harmonic series

American  

noun

Mathematics.

1. a series in which the reciprocals of the terms form an arithmetic progression.

2. the divergent infinite series, 1 + 1/2 + 1/3 + 1/4 + 1/5 + . . . .

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harmonic series British  

noun

1. maths a series whose terms are in harmonic progression, as in 1 + 1/ 2 + 1/ 3 + …

2. acoustics the series of tones with frequencies strictly related to one another and to the fundamental tone, as obtained by touching lightly the node points of a string while playing it. Its most important application is in the playing of brass instruments

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harmonic series Scientific  

1. A series whose terms are in harmonic progression, especially the series 1 + 1/2 + 1/3 + 1/4 + …. and so on.

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Etymology

Origin of harmonic series

First recorded in 1865–70

Example Sentences

However, checking the endpoints, we find that at x = 1 the series is the alternating harmonic series, which converges.

From Textbooks • Mar. 30, 2016

The terms in the alternating harmonic series can also be rearranged so that the new series converges to a different value.

From Textbooks • Mar. 30, 2016

The next few exercises are intended to give a sense of applications in which partial sums of the harmonic series arise.

From Textbooks • Mar. 30, 2016

In view of the previous exercise, it may be surprising that a subseries of the harmonic series in which about one in every five terms is deleted might converge.

From Textbooks • Mar. 30, 2016

For the purposes of understanding music theory, however, the important thing about standing waves in winds is this: the harmonic series they produce is essentially the same as the harmonic series on a string.

From "Understanding Basic Music Theory" by Catherine Schmidt-Jones and Russel Jones