Octave band

An octave band is a frequency band that spans one octave (Play ). In this context an octave can be a factor of 2[1] or a factor of 100.3.[2][3] 2/1 = 1200 cents ≈ 100.301.

Fractional octave bands such as ​ 1⁄3 or ​ 1⁄12 of an octave are widely used in engineering acoustics.[4]

Analyzing a source on a frequency by frequency basis is possible but time-consuming. The whole frequency range is divided into sets of frequencies called bands. Each band covers a specific range of frequencies. For this reason, a scale of octave bands and one-third octave bands has been developed. A band is said to be an octave in width when the upper band frequency is twice the lower band frequency. A one-third octave band is defined as a frequency band whose upper band-edge frequency (f2) is the lower band frequency (f1) times the cube root of two.

Octave bands

Calculation

If is the center frequency of an octave band, one can compute the octave band boundaries as

,

where is the lower frequency boundary and the upper one.

Naming
Band NumberNominal Frequency[5]Calculated FrequencyA-Weighting Adjustment
-116 Hz15.625 Hz
031.5 Hz31.250 Hz-39.4 dB
163 Hz62.500 Hz-26.2 dB
2125 Hz125.000 Hz-16.1 dB
3250 Hz250.000 Hz-8.6 dB
4500 Hz500.000 Hz-3.2 dB
51k Hz1000.000 Hz0 dB
62k Hz2000.000 Hz1.2 dB
74k Hz4000.000 Hz1 dB
88k Hz8000.000 Hz-1.1 dB
916k Hz16000.000 Hz-6.6 dB

Base 2 calculation

 
%% Calculate Third Octave Bands (base 2) in Matlab
fcentre  = 10^3 * (2 .^ ([-18:13]/3))
fd = 2^(1/6);
fupper = fcentre * fd
flower = fcentre / fd

Base 10 calculation

 
%% Calculate Third Octave Bands (base 10) in Matlab
fcentre = 10.^(0.1.*[12:43])
fd = 10^0.05;
fupper = fcentre * fd
flower = fcentre / fd

Naming
Band NumberNominal FrequencyBase-2 Calculated FrequencyBase-10 Calculated Frequency
116 Hz15.625 Hz15.849 Hz
220 Hz19.686 Hz19.953 Hz
325 Hz24.803 Hz25.119 Hz
431.5 Hz31.250 Hz31.623 Hz
540 Hz39.373 Hz39.811 Hz
650 Hz49.606 Hz50.119 Hz
763 Hz62.500 Hz63.096 Hz
880 Hz78.745 Hz79.433 Hz
9100 Hz99.213 Hz100 Hz
10125 Hz125.000 Hz125.89 Hz
11160 Hz157.490 Hz158.49 Hz
12200 Hz198.425 Hz199.53 Hz
13250 Hz250.000 Hz251.19 Hz
14315 Hz314.980 Hz316.23 Hz
15400 Hz396.850 Hz398.11 Hz
16500 Hz500.000 Hz501.19 Hz
17630 Hz629.961 Hz630.96 Hz
18800 Hz793.701 Hz794.43 Hz
191 kHz1000.000 Hz1000 Hz
201.25 kHz1259.921 Hz1258.9 Hz
211.6 kHz1587.401 Hz1584.9 Hz
222 kHz2000.000 Hz1995.3 Hz
232.5 kHz2519.842 Hz2511.9 Hz
243.150 kHz3174.802 Hz3162.3 Hz
254 kHz4000.000 Hz3981.1 Hz
265 kHz5039.684 Hz5011.9 Hz
276.3 kHz6349.604 Hz6309.6 Hz
288 kHz8000.000 Hz7943.3 Hz
2910 kHz10079.368 Hz10 kHz
3012.5 kHz12699.208 Hz12.589 kHz
3116 kHz16000.000 Hz15.849 kHz
3220 kHz20158.737 Hz19.953 kHz
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See also

References
  1. Crocker 1997 Archived 2017-12-05 at the Wayback Machine
  2. IEC 61260-1:2014
  3. IANSI S1-6-2016
  4. "Archived copy". Archived from the original on 2017-05-14. Retrieved 2017-11-23.CS1 maint: archived copy as title (link)
  5. "ANSI S1.11: Specification for Octave, Half-Octave, and Third Octave Band Filter Sets" (PDF). Retrieved 7 March 2018.


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