# harmonic series

nounMathematics.
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 + . . . .

## Origin of harmonic series

1
First recorded in 1865–70

## Words Nearby harmonic series

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

## How to use harmonic series in a sentence

• The euphonium gives out the fundamental, or first note of the harmonic series, readily, but no harmonic above the eighth.

• The unisonous quality of octaves is easily explained when we examine the “harmonic series” of upper partials (see Sound).

• It is left to the teacher to explain, by the ratios found in the overtones of the harmonic series, the validity of this statement.

Music: An Art and a Language | Walter Raymond Spalding
• We thus find a fundamental difference between the trumpet and the bugle as regards the harmonic series.

• The harmonic series consists of the harmonics from the 1st to the 8th.

## British Dictionary definitions for harmonic series

harmonic series

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

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Scientific definitions for harmonic series

harmonic series

1. A series whose terms are in harmonic progression, especially the series 1 + 12 + 13 + 14 + .... and so on.