Octave band

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. To remove the ambiguity, an alternative name suggested for a factor of 10^0.3 is "dectave", a portmanteau of "decimal" and "octave". An octave of 1200 cents in musical pitch corresponds to a frequency ratio of
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 are divided up by the wavelengths' power of ten 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 is the lower band frequency times the tenth root of ten, or : 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 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 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

Note that 1000.000 Hz, in octave 5, is the nominal central or reference frequency, and as such gets no correction.

One-third octave bands

Base 2 calculation

%% Calculate Third Octave Bands in Matlab
fcentre = 10^3 *
fd = 2^;
fupper = fcentre * fd
flower = fcentre / fd

Base 10 calculation

%% Calculate Third Octave Bands in Matlab
fcentre = 10.^
fd = 10^;
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.