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

We will show that whereas the harmonic series diverges, the alternating harmonic series converges.

From Textbooks • Mar. 30, 2016

Continuing in this way, we have found a way of rearranging the terms in the alternating harmonic series so that the sequence of partial sums for the rearranged series is unbounded and therefore diverges.

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

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

From Textbooks • Mar. 30, 2016

At each slide "position," the instrument gets a new harmonic series.

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