Mel Scale (Pitch Perception)

The mel scale is a psychoacoustic model that converts a physical frequency in hertz into a number meant to match how high or low a tone is perceived by listeners. It is not linear like Hz: equal steps in mels are intended to correspond more closely to equal perceived pitch differences, especially because human pitch discrimination becomes less sensitive as frequency rises. The logarithmic form reflects the fact that hearing compresses high frequencies, and the constant 700 Hz is a calibration choice that anchors the curve to common auditory observations.

Use this when comparing pitch on a perceptual scale rather than a physical frequency scale, such as in speech processing, audio engineering, and computational music analysis. It is especially useful when designing or interpreting mel filter banks, spectrograms, or models of human hearing.

• Using natural log instead of log base 10
• Forgetting to add 1 inside the logarithm before taking the log
• Treating mels as an exact physical unit instead of a perceptual scale