# Useful Representations of Log Audio Frequency Spectrum

1. Jun 20, 2013

### Deepsatchel

Hi everyone,

So I'm trying to basically generate a list of numbers between 20 and 20,000 (Hz) in log space that will give good resolution to parts of the audio spectrum that matter! After all that is the point of using log scale for frequency in the first place.

The list generator I have at this point gives very fine resolution between 20 and 100 Hz, and when it gets closer to 20kHz, it's counting by the thousands. A good audio log scale should expand the lows and compress the highs, but not to this degree! What I'm doing is unaltered "log," I believe. Here's exactly what my code looks like:

top = 20000
bottom = 20
bands = 12

loop i from 0 to bands
nextBand = 10^((i/bands)*log10(top-bottom+1))-1+bottom;
save the new frequency value to the list...
end loop

The result:

20, 21, 24, 30, 46, 80, 160, 341, 755, 1699, 3854, 8773, 20000.

In practice I will use many more bands. When I use 400 bands (a reasonable use case), I get 96 of them in the 20's! That is way too many. So if straight logarithmic scale is not what's normally used, then what is? I noticed pictures of Adobe Audition's spectral analyzer on Google Images had scales that seemed approximately logarithmic but expanded more in the middle than regular log.

Thanks, Elwood

2. Jun 20, 2013

### Deepsatchel

3. Jun 20, 2013

### Deepsatchel

I know I keep harping on and on, but it seems more likely that in fact the Adobe Audition scale is completely unrelated to an actual log function. I've never met a log function that does not hug the y-axis (thus give very fine resolution - small frequency steps) from 0 out to, say, 1. This is what gives the unwanted fine resolution in the lower frequencies. Therefore a mathematical log is not a foolproof choice to present audio data. Instead, probably, Audition splines a curve over a couple points.

It does resemple log space, but not down close to zero.

Any thoughts?