisions in a bit more than an 
octave, ie, just a bit under 5 bands per octave.

This number is not cast in concrete or anything like that, but it has been 
advocated in the past.  The original Matthews work on electronic violin 
suggested about 6 bands per octave.  The 2.1^(1/5) ratio was developed by 
R. Burhans and used for clavichord enhancement.  Its advantage is that with 
a base frequency of 50 Hz, none of the frequencies fall on top of the 
frequencies of the musical chromatic scale.

With 36 bands you can go from 50 to 9000 Hz.  I haven't found the lowest 
frequencies especially useful, so it might make sense to start at one of 
the higher frequencies, e.g., 90.5.  You can also , of course, use more 
than 36 frequencies.  There is no overlap with the musical scale up to 10 
octaves.

   Ian