Octave Band Frequency Calculator Formula
Understand the math behind the octave band frequency calculator. Each variable explained with a worked example.
Formulas Used
Lower Band Edge
f_lower = centre_freq / pow(2, 1 / (2 * band_fraction))Upper Band Edge
f_upper = centre_freq * pow(2, 1 / (2 * band_fraction))Bandwidth
bandwidth = centre_freq * pow(2, 1 / (2 * band_fraction)) - centre_freq / pow(2, 1 / (2 * band_fraction))Variables
| Variable | Description | Default |
|---|---|---|
centre_freq | Centre Frequency(Hz) | 1000 |
band_fraction | Fraction (1=octave, 3=third-octave) | 1 |
How It Works
Octave and Fractional-Octave Bands
Sound analysis often divides the spectrum into bands of constant percentage bandwidth.
Formulas
f_upper = f_c * 2^(1/(2N)) f_lower = f_c / 2^(1/(2N))
where N is the fraction denominator (1 for full octave, 3 for third-octave).
For a full octave band (N=1): f_upper/f_lower = 2 (one octave). For third-octave (N=3): the ratio is 2^(1/3) = 1.26.
Worked Example
1000 Hz full octave band.
- 01f_upper = 1000 * 2^(1/2) = 1000 * 1.4142 = 1414.2 Hz
- 02f_lower = 1000 / 2^(1/2) = 1000 / 1.4142 = 707.1 Hz
- 03Bandwidth = 1414.2 - 707.1 = 707.1 Hz
Frequently Asked Questions
Why use octave bands instead of equal-width bands?
Our hearing perceives pitch logarithmically. Octave bands have constant percentage bandwidth, matching how we hear. Each band sounds equally wide.
What are the standard octave band centre frequencies?
31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000, and 16000 Hz. These are preferred frequencies defined in ISO standards.
Why are third-octave bands used?
They provide finer frequency resolution while maintaining the constant-percentage-bandwidth advantage. They are standard for building acoustics and noise regulations.
Ready to run the numbers?
Open Octave Band Frequency Calculator