What is sound level meter?
11. Octave band analysis (Frequency analysis)
There are two methods for frequency analysis of acoustic vibration: narrowband analysis (FFT analysis) and octave band analysis.
Table 111: Frequency analysis methods 
Analysis band width  Typical application  

FFT analysis  Constant band width  Troubleshooting and resolution of physical problems 
Octave band analysis  Constant band ratio  Evaluation of noise and vibration 
Octave band analysis is also called CPB (Constant Percentage Bandwidth) analysis. The following paragraphs explain octave band analysis.
To devise noise reduction measures, the noise needs to be analyzed (frequency analysis). One of the noise analysis methods that have been used for many years is octave band analysis. An octave is a series of notes, with the note at the higher end of the series having twice the frequency of the note at the lower end. (Refer to "What is an octave?" below.)
Frequency characteristic felt by the human ear is a geometrical, making octave band analysis a popular means of analysis. The sound pressure level for each band of the noise being measured is determined across the audio frequency range using a bandpass filter meeting 1/1 octave or 1/3 octave standards. For the characteristics of filters and other relevant details, refer to IEC 61260 (JIS C1514:2002).
What is an octave? An octave is a series of notes, with the note, e.g. ‘do’, at the higher end of the series having twice the frequency of the note, e.g. ‘do’, at the lower end of the series. An octave band is a oneoctave range of frequencies straddling across a center frequency, which is called the center octave band frequency. A third of an octave band is called a 1/3 octave band. As shown in the figure on the right, in the 12tone equal temperament, an octave is divided into 12 parts with constant ratios between the frequencies of any two adjoining tones, with each part called a 1/12 octave band. 

112 JIS standards on octave filters
There are two JIS standards on octave filters.
JIS C1514:2002, which is a translation (IDT) of the corresponding IEC standards, specifies filter characteristics, covering a wide range of filters including not just octave and 1/3 octave filters but 1/N octave filters with required accuracy tolerances of three classes (Class 0, Class 1 and Class 2).
JIS C1513:2002 specifies necessary and sufficient specifications for sound and vibration analyzers while making references to the JIS C1514:2002 specifications for the characteristics of octave and 1/3 octave filters. It specifies only Class 1 and Class 2 tolerances, which have steeper characteristics than the conventional Type II and Type III classes. When numbers are smaller, more stringent standards apply.
Table 112 shows the center frequencies of octave and 1/3 octave filters. These numbers are the nominal center frequencies specified by ISO 266. The exact center frequencies of JIScompliant filters are determined using calculations specified in JIS C1514:2002 (IEC 61260:1995).
Table 112: Center frequencies of 1/1 octave and 1/3 octave bandpass filters 
Center frequency (Hz)  1/1 octave  1/3 octave  Center frequency (Hz)  1/1 octave  1/3 octave  Center frequency (Hz)  1/1 octave  1/3 octave 

0.8  ○  25  ○  800  ○  
1  ○  ○  31.5  ○  ○  1000  ○  ○ 
1.25  ○  40  ○  1250  ○  
1.6  ○  50  ○  1600  ○  
2  ○  ○  63  ○  ○  2000  ○  ○ 
2.5  ○  80  ○  2500  ○  
3.15  ○  100  ○  3150  ○  
4  ○  ○  125  ○  ○  4000  ○  ○ 
5  ○  160  ○  5000  ○  
6.3  ○  200  ○  6300  ○  
8  ○  ○  250  ○  ○  8000  ○  ○ 
10  ○  315  ○  10000  ○  
12.5  ○  400  ○  12500  ○  
16  ○  ○  500  ○  ○  16000  ○  ○ 
20  ○  630  ○  20000  ○ 
113 Octave filter bandwidth and center frequency
1/1 and 1/3 octaves consist of a number of frequency bandwidths. When:
f_{1} is the lower cutoff frequency,
f_{2} is the upper cutoff frequency, and
f_{m} is the center frequency,
then the following equations are true for each octave band.
1/1 octave band filter

(Equation 111)

Figure 111: Center frequency, upper and lower cutoff frequencies and bandwidth of 1/1 octave band 
1/3 octave band filter

(Equation 112) 
Figure 112: Center frequency, upper and lower cutoff frequencies and bandwidth of 1/3 octave band 
[Supplement] The following briefly explains how to determine center frequency f_{m} (Source: IEC 61260:1995 (JIS C1514)). According to IEC 61260 (JIS C1514), exact center frequencies can be determined using the following equations.
When N is an even number (e.g. 6, 12 or 24)
.................... where:
The following two methods are specified for determining G.
By definition, the use of the powers of 2 form should raise no objections. The powers of 10 form was used due to the fact that 10 octaves are almost equal to three decades (2^{10} ≒ 10^{3}), which makes G_{10} in Equation 115 around 2 (1.9953). The power of 10 form consists of multiples of 10 and also works well with decimal numbers, making itself a recommended system in standards.
The following figures show characteristics of 1/1 and 1/3 octave band filters (Source: JIS C1513).

[Refernce] When converting known 1/3 octave data in dB into corresponding 1/1 octave data in dB, add up the 1/3 octave data in dB that corresponds to the target 1/1 octave data. For example, when determining the 1/1 octave band data around the center frequency of 1000 Hz and the corresponding 1/3 octave band has the following data in dB,
the 1/1 octave band data around the center frequency of 1000 Hz can be determined using the following equation.
