Octave bands

Sound has a wide range of frequencies. To represent sound, it is divided in sections, called bands. The lower band frequency and the upper band frequency for the octave bands are defined as follows:

where:

• f_{1} is the lower band frequency

• f_{2} is the upper band frequency

• is the octave ratio

• is the bandwidth designator

• f_{m} is the midband frequency

The octave ratio for the base two system is defined as:

The bandwidth designator for the 1/3 octave is 3 and for the 1/12 octave is 12.

The midband frequency is defined using the following formula:

where:

• f_{r}is the reference frequency (that is, 1000 Hz)

• x is an integer

The following tables list the nominal values for upper, central, and lower band frequencies for octave, 1/3 octave, and 1/12 frequency band.

Octave Band

f_{1}	f_{m}	f_{2}
5.5	8	11
11	16	22
22	31.5	44
44	63	88
88	125	177
177	250	355
355	500	710
710	1000	1420
1420	2000	2840
2840	4000	5680
5680	8000	11360
11360	16000	22720
22720	31500	45540
45540	63000	91080

1/3 Octave Band

f_{1}	f_{m}	f_{2}
8.9	10	11.2
11.2	12.5	14.1
14.1	16	17.8
17.8	20	22.4
22.4	25	28.2
28.2	31.5	35.5
35.5	40	44.7
44.7	50	56.2
56.2	63	70.8
70.8	80	89.1
89.1	100	112
112	125	141
141	160	178
178	200	224
224	250	282
282	315	355
355	400	447
447	500	562
562	630	708
708	800	891
891	1000	1122
1122	1250	1413
1413	1600	1778
1778	2000	2239
2239	2500	2818
2818	3150	3548
3548	4000	4467
4467	5000	5623
5623	6300	7079
7079	8000	8913
8913	10000	11220
11220	12500	14130
14130	16000	17780
17780	20000	22390
22390	25000	28180
28180	31500	35480
35480	40000	44670
44670	50000	56230
56230	63000	70790
70790	80000	89130
89130	100000	112200

1/12 Octave Band

f_{1}	f_{m}	f_{2}
10	10.3	10.592537
10.592537	10.9	11.220185
11.220185	11.5	11.885022
11.885022	12.2	12.589254
12.589254	13	13.335214
13.335214	13.7	14.125375
14.125375	14.5	14.962357
14.962357	15.4	15.848932
15.848932	16.3	16.78804
16.78804	17.3	17.782794
17.782794	18.3	18.836491
18.836491	19.4	19.952623
19.952623	20.5	21.13489
21.13489	21.8	22.387211
22.387211	23	23.713737
23.713737	24.4	25.118864
25.118864	25.9	26.607251
26.607251	27.4	28.183829
28.183829	29	29.853826
29.853826	30.7	31.622777
31.622777	32.5	33.496544
33.496544	34.5	35.481339
35.481339	36.5	37.58374
37.58374	38.7	39.810717
39.810717	41	42.16965
42.16965	43.4	44.668359
44.668359	46	47.315126
47.315126	48.7	50.118723
50.118723	52	53.088444
53.088444	55	56.234133
56.234133	58	59.566214
59.566214	61	63.095734
63.095734	65	66.834392
66.834392	69	70.794578
70.794578	73	74.989421
74.989421	77	79.432823
79.432823	82	84.139514
84.139514	87	89.125094
89.125094	92	94.406088
94.406088	97	100
100	103	105.925373
105.925373	109	112.201845
112.201845	115	118.850223
118.850223	122	125.892541
125.892541	130	133.352143
133.352143	137	141.253754
141.253754	145	149.623566
149.623566	154	158.489319
158.489319	163	167.880402
167.880402	173	177.827941
177.827941	183	188.364909
188.364909	194	199.526231
199.526231	205	211.348904
211.348904	218	223.872114
223.872114	230	237.137371
237.137371	244	251.188643
251.188643	259	266.072506
266.072506	274	281.838293
281.838293	290	298.538262
298.538262	307	316.227766
316.227766	325	334.965439
334.965439	345	354.813389
354.813389	365	375.837404
375.837404	387	398.107171
398.107171	410	421.696503
421.696503	434	446.683592
446.683592	460	473.151259
473.151259	487	501.187234
501.187234	520	530.884444
530.884444	550	562.341325
562.341325	580	595.662144
595.662144	610	630.957344
630.957344	650	668.343918
668.343918	690	707.945784
707.945784	730	749.894209
749.894209	770	794.328235
794.328235	820	841.395142
841.395142	870	891.250938
891.250938	920	944.060876
944.060876	970	1000
1000	1030	1059.253725
1059.253725	1090	1122.018454
1122.018454	1150	1188.502227
1188.502227	1220	1258.925412
1258.925412	1300	1333.521432
1333.521432	1370	1412.537545
1412.537545	1450	1496.235656
1496.235656	1540	1584.893192
1584.893192	1630	1678.804018
1678.804018	1730	1778.27941
1778.27941	1830	1883.649089
1883.649089	1940	1995.262315
1995.262315	2050	2113.48904
2113.48904	2180	2238.721139
2238.721139	2300	2371.373706
2371.373706	2440	2511.886432
2511.886432	2590	2660.72506
2660.72506	2740	2818.382931
2818.382931	2900	2985.382619
2985.382619	3070	3162.27766
3162.27766	3250	3349.654392
3349.654392	3450	3548.133892
3548.133892	3650	3758.374043
3758.374043	3870	3981.071706
3981.071706	4100	4216.965034
4216.965034	4340	4466.835922
4466.835922	4600	4731.51259
4731.51259	4870	5011.872336
5011.872336	5200	5308.844442
5308.844442	5500	5623.413252
5623.413252	5800	5956.621435
5956.621435	6100	6309.573445
6309.573445	6500	6683.439176
6683.439176	6900	7079.457844
7079.457844	7300	7498.942093
7498.942093	7700	7943.282347
7943.282347	8200	8413.951416
8413.951416	8700	8912.509381
8912.509381	9200	9440.608763
9440.608763	9700	10000
10000	10300	10592.53725
10592.53725	10900	11220.18454
11220.18454	11500	11885.02227
11885.02227	12200	12589.25412
12589.25412	13000	13335.21432
13335.21432	13700	14125.37545
14125.37545	14500	14962.35656
14962.35656	15400	15848.93193
15848.93193	16300	16788.04018
16788.04018	17300	17782.7941
17782.7941	18300	18836.4909
18836.4909	19400	19952.62315
19952.62315	20500	21134.8904
21134.8904	21800	22387.21139
22387.21139	23000	23713.73706
23713.73706	24400	25118.86432
25118.86432	25900	26607.2506
26607.2506	27400	28183.82931
28183.82931	29000	29853.82619
29853.82619	30700	31622.7766
31622.7766	32500	33496.54392
33496.54392	34500	35481.33892
35481.33892	36500	37583.74043
37583.74043	38700	39810.71706
39810.71706	41000	42169.65034
42169.65034	43400	44668.35922
44668.35922	46000	47315.1259
47315.1259	48700	50118.72336
50118.72336	52000	53088.44442
53088.44442	55000	56234.13252
56234.13252	58000	59566.21435
59566.21435	61000	63095.73445
63095.73445	65000	66834.39176
66834.39176	69000	70794.57844
70794.57844	73000	74989.42093
74989.42093	77000	79432.82347
79432.82347	82000	84139.51417
84139.51417	87000	89125.09381
89125.09381	92000	94406.08763
94406.08763	97000	100000
100000	103000	105925.3725

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