third
A third is a musical interval in which the higher note is two steps above the lower note. In terms of frequency, a third has a frequency range that fits three times into an octave. As with the octave, the center frequency of the third is determined geometrically. There is a standardized third-octave center frequency series.
Theoretically, the third-octave center frequency is 1/3 of the octave frequency, or `2^(1/3)`, which is 1.260 times. Thus, the next higher third-octave frequency corresponds to the reference frequency multiplied by 1.26, and the next lower one results from multiplication by 0.794.
With a reference frequency of 1 kHz, the next third-octave center frequency would be 1.260 kHz. This value has been rounded down to 1.25 kHz by ANSI and the International Standards Organization( ISO). The same applies to the next lower third-octave center frequency. This would theoretically be 794 Hz, but has been rounded up to 800 Hz.
Since the value for `2^(1/3)` is almost exactly equal to the value of `10^(1/10)`, third octave frequencies can be determined by dividing the octave into thirds or the decade into tenths.