Octave Band Center⚠ unverified
Physics / Acoustics · Compute the geometric mean center frequency of a band
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| f_low | flow | Hz | 1.0 | Lower band-edge frequency |
| f_high | fhigh | Hz | 1.0 | Upper band-edge frequency |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | fc | Hz | Geometric mean center frequency, in hertz (Hz) |
The science & history
Understanding the Parameters
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$f_{\mathrm{low}}$, $f_{\mathrm{high}}$ — must be positive; for standard octave/third-octave filters, edges are preferred numbers (ISO 266 / ANSI S1.11).
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$f_c$ — preferred centre (e.g. 1000 Hz octave) used to label the band in noise spectra.
Derivation (Approaching a Proof)
On a logarithmic frequency axis, the midpoint between $\ln f_{\mathrm{low}}$ and $\ln f_{\mathrm{high}}$ is $\tfrac12(\ln f_L + \ln f_H) = \ln\sqrt{f_L f_H}$, hence $f_c = \sqrt{f_L f_H}$. Arithmetic means would bias high on log scales used in hearing and noise control.
History
Octave and 1/3-octave analysis is the workhorse of industrial and architectural acoustics spectra.
Related Concepts: Sound Pressure Level, A Weighted Level, Sound Power Level
Notes: Registry calculator octave-band-center (unverified). Geometric mean only.