# what is the mel scale?

I am not sure I understand what the Mel Scale is.

Googling doesn't give me various answers. I seem to be getting the same response again and again.

Which would be something like:

"The mel scale reflects how people hear musical tone"

First of all, does the concert pitch has a specific frequency? So why do we even have a scale stating how do people hear it?

I am currently trying to understand how MFCC uses them, and it seems like it maps the frequency to the Mel scale, or there are some filter banks which are applied on the given frames

To stand on @hotpaw2's answers, think of Mel as one kind of pyscho-acoustic scale, derived from a set of experiments on human subjects, others are Bark & ERB

Why have such a scale?

• Imagine a 100 Hz sine wave playing in your head, .... wait for it to stick ...okay... Good.
• Imagine now, a 200 Hz sine wave playing ... marinate in it. Good work.
• Now compare the two, they have some "perceptual distance". Perceptual only because we're using your soft-grey matter as a measuring instrument.
• Finally, if you were you repeat this experiment with 1100 Hz & 1200 Hz, and again with 10,100Hz and 10,200Hz, your opinion of this percpetual distance might diminish, i.e. 100 & 200 Hz can sound "farther apart" than do 10,100 & 10,200Hz, even though in all cases the differences are equivalent to 100Hz.

These pyschoacoustic scales try to capture these distances from low (20Hz) to high frequency (20kHz).

Why have such a scale? One reason would be to understand what typical people can hear and not hear regarding the difference between two sounds. These perceptual differences (experimentally determined and statistically averaged) are not constant nor linearly proportional with frequency.

Some audio compression and music fingerprinting schemes try to discard or ignore differences that most people can't hear very well. Thus the value of filter banks that help determine what to keep and what to discard. Or what to match between two sounds to determine if a typical person would estimate they might be the same in some way. The Mel scale is one scale experimentally determined to be useful for building such filter banks.

Aside: Most professional musicians do not have perfect pitch, and thus could not reliably tell if a sinusoidal tone burst played in isolation (e.g. long after hearing any other musical sounds) was concert pitch 440 Hz or not (unless the difference was big enough).