harmonic series

Noun

Meaning

(mathematics, mathematical analysis) The divergent series whose terms are the reciprocals of the positive integers; the series





∑

n
=
1


∞




1
n





{\displaystyle \textstyle \sum _{n=1}^{\infty }{\frac {1}{n}}}

.

(music, physics) The sequence of all positive integer multiples of a base frequency.

Synonyms

Examples

Accomplished alphornists often command a range of nearly three octaves, consisting of the 2nd through the 16th notes of the harmonic series. Source: Internet

A harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. Source: Internet

He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula ) and was the first to use power series with confidence and to revert power series. Source: Internet

An illustration of the harmonic series in musical notation. Source: Internet

As the bell is smaller than a modern trombone, the harmonic series is closer to a perfect harmonic series, which is the basis for just tuning. Source: Internet

'Harmonic', 'inverted', 'broken' or 'false' glissandos are those that cross one or more harmonic series, requiring a simulated or faked glissando effect. Source: Internet

Close letter words and terms