# harmonic series

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 + . . . .
Origin of harmonic series
1865-1870
1865-70
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the Web for harmonic series
Historical Examples
• This volume is an aid to the study of the “harmonic series.”

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

Walter Raymond Spalding
• 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).

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

• We thus find a fundamental difference between the trumpet and the bugle as regards the harmonic series.

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
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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harmonic series in Science
 harmonic series   A series whose terms are in harmonic progression, especially the series 1 + 1/2 + 1/3 + 1/4 + .... and so on.
The American Heritage® Science Dictionary
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### Difficulty index for harmonic series

Few English speakers likely know this word

### Word Value for harmonic

15
17
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