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.
1
2
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
3
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