# Octave band

Analyzing a source on a frequency by frequency basis is possible but time consuming[citation needed]. The whole frequency range is divided into sets of frequencies called bands. Each band covers a specific range of frequencies. For this reason, a scale of octave bands and one-third octave bands has been developed. A band is said to be an octave in width when the upper band frequency is twice the lower band frequency. A one-third octave band is defined as a frequency band whose upper band-edge frequency (f2) is the lower band frequency (f1) times the cube root of two.

## Octave Bands

### Calculation

If ${\displaystyle f_{c}}$ is the center frequency of an octave band, one can compute the octave band boundaries as

${\displaystyle f_{c}={\sqrt {2}}f_{min}={\frac {f_{max}}{\sqrt {2}}}}$,

where ${\displaystyle f_{min}}$ is the lower frequency boundary and ${\displaystyle f_{max}}$ the upper one.

### Naming

Band Number Nominal Frequency[1] Calculated Frequency A-Weighting Adjustment
-1 16 Hz 15.625 Hz
0 31.5 Hz 31.250 Hz -39.4 dB
1 63 Hz 62.500 Hz -26.2 dB
2 125 Hz 125.000 Hz -16.1 dB
3 250 Hz 250.000 Hz -8.6 dB
4 500 Hz 500.000 Hz -3.2 dB
5 1k Hz 1000.000 Hz 0 dB
6 2k Hz 2000.000 Hz 1.2 dB
7 4k Hz 4000.000 Hz 1 dB
8 8k Hz 8000.000 Hz -1.1 dB
9 16k Hz 16000.000 Hz -6.6 dB

## One-third octave bands

### Base 2 calculation

%% Calculate Third Octave Bands (base 2) in Matlab
fcentre  = 10^3 * (2 .^ ([-18:13]/3))
fd = 2^(1/6);
fupper = fcentre * fd
flower = fcentre / fd


### Base 10 calculation

%% Calculate Third Octave Bands (base 10) in Matlab
fcentre = 10.^(0.1.*[12:43])
fd = 10^0.05;
fupper = fcentre * fd
flower = fcentre / fd


### Naming

Band Number Nominal Frequency Base-2 Calculated Frequency Base-10 Calculated Frequency
1 16 Hz 15.625 Hz 15.849 Hz
2 20 Hz 19.686 Hz 19.953 Hz
3 25 Hz 24.803 Hz 25.119 Hz
4 31.5 Hz 31.250 Hz 31.623 Hz
5 40 Hz 39.373 Hz 39.811 Hz
6 50 Hz 49.606 Hz 50.119 Hz
7 63 Hz 62.500 Hz 63.096 Hz
8 80 Hz 78.745 Hz 79.433 Hz
9 100 Hz 99.213 Hz 100 Hz
10 125 Hz 125.000 Hz 125.89 Hz
11 160 Hz 157.490 Hz 158.49 Hz
12 200 Hz 198.425 Hz 199.53 Hz
13 250 Hz 250.000 Hz 251.19 Hz
14 315 Hz 314.980 Hz 316.23 Hz
15 400 Hz 396.850 Hz 398.11 Hz
16 500 Hz 500.000 Hz 501.19 Hz
17 630 Hz 629.961 Hz 630.96 Hz
18 800 Hz 793.701 Hz 794.43 Hz
19 1 kHz 1000.000 Hz 1000 Hz
20 1.25 kHz 1259.921 Hz 1258.9 Hz
21 1.6 kHz 1587.401 Hz 1584.9 Hz
22 2 kHz 2000.000 Hz 1995.3 Hz
23 2.5 kHz 2519.842 Hz 2511.9 Hz
24 3.150 kHz 3174.802 Hz 3162.3 Hz
25 4 kHz 4000.000 Hz 3981.1 Hz
26 5 kHz 5039.684 Hz 5011.9 Hz
27 6.3 kHz 6349.604 Hz 6309.6 Hz
28 8 kHz 8000.000 Hz 7943.3 Hz
29 10 kHz 10079.368 Hz 10 kHz
30 12.5 kHz 12699.208 Hz 12.589 kHz
31 16 kHz 16000.000 Hz 15.849 kHz
32 20 kHz 20158.737 Hz 19.953 kHz