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1

Center Frequencies and High/Low

Frequency Limits for Octave Bands, 1/2- and 1/3-Octave Bands

Octave Bands:

The audio spectrum from ~ 20 Hz to ~ 20 KHz can be divided up into ~ 11 octave bands.

If we set/define the 7

th octave band's center frequency to be 7 1000
ctr fHz, then all lower center frequencies for octave bands can be defined from each other using the formula 1 2 ctr ctr nn ff Conversely, all higher center frequencies for octave bands can be defined from each other using the formula 1 2 ctr ctr nn ff . Then for each center frequency, the half-octave low (high) frequency for each octave band are (respectively) given by the formulae 12 2 low nn ff and 12 2 high nn ff . The per-cent fractional bandwidth per octave band is constant:

100 70.7%

high low ctr nnn

BW f f f

Please see the octave band table on the next page.

1/2-Octave Bands:

The audio spectrum from ~ 20 Hz to ~ 20 KHz can be divided up into ~ 21 1/2-octave bands.

If we set/define the 13

th half-octave band's center frequency to be

131000

ctr fHz, then all lower center frequencies for 1/2-octave bands can be defined from each other using the formula 12 1 2 ctr ctr nn ff

Conversely, all

higher center frequencies for 1/2-octave bands can be defined from each other using the formula 12 1 2 ctr ctr nnff . Then for each center frequency, the 1/4-octave low (high) frequency for each

1/2-octave band are (respectively) given by the formulae

14 2 low nn ff and 14 2 high nn ff. The per-cent fractional bandwidth per 1/2-octave band is constant:

100 34.8%

high low ctr nnnBW f f f Please see the 1/2-octave band table on the next page.

1/3-Octave Bands:

The audio spectrum from ~ 20 Hz to ~ 20 KHz can be divided up into ~ 31 1/3-octave bands.

If we set/define the 19

th

1/3-octave band's center frequency to be

19 1000
ctr fHz, then all lower center frequencies for 1/3-octave bands can be defined from each other using the formula 13 1 2 nn ff

Conversely, all

higher center frequencies for 1/3-octave bands can be defined from each other using the formula 13 1 2 nn ff . Then for each center frequency, the 1/6-octave low (high) frequency for each

1/3-octave band are (respectively) given by the formulae

162
low nn ff and 16 2 high nn ff. The per-cent fractional bandwidth per 1/3-octave band is constant:

100 23.2%

high low ctr nnn

BW f f f

Please see the 1/3-octave band table on the next page. 2 3 Each octave band may be separated into three ranges - referred to as one-third-octave bands.

Octave Bands 1/3 Octave Bands

Lower Band

Limit (Hz)

Center

Frequency(Hz)

Upper Band

Limit (Hz)

Lower Band

Limit (Hz)

Center

Frequency(Hz)

Upper Band

Limit(Hz)

11 16 22 14.1 16 17.8

17.8 20 22.4

22.4 25 28.2

22 31.5 44

28.2 31.5 35.5

35.5 40 44.7

44.7 50 56.2

44 63 88

56.2 63 70.8

70.8 80 89.1

89.1 100 112

88 125 177

112 125 141

141 160 178

178 200 224

177 250 355

224 250 282

282 315 355

355 400 447

355 500 710

447 500 562

562 630 708

708 800 891

710 1000 1420

891 1000 1122

1122 1250 1413

1413 1600 1778

1420 2000 2840

1778 2000 2239

2239 2500 2818

2818 3150 3548

2840 4000 5680

3548 4000 4467

4467 5000 5623

5623 6300 7079

5680 8000 11360

7079 8000 8913

8913 10000 11220

11220 12500 14130

11360 16000 22720

14130 16000 17780

17780 20000 22390

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