[sdiy] Filtering for chromatic scale frequencies?

rburnett at richieburnett.co.uk rburnett at richieburnett.co.uk
Thu May 31 13:52:33 CEST 2018

You can do this with a bunch of high-Q filters, and it does sort of 
work, but only a little bit.

The problem is this...  Musical tones are far more complex than just 
single frequencies.  So you won't have much success with just 128 narrow 
band-pass filters tuned to each of the fundamental frequencies of MIDI 
notes in the chromatic scale.

Real musical tones _usually_ consist of a series of partials that are 
"more or less" harmonic.  (Instruments like bells and pianos are less 
harmonic that strings or brass.)  So in order to pass a Middle-C trumpet 
tone you'd need a bunch of narrow bandpass filters tuned to 261.6Hz and 
all of it's harmonics that you consider to be essential to preserve the 
tone.  And that's just for a single pitch.  And the higher partials of 
something like a piano note might start to wander outside the passband 
of some of the higher harmonic filters!

Musical notes also tend to contain important transients like chiffs of 
breath, or plucks or strikes of strings, etc.  These transients contain 
additional frequencies that are not harmonically related to the 
fundamental, but that _are_ important to your perception of the 
instruments timbre.  Most of this energy would be removed by a bunch of 
narrow harmonically spaced BPFs.

Finally, high-Q filters with a narrow bandwidth tend to have a long 
settling time in the time-domain.  In other words they tend to smear 
"onset" and "off-set" transients in time.  As an example of this 
phenomenon if you pass a morse-code message through progressively 
narrower and narrower (higher-Q) filters it initially becomes easier to 
identify the dots and dashes in the message as any out-of-band 
background noise gets removed.  But eventually, when the bandpass filter 
becomes very narrow around the morse tone frequency, it ultimately 
becomes harder to identify the actual dots and dashes in the message as 
they begin to "run into each other".  The ring-up and ring-down times of 
a high-Q (narrowband) filter eventually become so long that they 
perceptually smear the timing information in the signal.

So if you do pass music through a bunch of chromatically spaced 
narrowband BPFs, expect the result to sound pretty devoid of the 
original signal's timbre and rhythm!


On 2018-05-31 06:49, Mike Beauchamp wrote:
> This might be bit of a strange one.. I'm wondering if there's any way
> to filter an audio signal to favour frequencies that are within the
> chromatic scale?
> So, sort of like "autotune" - but instead of correctively altering the
> pitch of 'wrong' notes, the filter is just lowering their amplitude
> significantly.
> Mike
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