Adding decibels of one-third octave bands
to level of one octave band and vice versa

Spectral data analysis − spectrum analyzer − one-third octave band = 1/3 octave band
Filter Equalizer EQ

Three adjacent one-third octave bands (1/3 octave bands) belong to one octave band.
 Level of one-third octave band 1 dB Level of one-third octave band 2 dB Level of one-third octave band 3 dB ↓ Combined octave band level dB
 Octave band level dB ↓ Level of one-third octave band 1 dB Level of one-third octave band 2 dB Level of one-third octave band 3 dB
 Should the level of an octave band be converted to one-third octave bands, the energy of the octave band can be divided by three. This corresponds to a reduction of (−)4.771 dB for each 1/3 octave band.

 Calculate: Octave band level LΣ of three one-third octave band levels L1, L2, and L3:

Calculator: Adding of equal levels of 1/3 octave bands

Octave-band filters (1/1) and one-third octave-band filters (1/3)

 Simply enter the value to the left or the right side. The calculator works in both directions of the ↔ sign.

 Number of 1/3 oct bands n ↔ Increase of level Δ L  dB Three 1/3 octave bands are one octave band

The total level in dB is the level of one band plus the increase in level.

Octave bands                                      One-third octave bands

 ISO Band numbers Octave band Center frequency One-third octave band Center frequencies 11, 12, 13 16 Hz 12.5 Hz, 16 Hz, 20 Hz 14, 15, 16 31.5 Hz 25 Hz, 31.5 Hz, 40 Hz 17, 18, 19 63 Hz 50 Hz, 63 Hz, 80 Hz 20, 21, 22 125 Hz 100 Hz, 125 Hz, 160 Hz 23, 24, 25 250 Hz 200 Hz, 250 Hz, 315 Hz 26, 27, 28 500 Hz 400 Hz, 500 Hz, 630 Hz 29, 30, 31 1000 Hz 800 Hz, 1000 Hz, 1250 Hz 32, 33, 34 2000 Hz 1600 Hz, 2000 Hz, 2500 Hz 35, 36, 37 4000 Hz 3150 Hz, 4000 Hz, 5000 Hz 38, 39, 40 8000 Hz 6300 Hz, 8000 Hz, 10000 Hz 41, 42, 43 16000 Hz 12500 Hz, 16000 Hz, 20000 Hz

Standard frequencies for acoustic measurements according to EN ISO 266

 1st octave cycle 31.5 63 125 250 2nd octave cycle 45 90 180 1st 1/3 octave cycle 31.5 40 50 63 80 100 125 160 200 250 2nd 1/3 octave cycle 35,5 45 56 71 90 112 140 180 224 280 1st octave cycle 500 1000 2000 2nd octave cycle 355 710 1400 2800 1st 1/3 octave cycle 315 400 500 630 800 1000 1250 1600 2000 2500 2nd 1/3 octave cycle 355 450 560 710 900 1120 1400 1800 2240 2800 1st octave cycle 4000 8000 16000 2nd octave cycle 5600 11200 22400 1st 1/3 octave cycle 3150 4000 5000 6300 8000 10000 12500 16000 20000 25000 2nd 1/3 octave cycle 3550 4500 5600 7100 9000 11200 14000 18000

 Center, lower, and upper frequencies for standard set of octave and 1/3 octave bands covering the audible frequency range.

 Octave Band 1/3 Octave Band Lower Frequency f1 (Hz) Center Frequency f0 (Hz) Upper Frequency f2 (Hz) Lower Frequency f1 (Hz) Center Frequency f0 (Hz) Upper Frequency f2 (Hz) 22 31.5 44 22.4 25 28.2 28.2 31.5 35.5 35.5 40 44.7 44 63 88 44.7 50 56.2 56.2 63 70.8 70.8 80 89.1 88 125 177 89.1 100 112 112 125 141 141 160 178 177 250 355 178 200 224 224 250 282 282 315 355 355 500 710 355 400 447 447 500 562 562 630 708 710 1,000 1,420 708 800 891 891 1,000 1,122 1,122 1,250 1,413 1,420 2,000 2,840 1,413 1,600 1,778 1,778 2,000 2,239 2,239 2,500 2,818 2,840 4,000 5,680 2,818 3,150 3,548 3,548 4,000 4,467 4,467 5,000 5,623 5,680 8,000 11,360 5,623 6,300 7,079 7,079 8,000 8,913 8,913 10,000 11,220 11,360 16,000 22,720 11,220 12,500 14,130 14,130 16,000 17,780 17,780 20,000 22,390

 A, B, and C Electrical Weighting Networks for the Sound-Level Meter. These numbers assume a diffuse-field (random incidence) response for the sound level meter and microphone.

 Frequency (Hz) A-weighting relative response (dB) B-weighting relative response (dB) C-weighting relative response (dB) 25           31.5        40 −44.7 −39.4 −34.6 −20.4 −17.1 −14.2 −4.4 −3.0 −2.0 50        63        80 −30.2 −26.2 −22.5 −11.6 −9.3 −7.4 −1.3 −0.8 −0.5 100      125      160 −19.1 −16.1 −13.4 −5.6 −4.2 −3.0 −0.3 −0.2 −0.1 200      250      315 −10.9 −8.6 −6.6 −2.0 −1.3 −0.8 0 0 0 400      500      630 −4.8 −3.2 −1.9 −0.5 −0.3 −0.1 0 0 0 800   1,000   1,250 −0.8 0 +0.6 0 0 0 0 0 0 1,600   2,000   2,500 +1.0 +1.2 +1.3 0 −0.1 −0.2 −0.1 −0.2 −0.3 3,150   4,000   5,000 +1.2 +1.0 +0.5 −0.4 −0.7 −1.2 −0.5 −0.8 −1.3 6,300   8,000 10,000 −0.1 −1.1 −2.5 −1.9 −2.9 −4.3 −2.0 −3.0 −4.4 12,500 16,000 20,000 −4.3 −6.6 −9.3 −6.1 −8.4 −11.1 −6.2 −8.5 −11.2

 The total level adding of incoherent sound sources means power sum and power addition or sound power sum and sound power addition

Generation law for octave and third octave bands

 Octave band − oct. filter 1/3 Octave band − third oct. filter f1 = Lower cut-off frequency of the octave or 1/3 octave in Hz  f2 = Upper cut-off frequency of the octave or 1/3 octave in Hz  f0 = Center frequency of the octave or 1/3 octave in Hz  B = Bandwidth (BW) of the filter f2 − f1 in Hz

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