# Harmonic Series

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Related to Harmonic Series: geometric series, Harmonic sequence

## harmonic series

[här¦män·ik ′sir‚ēz]
(mathematics)
A series whose terms form a harmonic progression.

## Harmonic Series

the numerical series

Each term of the series (starting with the second) is the harmonic mean of the two adjacent terms (hence the name “harmonic series”). The terms of a harmonic series approach zero, but the series is divergent (G. Leibniz, 1673). The sum of the first n terms has the following asymptotic expression (L. Euler, 1740):

Sn = ln n + C + єn

where C = 0.577215 … is Euler’s constant and єn→ as n→∞.

## Harmonic Series

in musical acoustics, the ascending series of overtones, or partial tones: the series of harmonics beginning with the fundamental tone.

The relationship of the frequencies of the overtones is expressed by a series of prime numbers. In order that these prime numbers correspond to the ordinal numbers of the overtones, the fundamental tone of the harmonic series by convention is called the first overtone.

Because of a difference in frequencies, the pitch of some overtones differs slightly from the corresponding tempered pitch. Overtones whose pitch is higher than the tempered pitch are marked with a plus sign. The six lowest overtones are part of the major triad, which thus conforms to acoustic laws.

References in periodicals archive ?
We worked through a series of harmonic series exercises as well.
The other volumes will be: lit'ap to Expand the Harmonic Series, covering instruments that use methods such as slides, finger holes, and keys to fill in notes outside the harmonic series; Valves Evolve, covering the development of various valve mechanisms in the nineteenth century; Heyday of the Cornet; and The Modern Trumpet, covering twentieth-century trumpet development.
Alternatively, the external gravitational potential can be modeled by harmonic series expansions (e.
He explains the tuning process and related issues, historical factors, and theories including frequency, ratios, cents, fixed intonation, and the harmonic series.
In the new tuning system the major third was an imperfect consonance that could be directly equated with the harmonic series.
5) Thanks to his encounter with Helmholtz's work, the harmonic series formed a major source of Partch's investigations in the years 1923-28, when his theoretical ideas were crystallizing.
The reason given was that a "zero" frequency does not ft into the harmonic series of the sound source.
I'm not referring to the harmonic series warm-up arpeggio s that you probably do in some form.
Not to be missed catch Deerhunter tonight at The Button Factory as part of a new Harmonic series.
The slide action of the trombone permits the chromatic filling-in of the scale of the instrument between the second and third partials of the harmonic series of the basic instrument and thereby renders it fully chromatic over a range starting at an augmented fourth below the second partial up to an upper bound determined only by the skill and strength of the performer.
The pattern in question is the pitch pattern formed by the audible harmonics of the tone, corresponding to the lower echelons of the harmonic series.
More specifically, can the odd harmonic series be different from the even harmonic series?

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