An octave band is a frequency band that spans one octave (ⓘ). In this context an octave can be a factor of 2 or a factor of 100.3.[full citation needed] To remove the ambiguity, an alternative name suggested for a factor of 100.3 is "dectave", a portmanteau of "decimal" and "octave". An octave of 1200cents in musical pitch (a logarithmic unit) corresponds to a frequency ratio of ⁠2/1⁠ ≈ 100.301 .

An international standard set of octave bands and one-third octave bands has been developed for frequency analysis in acoustics. A band is said to be an octave in width when the upper band frequency is approximately twice the lower band frequency.

Frequency bands

A whole frequency range can be divided into sets of frequencies called bands, with each band covering a specific range of frequencies. For example, radio frequencies are divided into multiple levels of band divisions and subdivisions, and rather than octaves, the highest level of radio bands (VLF, LF, MF, HF, VHF, etc.) are divided up by the wavelengths' power of ten (decads, or decils)[citation needed] that is the same for all radio waves in the same band, rather than the power of two, as in analysis of acoustical frequencies.

In acoustical analysis, a one-third octave band is defined as a frequency band whose upper band-edge frequency ( f2 or fmax ) is the lower band frequency ( f1 or fmin ) times the tenth root of ten, or 1.2589: The first of the one-third octave bands ends at a frequency 25.9% higher than the starting frequency for all of them, the base frequency, or approximately 399 musical cents above the start (the same frequency ratio as the musical interval between the notes c–e. The second one-third octave begins where the first-third ends and itself ends at a frequency 1.2589 ² = 1.5849 × , or 58.5% higher than the original starting frequency. The third-third, or last band ends at 1.2589 ³ = 1.9953 × , or 199.5% of the base frequency.

Any useful subdivision of acoustic frequencies is possible: Fractional octave bands such as ⁠1/3⁠ or ⁠1/12⁠ of an octave (the spacing of musical notes in 12 tone equal temperament) are widely used in acoustical engineering.

Analyzing a source on a frequency by frequency basis is possible, most often using Fourier transform analysis.

Octave bands

Calculation

If f c {\displaystyle \ f_{\mathsf {c}}\ } is the center frequency of an octave band, one can compute the octave band boundaries as

f c = 2 f m i n = f m a x 2 , {\displaystyle \ f_{c}={\sqrt {2}}f_{\mathsf {min}}={\frac {\ f_{\mathsf {max}}\ }{\ {\sqrt {2\ }}\ }}\ ,}

where f m i n {\displaystyle \ f_{\mathsf {min}}\ } is the lower frequency boundary and f m a x {\displaystyle \ f_{\mathsf {max}}\ } the upper one.

Naming

Band number Nominal frequency Calculated frequency A-weight adjustment −116Hz15.625Hz 031.5Hz31.250Hz−39.4dB 163Hz62.500Hz−26.2dB 2125Hz125.000Hz−16.1dB 3250Hz250.000Hz−8.6dB 4500Hz500.000Hz−3.2dB 51kHz1000.000Hz0dB 62kHz2000.000Hz+1.2dB 74kHz4000.000Hz+1.0dB 88kHz8000.000Hz−1.1dB 916kHz16000.000Hz−6.6dB

Note that 1000.000Hz, in octave5, is the nominal central or reference frequency, and as such gets no correction.

One-third octave bands

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^(1/20); fupper=fcentre*fd flower=fcentre/fd

Naming

Due to slight rounding differences between the base two and base ten formulas, the exact starting and ending frequencies for various subdivisions of the octave come out slightly differently.

Band numberNominal frequencyBase 2 calculated frequencyBase 10 calculated frequency 116Hz15.625Hz15.849Hz 220Hz19.686Hz19.953Hz 325Hz24.803Hz25.119Hz 431.5Hz31.250Hz31.623Hz 540Hz39.373Hz39.811Hz 650Hz49.606Hz50.119Hz 763Hz62.500Hz63.096Hz 880Hz78.745Hz79.433Hz 9100Hz99.213Hz100Hz 10125Hz125.000Hz125.89Hz 11160Hz157.490Hz158.49Hz 12200Hz198.425Hz199.53Hz 13250Hz250.000Hz251.19Hz 14315Hz314.980Hz316.23Hz 15400Hz396.850Hz398.11Hz 16500Hz500.000Hz501.19Hz 17630Hz629.961Hz630.96Hz 18800Hz793.701Hz794.43Hz 191kHz1000.000Hz1000Hz 201.25kHz1259.921Hz1258.9Hz 211.6kHz1587.401Hz1584.9Hz 222kHz2000.000Hz1995.3Hz 232.5kHz2519.842Hz2511.9Hz 243.150kHz3174.802Hz3162.3Hz 254kHz4000.000Hz3981.1Hz 265kHz5039.684Hz5011.9Hz 276.3kHz6349.604Hz6309.6Hz 288kHz8000.000Hz7943.3Hz 2910kHz10079.368Hz10kHz 3012.5kHz12699.208Hz12.589kHz 3116kHz16000.000Hz15.849kHz 3220kHz20158.737Hz19.953kHz

See also

Notes