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Convert between Hz and the mel scale both ways using the O'Shaughnessy 1987 formula 2595·log10(1 + Hz/700), with 8 reference anchors from 20 Hz to 20 kHz.

📘 How to Use

  1. Type the value you want to convert into the Frequency (Hz) field
  2. Read the matching value in the linked Mel scale field
  3. Enter a value in the Mel scale field to convert back to Hz

Mel Scale ⇄ Hz Converter

Hz
mel

※ Formula: mel = 2595 · log₁₀(1 + Hz / 700)

※ Hz = 700 · (10^(mel / 2595) − 1)

Target Hz mel

※ Formula source: O'Shaughnessy 1987 (mel = 2595·log10(1 + Hz/700))

※ Uses: MFCC feature extraction, speech recognition, psychoacoustic models, filterbank design

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Article

Mel Scale ⇄ Hz Converter | Bidirectional Conversion with the O'Shaughnessy 1987 Formula

Convert between Hz and the psychoacoustic mel scale in both directions. Built on the O'Shaughnessy 1987 formula mel = 2595·log10(1 + Hz/700), it shows mel values for eight reference anchors from the 20 Hz audible floor to the 20 kHz ceiling on a single screen.

💡 About this tool

When you design a mel filterbank for MFCC extraction or a speech-recognition front end, you place the band edges at equal spacing on the mel axis rather than on the linear Hz axis. Punching 2595·log10(1 + Hz/700) into a calculator for every edge is tedious, and the inverse Hz = 700·(10^(mel/2595) − 1) doubles the round trips.

This tool links the Hz field and the mel field so that editing one updates the other. If you want to lay out filterbank edges at uniform mel steps, you can read back the Hz of each step directly. The reference table on the right lists eight perceptual landmarks — female-voice fundamental, cymbal shimmer and more — so the logarithmic behavior is visible at a glance: the mel axis stretches the low end and compresses the high end.

It is aimed at speech-processing engineers building MFCC features, researchers working with psychoacoustic models, and DSP developers placing filterbank edges.

🧐 Frequently Asked Questions

Q. Which mel formula does this use? The O'Shaughnessy 1987 form mel = 2595·log10(1 + Hz/700). This 700 Hz corner version is the one most widely used in speech processing.

Q. Can it convert the other way, from mel to Hz? Yes. Type a value into the mel field and the inverse Hz = 700·(10^(mel/2595) − 1) fills the Hz field for you.

Q. What is 0 Hz in mels? 0 mel. Substituting Hz = 0 gives log10(1) = 0, so the origins line up exactly.

Q. Will the values match librosa or other libraries? They match HTK-style implementations (the O'Shaughnessy 2595/700 form). librosa defaults to the Slaney scale, which uses a different mapping and diverges in the low range, so cross-check before comparing.

Q. How were the eight reference points chosen? The audible bounds 20 Hz and 20 kHz anchor the ends, with female-voice fundamental, A4, vowel formant and cymbal shimmer placed as perceptual landmarks in between.

📚 Why the mel scale bends the frequency axis

Humans hear small pitch changes far more clearly at low frequencies than at high ones. The perceived gap between 100 Hz and 200 Hz is much larger than the gap between 10,000 Hz and 10,100 Hz, even though both are 100 Hz apart. The mel scale folds that non-linear sensitivity into a single axis, which is why Stevens, Volkmann and Newman named it in 1937 as a measure of pitch judged equal in spacing.

The popular 700 Hz corner formula came later: Makhoul and Cosell published it in 1976, and O'Shaughnessy's 1987 book made it standard. That is exactly why an MFCC filterbank uses narrow filters down low and wide ones up high — the machine mirrors the ear, spending its resolution where human hearing is sharpest.