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

To illustrate how the integral test works, use the harmonic series as an example.

From Textbooks • Mar. 30, 2016

We also discuss the harmonic series, arguably the most interesting divergent series because it just fails to converge.

From Textbooks • Mar. 30, 2016

In this section we use a different technique to prove the divergence of the harmonic series.

From Textbooks • Mar. 30, 2016

Compare to a plot of the first 1000 partial sums of the harmonic series.

From Textbooks • Mar. 30, 2016

A harmonic series can start on any note, so there are many harmonic series, but every harmonic series has the same set of intervals and the same frequency ratios.

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