octave-bands

Frequency limits for fractional Octave Bands.

A small, lightweight package for calculating the frequency bounds for fractional octave bands.
Calculate the frequency bounds for 1/2, 1/3, ... 1/N octave bands.

Install

npm install octave-bands

import { octaves, bandwidth, equalizer } from 'octave-bands';

Usage

Get frequency limits for 11 octave bands:

import { octaves } from 'octave-bands';

const bands = octaves(); // or `octaves(1)`
console.table(bands);

/*
┌─────────┬───────────┬────────┬───────────┐
│ (index) │     0     │   1    │     2     │
├─────────┼───────────┼────────┼───────────┤
│    0    │  11.049   │ 15.625 │  22.097   │
│    1    │  22.097   │ 31.25  │  44.194   │
│    2    │  44.194   │  62.5  │  88.388   │
│    3    │  88.388   │  125   │  176.777  │
│    4    │  176.777  │  250   │  353.553  │
│    5    │  353.553  │  500   │  707.107  │
│    6    │  707.107  │  1000  │ 1414.214  │
│    7    │ 1414.214  │  2000  │ 2828.427  │
│    8    │ 2828.427  │  4000  │ 5656.854  │
│    9    │ 5656.854  │  8000  │ 11313.708 │
│   10    │ 11313.708 │ 16000  │ 22627.417 │
└─────────┴───────────┴────────┴───────────┘
*/

The octaves function returns an array of band frequencies, where each band is a tuple of its low, center and high frequency in the form of [low, center, high].

To get only the center frequencies:

import { octaves } from 'octave-bands';

const bands = octaves();
console.table(bands.map(([low, center, high]) => center));

/*
┌─────────┬────────┐
│ (index) │ Values │
├─────────┼────────┤
│    0    │ 15.625 │
│    1    │ 31.25  │
│    2    │  62.5  │
│    3    │  125   │
│    4    │  250   │
│    5    │  500   │
│    6    │  1000  │
│    7    │  2000  │
│    8    │  4000  │
│    9    │  8000  │
│   10    │ 16000  │
└─────────┴────────┘
*/

Get one-third-octave bands:

import { octaves } from 'octave-bands';

const bands = octaves(1 / 3);
console.table(bands);

/*
┌─────────┬───────────┬───────────┬───────────┐
│ (index) │     0     │     1     │     2     │
├─────────┼───────────┼───────────┼───────────┤
│    0    │   13.92   │  15.625   │  17.538   │
│    1    │  17.538   │  19.686   │  22.097   │
...............................................
│   18    │  890.899  │   1000    │ 1122.462  │
...............................................
│   31    │ 17959.393 │ 20158.737 │ 22627.417 │
└─────────┴───────────┴───────────┴───────────┘
*/

Get the frequency limits for a 21-band equalizer covering an audio spectrum from 20Hz to 20kHz

import { equalizer } from 'octave-bands';

const bands = equalizer(21, { spectrum: [20, 20000] });
console.table(bands);

/*
┌─────────┬───────────┬───────────┬───────────┐
│ (index) │     0     │     1     │     2     │
├─────────┼───────────┼───────────┼───────────┤
│    0    │  16.828   │    20     │   23.77   │
│    1    │   23.77   │  28.251   │  33.576   │
│    2    │  33.576   │  39.905   │  47.427   │
│    3    │  47.427   │  56.368   │  66.993   │
...............................................
│   19    │ 11913.243 │ 14158.916 │ 16827.903 │
│   20    │ 16827.903 │   20000   │ 23770.045 │
└─────────┴───────────┴───────────┴───────────┘
*/

To get the fractional bandwidth constant:

import { bandwidth } from 'octave-bands';

console.log('octave bandwidth', bandwidth()); // ~0.707
console.log('1/2 octave bandwidth', bandwidth(1 / 2)); // ~0.348
console.log('1/3 octave bandwidth', bandwidth(1 / 3)); // ~0.232

API

octaves(fraction: number = 1, options?: Options): [number, number, number][]

Calculates the frequencies for fractional octave bands.

Arguments:

• fraction - octave fraction (defaults to 1)
• options - additional options:

type Options: {
    center?: number,
    spectrum?: [number, number]
}

• center the center frequency of the band that will be used as a starting point to calculate other bands (defaults to 1000).
• spectrum - a two-numbers array representing the min and max values to include for center frequencies (defaults to [15, 21000])

Returns:

• [number, number, number][] returns an array where each element represents the frequency bounds of a band [low, center, high]

equalizer(bands: number, options?: Options): [number, number, number][]

Calculates the frequency bounds for a given number of bands that should cover an audio spectrum.
This is similar to octaves function, but instead of using octave's fraction to calculate the frequencies, it uses the number of bands to output.

Arguments:

• bands - the number of bands to output

• options - additional options:

type Options: {
    spectrum?: [number, number]
}

• spectrum - a two-numbers array representing the min and max values to include for center frequencies (defaults to [15, 21000])

Returns:

• [number, number, number][] returns an array where each element represents the frequency bounds of a band [low, center, high]

bandwidth(fraction: number): number

Calculates the constant bandwidth per 1/N-octave.

Arguments:

• fraction - octave fraction (defaults to 1)

Returns:

• number the bandwidth constant

Formula

The following formula for calculating 1/N octave bands in a given audio spectrum (ex. ~20Hz to ~20KHz) is used:

// 1/N: one-Nth-octave

f_center_0 = 1000

// Center frequency of i-th band
f_center(i) = f_center(i-1) * 2^(1 / N) = f_center(i+1) * 1 / 2^(1 / N)

// Lower center frequency of n-th band
f_low(i) = f_center(i) * 1 / 2^(1 / 2*N)

// Higher center frequency of n-th band
f_high(i) = f_center(i) * 2^(1 / 2*N)

// And for every i-th band holds:
spectrum[0] <= f_center(i) <= spectrum[1]

// Fractional band width per 1/N-octave band (constant):
BW = (f_high - f_low) / f_center // for every one-Nth-octave band

License

MIT