Mel Scale

The Mel, named by Stevens, Volkmann, and Newman in 1937 [Stevens37], is a perception criterion for pitches which is claimed by audience to be heard from equal distances. The name Mel comes from melody to indicate the fact that scale is based on pitch comparisons [wiki_mel].

The formula for converting Hertz to Mel is as follows:

Mel = 1127 x ln(1+(f/700))

Obviously the reverse is as:

f = 700 x ( exp(Mel/1127) - 1 )

References

[Stevens37]

Stevens, Stanley Smith; Volkmann; John & Newman, Edwin B. (1937). "A scale for the measurement of the psychological magnitude pitch". Journal of the Acoustical Society of America. 8 (3): 185–190.

[wiki_mel]

https://en.wikipedia.org/wiki/Mel_scale.