Center Frequencies and High/Low Frequency Limits for ...

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 7th octave band's center frequency to be

f ctr 7

1000

Hz

,

then

all

lower

center

frequencies for octave bands can be defined from each other using the formula

f ctr n1

f ctr n

2.

Conversely, all higher center frequencies for octave bands can be defined from each other using the

formula

f ctr n1

2

f ctr n

.

Then

for

each

center

frequency,

the

half-octave

low

(high)

frequency

for

each

octave band are (respectively) given by the formulae

f low n

fn

21 2

and

f high n

21 2

fn .

The

per-cent

fractional bandwidth per octave band is constant:

BW 100

f high n

f low n

f

ctr n

70.7%

.

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 13th half-octave band's center frequency to be

f ctr

13

1000

Hz

,

then

all

lower

center

frequencies for 1/2-octave bands can be defined from each other using the formula

f ctr n1

f ctr n

21 2 .

Conversely, all higher center frequencies for 1/2-octave bands can be defined from each other using the

formula

f ctr n1

21

2

f ctr n

.

Then

for

each

center

frequency,

the

1/4-octave

low

(high)

frequency

for

each

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

f low n

fn

21 4

and

f high n

21 4

fn .

The

per-cent

fractional bandwidth per 1/2-octave band is constant:

BW 100

f high n

f low n

f ctr n

34.8%

.

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 19th

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

f ctr

19

1000

Hz

,

then

all

lower

center

frequencies for 1/3-octave bands can be defined from each other using the formula fn1 fn 21 3 .

Conversely, all higher center frequencies for 1/3-octave bands can be defined from each other using the

formula fn1 21 3 fn . Then for each center frequency, the 1/6-octave low (high) frequency for each

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

f low n

fn

21 6

and

f high n

21 6

fn .

The

per-cent

fractional bandwidth per 1/3-octave band is constant:

BW 100

f high n

f low n

f

ctr n

23.2%

.

Please see the 1/3-octave band table on the next page.

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Each octave band may be separated into three ranges - referred to as one-third-octave bands.

Lower Band Limit (Hz)

Octave Bands

Center Frequency(Hz)

Upper Band Limit (Hz)

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 11360

8000 16000

11360 22720

Lower Band Limit (Hz)

14.1 17.8 22.4 28.2 35.5 44.7 56.2 70.8 89.1 112 141 178 224 282 355 447 562 708 891 1122 1413 1778 2239 2818 3548 4467 5623 7079 8913 11220 14130 17780

1/3 Octave Bands Center

Frequency(Hz) 16 20 25 31.5 40 50 63 80 100 125 160 200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000 6300 8000

10000 12500 16000 20000

Upper Band Limit(Hz)

17.8 22.4 28.2 35.5 44.7 56.2 70.8 89.1 112 141 178 224 282 355 447 562 708 891 1122 1413 1778 2239 2818 3548 4467 5623 7079 8913 11220 14130 17780 22390

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