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

See Examples For:

harmonic series

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

From Textbooks ● Mar. 30, 2016

It is obtained from the harmonic series by deleting all terms in which n is odd.

From Textbooks ● Mar. 30, 2016

This is the harmonic series, which is divergent.

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

The negative aspect is that it means that all intervals except for octaves are slightly out of tune with regard to the actual harmonic series.

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