Mel scale

Mel-Hz plot

A440

File:Mel-scale from 200 to 1500, in intervals of 50.ogg Mel Scale is a perceptual scale of pitches judged by listeners to be equal in distance from one another. The point of reference between this scale and actual frequency measurement is the pitch of a 1 kHz tone, 40 dB above the listener's threshold of hearing, which is arbitrarily assigned a pitch of 1000 mels. The scale is named after the word 'melody' to indicate that the scale is based on pitch comparisons. The concept of the Mel Scale is crucial in the fields of music, acoustics, and particularly in speech recognition and audio processing technologies.

Overview

The Mel Scale was developed as a way to represent pitches perceived by the human ear. Human hearing does not perceive pitches linearly; instead, changes in pitch at lower frequencies are detected more easily than changes at higher frequencies. This non-linear perception is quantified by the Mel Scale, which more closely aligns with the human auditory system's response than the standard linear frequency scale measured in Hertz (Hz).

History

The concept of the Mel Scale was introduced in the 1930s by Stevens, Volkmann, and Newman. The researchers were interested in understanding the relationship between the physical properties of sound and the perceived pitch. They conducted experiments asking listeners to judge the pitch of sounds in order to develop a scale that would more accurately reflect the human perception of pitch.

Calculation

The frequency in mels, \(M\), can be calculated from frequency in Hertz, \(f\), using various formulas. A commonly used formula is: \[ M = 2595 \log_{10}\left(1 + \frac{f}{700}\right) \] This formula approximates the human ear's response more closely than linear scales, especially for frequencies below 1000 Hz.

Applications

The Mel Scale is widely used in audio and speech processing. One of its most significant applications is in the development of Mel Frequency Cepstral Coefficients (MFCCs), which are features derived from the Mel Scale that are used in automatic speech recognition (ASR) and speaker identification systems. The scale's ability to mimic the human ear's response makes MFCCs particularly effective for these applications.

See Also

• Pitch
• Frequency
• Acoustics
• Speech Recognition
• Audio Processing
• MFCC

Mel scale Resources
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