1/3rd Octave Band

OCTAVE 1/3^RD BAND

Introduction

The word ‘octave’ is derived from the Latin word meaning ‘eight’. In the musical world where there are 7 notes, the 8^th note sounds twice as high as the 1^st note. The 8^th note is an octave higher than the 1^st note. Similarly in the octave band, the upper limit frequency is twice the lower limit frequency. Octave bands are very useful in engineering applications because they reveal the spectral content, meaning they represent the change in noise levels with respect to the frequency of sound. This helps in identifying which frequency is responsible for the noise which helps in nailing down the component in a machine responsible for the frequency.

Octave 1/3^rd band is similar to the octave 1/1 band but has higher spectral resolution. Octave 1/3^rd band is octave 1/1 band where each frequency band is divided equally into 3 parts. This helps in increasing the frequency resolution as more accurate frequency information is available at a reasonable data space.

Octave 1/3 Band

Fig .1 Octave 1/3rd band

Equations

The relation between the next and the previous center frequency is given by,

n = 3 for 1/3^rd octave band

C_F – center frequency

C_Fnext – next center frequency

C_Fprev – previous center frequency

The relation between the upper band and lower band frequency limit for a given frequency band is given by,

C_L – lower band limit for a given center frequency

C_U – upper band limit for a given center frequency

Tabular column

Frequencies bands in the entire range, upper & lower band limits

Octave 1/3 band	Center frequency	Lower band limit	Upper band limit
	Hz	Hz	Hz
Band1	16	13.9	17.5
Band2	20	17.5	22.1
Band3	25	22.1	27.8
Band4	31.5	27.8	35.1
Band5	40	35.1	44.2
Band6	50	44.2	55.7
Band7	63	55.7	70.2
Band8	80	70.2	88.4
Band9	100	88.4	111.4
Band10	125	111.4	140.3
Band11	160	140.3	176.8
Band12	200	176.8	222.7
Band13	250	222.7	280.6
Band14	315	280.6	353.6
Band15	400	353.6	445.4
Band16	500	445.4	561.2
Band17	630	561.2	707.1
Band18	800	707.1	890.9
Band19	1000	890.9	1122.5
Band20	1250	1122.5	1414.2
Band21	1600	1414.2	1781.8
Band22	2000	1781.8	2244.9
Band23	2500	2244.9	2828.4
Band24	3150	2828.4	3563.6
Band25	4000	3563.6	4489.8
Band26	5000	4489.8	5656.9
Band27	6300	5656.9	7127.2
Band28	8000	7127.2	8979.7
Band29	10000	8979.7	11313.7
Band30	12500	11313.7	14254.4
Band31	16000	14254.4	17959.4

Octave 1/3 Band Real Time Analysis

Fig .2 Real time Octave 1/3rd band