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Octave

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

Band Number	Nominal Centre Frequency Hz	Exact Centre Frequency Hz	Passband Hz
3	2	2.00	1.41 - 2.82
6	4	3.98	2.82 - 5.62
9	8	7.94	5.62 - 11.2
12	16	15.85	11.2 - 22.4
15	31.5	31.62	22.4 - 44.7
18	63	63.10	44.7 - 89.1
21	125	125.89	89.1 - 178
24	250	251.19	178 - 355
27	500	501.19	355 - 708
30	1000	1000.0	708 - 1410
33	2000	1995.3	1410 - 2820
36	4000	3981.1	2820 - 5620
39	8000	7943.3	5620 - 11200
42	16000	15848.9	11200 - 22400

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: f_c = 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 Number	Nominal Centre Frequency Hz	Exact Centre Frequency Hz	Passband Hz
1	1.25	1.26	1.12 - 1.41
2	1.6	1.58	1.41 - 1.78
3	2	2.00	1.78 - 2.24
4	2.5	2.51	2.24 - 2.82
5	3.15	3.16	2.82 - 3.55
6	4	3.98	3.55 - 4.47
7	5	5.01	4.47 - 5.62
8	6.3	6.31	5.62 - 7.08
9	8	7.94	7.08 - 8.91
10	10	10.0	8.91 - 11.2
11	12.5	12.59	11.2 - 14.1
12	16	15.85	14.1 - 17.8
13	20	19.95	17.8 - 22.4
14	25	25.12	22.4 - 28.2
15	31.5	31.62	28.2 - 35.5
16	40	39.81	35.5 - 44.7
17	50	50.12	44.7 - 56.2
18	63	63.10	56.2 - 70.8
19	80	79.43	70.8 - 89.1
20	100	100.00	89.1 - 112
21	125	125.89	112 - 141
22	160	158.49	141 - 178
23	200	199.53	178 - 224
24	250	251.19	224 - 282
25	315	316.23	282 - 355
26	400	398.11	355 - 447
27	500	501.19	447 - 562
28	630	630.96	562 - 708
29	800	794.33	708 - 891
30	1000	1000.0	891 - 1120
31	1250	1258.9	1120 - 1410
32	1600	1584.9	1410 - 1780
33	2000	1995.3	1780 - 2240
34	2500	2511.9	2240 - 2820
35	3150	3162.3	2820 - 3550
36	4000	3981.1	3550 - 4470
37	5000	5011.9	4470 - 5620
38	6300	6309.6	5620 - 7080
39	8000	7943.3	7080 - 8910
40	10000	10000.0	8910 - 11200
41	12500	12589.3	11200 - 14100
42	16000	15848.9	14100 - 17800
43	20000	19952.6	17800 - 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.


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.

Subjects:

Noise & Vibration