Octave

Two frequencies are an octave apart if the ratio of the higher frequency to the lower frequency is two.

It is called an octave from the music tradition where an octave spans eight notes of the scale. The second harmonic of a spectral component is one octave above the fundamental. In acoustical measurements, sound pressure level is often measured in octave bands, and the centre frequencies of these bands are defined by the ISO.

Band NumberNominal Centre Frequency HzExact Centre Frequency HzPassband Hz
322.001.41 - 2.82
643.982.82 - 5.62
987.945.62 - 11.2
121615.8511.2 - 22.4
1531.531.6222.4 - 44.7
186363.1044.7 - 89.1
21125125.8989.1 - 178
24250251.19178 - 355
27500501.19355 - 708
3010001000.0708 - 1410
3320001995.31410 - 2820
3640003981.12820 - 5620
3980007943.35620 - 11200
421600015848.911200 - 22400

1/3 Octave Bands
Preferred centre frequencies and passbands are defined by ISO R 266 and ANSI S1.6-1984. The nominal centre frequencies are used to identify the bands and are normally what is reported. The true centre frequencies are calculated using
where
fc = true centre frequency [Hz]
n = band number

1/3 octave filters are sometimes referred to as 1/10 decade filters.

For convenience, 1/3-octave bands are sometimes numbered from band No. 1 (1.25 Hz third-octave centre frequency, which cannot be heard by humans) to band No. 43 (20000 Hz third-octave centre frequency).

Band NumberNominal Centre Frequency HzExact Centre Frequency HzPassband Hz
11.251.261.12 - 1.41
21.61.581.41 - 1.78
322.001.78 - 2.24
42.52.512.24 - 2.82
53.153.162.82 - 3.55
643.983.55 - 4.47
755.014.47 - 5.62
86.36.315.62 - 7.08
987.947.08 - 8.91
101010.08.91 - 11.2
1112.512.5911.2 - 14.1
121615.8514.1 - 17.8
132019.9517.8 - 22.4
142525.1222.4 - 28.2
1531.531.6228.2 - 35.5
164039.8135.5 - 44.7
175050.1244.7 - 56.2
186363.1056.2 - 70.8
198079.4370.8 - 89.1
20100100.0089.1 - 112
21125125.89112 - 141
22160158.49141 - 178
23200199.53178 - 224
24250251.19224 - 282
25315316.23282 - 355
26400398.11355 - 447
27500501.19447 - 562
28630630.96562 - 708
29800794.33708 - 891
3010001000.0891 - 1120
3112501258.91120 - 1410
3216001584.91410 - 1780
3320001995.31780 - 2240
3425002511.92240 - 2820
3531503162.32820 - 3550
3640003981.13550 - 4470
3750005011.94470 - 5620
3863006309.65620 - 7080
3980007943.37080 - 8910
401000010000.08910 - 11200
411250012589.311200 - 14100
421600015848.914100 - 17800
432000019952.617800 - 22400

For 1/3 octave filters the time required for the amplitude to approach the final value is ~1/B where B=filter bandwidth. For 100Hz centre, 23.1Hz bandwidth 1/B=1/23=0.04s.

For broadband random signals the standard deviation of each 1/3 octave band can be estimated by:

where
σ = standard deviation [dB]
B = bandwidth of the signal [Hz], this is 23.1% of the 1/3 octave centre frequency
T = measurement time [s]

This shows that the level of the higher frequency 1/3 octave bands stabilises much quicker than the lower centre frequency bands. For the 100Hz 1/3 octave centre frequency a measurement time of 82 seconds is required for a standard deviation of 0.1dB.

See also: Bandwidth Time Product, Constant Percentage Bandwidth Filter, Frequency, Octave Band.

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Subjects: Noise & Vibration