# Giampiero Salvi :: Auditory Scales

## Comparison between ERB, Mel and Bark scale

There are three commonly used psychoacoustical scales that relate physical frequency (in Hz) to subjective perception of pitch.

ScaleRange (approx.)Reference
ERB 0-425 stanford
Mel 0-4000 wikipedia
Bark 1-24 wikipedia

The next plot compares the normalized scales in order to give an idea of the relative differences. Note that this comparison is only qualitative because the scales are defined in arbitrary units (see at the end of the page for more info). The frequency range is between 0 and 22050 Hz:

This is a zoom with frequency between 0 to 8000 Hz:

### Matlab code:

``` f = 0:10:22050; erb = 214*log10(0.00437*f+1); mel = 1127.01048*log(1+f/700); bark = 13*atan(0.00076*f)+3.5*atan((f/7000).^2); all = [erb;mel;bark]; normall = all./(max(all,[],2)*ones(1,size(all,2))); plot(f,normall) legend('ERB', 'Mel', 'Bark', 'Location', 'SouthEast') xlabel('frequency (Hz)') ylabel('normalized scales') ```

### Note:

Note that the comparison might be misleading because of the normalization that is done at 22050Hz in the examples. To see how the the difference between the scales changes with normalization, try changing the frequency range, for example with

``` f = 0:10:11025; ```

or

``` f = 0:10:4000; ```