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 ?
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.
Rather, the many instruments that produce their tones from a single harmonic series are grouped into broad categories, each of which is treated completely before turning to the next.
He explains the tuning process and related issues, historical factors, and theories including frequency, ratios, cents, fixed intonation, and the harmonic series.
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.
Anumber of new gigs have been added to the Harmonic series which is set to take place throughout October and November.