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

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

Argue that this depleted harmonic series converges by answering the following questions.

From Textbooks • Mar. 30, 2016

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

From Textbooks • Mar. 30, 2016

Since this is the alternating harmonic series, it converges.

From Textbooks • Mar. 30, 2016

NOTE: If you have been looking at the harmonic series above closely, you may have noticed that some notes that are written to give the same interval have different frequency ratios.

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