octave-bands
v1.1.0
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Frequency limits for fractional Octave Bands
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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 to1
)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 to1000
).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 outputoptions
- 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 to1
)
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