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In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals. As a simple example, the harmonic mean of 1, 2, and 4 is 3 1 1 + 1 2 + 1 4 = 1 1 3 ( 1 1 + 1 2 + 1 4 ) = 12 7 .
The harmonic series is an arithmetic series (1Ãf, 2Ãf, 3Ãf, 4Ãf, 5Ãf, ...). In terms of frequency (measured in cycles per second, or hertz (Hz) where f is the fundamental frequency), the difference between consecutive harmonics is therefore constant and equal to the fundamental.he harmonic series is an arithmetic series (1Ãf, 2Ãf, 3Ãf, 4Ãf, 5Ãf, ...). In terms of frequency (measured in cycles per second, or hertz (Hz) where f is the fundamental frequency), the difference between consecutive harmonics is therefore constant and equal to the fundamental.