Octave band
An octave band is a frequency band that spans one octave. In this context an octave can be a factor of 2 or a factor of 100.3. 2/1 = 1200 cents ≈ 10.
Fractional octave bands such as or of an octave are widely used in engineering acoustics.
Analyzing a source on a frequency by frequency basis is possible but time-consuming. 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 is the lower band frequency times the cube root of two.
Octave bands
Calculation
If is the center frequency of an octave band, one can compute the octave band boundaries aswhere is the lower frequency boundary and the upper one.
Naming
Band Number | Nominal Frequency | 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 in Matlab
fcentre = 10^3 *
fd = 2^;
fupper = fcentre * fd
flower = fcentre / fd
Base 10 calculation
%% Calculate Third Octave Bands in Matlab
fcentre = 10.^
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 |