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What is an octave?

Piano manual

Figure 1: Two octaves on a piano

The octave is an auxiliary unit of measurement for representing frequency intervals with a frequency ratio of two to one.

The term is taken from music. An octave comprises eight notes. The eighth note has twice the frequency of the first note of an octave. The “concert pitch a¹” has a frequency of exactly 440 Hz. The so-called “two-stroke a” (i.e. a² or a") therefore has a frequency of 880 Hz. The frequency interval from a² to a¹ is exactly one octave.

In high-frequency technology, the specification of frequency ranges in “octaves” is commonly used when the bandwidth depends on the frequency, and exact cut-off frequencies are either variable or irrelevant. In this context, an octave is defined as the upper cut-off frequency being twice the value of the lower cut-off frequency. For example, a module with a bandwidth of one octave could be