Overtones

with each natural toner generation apart from the basic frequency still another multiplicity of higher tones is produced. These hot overtones, Partialtöne, partial tones, or harmonious ones. The consequence of these tones is called overtone row, nature clay/tone row or partial clay/tone row. ThoseWhole of basic clay/tone and overtones results in the frequency spectrum of a clay/tone.

basic clay/tone, partial tones, overtones

all partial tones are present in the form of sinus oscillations. The deepest partial clay/tone is called also „basic clay/tone “, it specifies the basic frequency and determinedthe felt pitch. All further partial tones are together seized under the term „overtones “. The frequencies of the overtones are mostly integral multiple of the frequency of the basic clay/tone. The term „overtones “does not include thus the basic frequency also; The 1. Overtone is thereforethe 2. Partial clay/tone/the 2.Harmonious one.

With the help of the Fourieranalyse a clay/tone can be divided into its Teilschwingungen.

overtone rows

frequency relations

the musical interval of one Oktave corresponds to a doubling of the frequency. Thus the following harmonious ones lie in each case in the Oktav distance to each other: 1. , 2. , 4. , 8. , 16. , etc.

Example: Basic clay/tone of 440 cycles per second

Frequency conditions of the partial tones can be expressed approach in musical intervals:

This list applies however only with pure tendency exactly. With equivalent tendency only tones in the Oktav distance possess an integral frequency relationship to each other, D. h. Quinten, Quarten and thirds in higher Oktavräumen meet the harmonious ones no longer exactly.

musical feeling

musical intervals or chords from two arbitrary tones rings out all the more consonant (thus more harmoniously and probably), the more overtones it together possesses and/or. closely neighbouring are. As experimental confirmation Pythagoras already used the Monochord.

Residualton

the human hearing center is able to notice to (also only partly) a ringing out overtone spectrum the basic frequency even if this does not ring out. These „added “basic clay/tone calls one also Residualton.

This technologyone uses, in order to simulate on loudspeaker systems basses, which it could not show purely technically at all. Thus one recognizes the played pitch of a retort bass in the portable receiver, although the frequency cannot be shown by the small loudspeakers. Also withTelephone develops this effect: The basic clay/tone of the human voice is not transferred over the telephone, the frequency range of the telephone is too narrow, the being correct transmission begins only up. But the brain notices the basic clay/tone.

This phenomenon becomes also traditional in Building of organs used: With simultaneous employment of the 8-Fuss and 5 ^{the 1}/₃ - foot, which lies a Quinte over it, one hears the 16-Fuss, thus a Oktave under the 8-Fuss.

Background is that the hearing not only the overtone spectrum, but alsothe period of the acoustic Zeitsignals evaluates. With a harmonious overtone spectrum however the period of the Zeitsignals remains, even if the basic clay/tone is removed.

overtones and tone quality

of overtones of the human voice

the different sound of Vocal ones comes by their specific structure of overtone to conditions. Differently strongly represented overtones are also a reason, why the voices of different humans have different tone qualities. By the individual size and form from mouth and throat some become in this resonance area, Other one strengthens frequencies decreased. One calls the frequency ranges, which are strengthened by appropriate resonances, also Formanten.

In the human voice , exactly as also in most sound-producing physical systems, natural a complex overtone spectrum swings. In the special singing technology of the Overtone singing can bring one these high frequencies to dominating.

overtones of different instruments

The specific sound of an instrument results from the following parameters:

• Which partial tones are at allavailable? - (1. , 2. , 3. , 5. , 9. , etc.)
• How loud are these partial tones in the relationship to each other? - First does not have to be the loudest.
• How does the volume of the individual partial tones change, while the clay/tone rings out (fine modulation)?
• WhichBackground noises come in addition (notice noises, blowing noises etc.)?

The frequencies of the overtones depend it on the respective sound producer, are its natural frequencies. There are instruments with harmonious and such with not-harmonious overtone rows.

With instruments with harmonious overtone rows are the frequencies of the overtonesintegral multiple of the frequency of the basic clay/tone. To it those belong to choir doping hone (stringed instruments) and the Aerophone with swinging air column. In this case one calls the overtones also harmonious ones. That is naturally also only an idealized acceptance. The straight very small deviationsby the ideal harmonious ones make unmistakable and alive the sound of an individual instrument.

With instruments with not-harmonious overtone rows the frequencies of the partial tones do not stand to each other in complicated integral conditions. The overtones of the Membranophone with round diaphragm have the natural frequencies of one Bessel's differential equation. In the case of Idiophonen completely different overtone rows can result depending upon the form of the ochestra - with the staff plays about there is the natural frequencies of the bending vibration of a bar.

Higher overtones usually are with natural tonesmore quietly (more level-weakly) than deeper, since for their faster oscillation is lost to more energy.

Generally tones sound the „more sharply “, the more overtones them have. Pure tones without overtones cannot in nature (acoustic), but produces only electronically as sinus oscillationsbecome. They sound extremely dull. An example is the 1000-Hertz-Ton of the television test pattern, whereby the loudspeaker adds however already again its own, however small, overtone spectrum.

Artificially from pures tone one calls manufactured overtone spectra synthetic sounds (see sound synthesis, Synthesizer).

The following instrumentshave a particularly characteristic structure of partial clay/tone:

• Caper instruments possess a very rich partial clay/tone spectrum. Nearly all partial tones are contained.
• Clarinets stress the volume of the odd partial tones.
• With the bassoon the basic clay/tone is very much weaker than the first harmonious ones.
• Bells often stress thoseThirds very strongly and contain also non-harmonious overtones.
• Tuning forks produce nearly only the basic clay/tone, therefore their sound that is very similar a pure sinusoidal curve.

one can make

overtones clearly audible for audibility of overtones also within the instrumentalen range.Typical instruments for this are z. B. the Didgeridoo or sound bowls. On the piano one can make overtones audible, by depressing the keys of a chord from the overtone row gently, without the hammers affect the string, and then that Basic clay/tone within the bass range fastens briefly and strongly. The overtones produce now a resonance depressed on the undamped strings of the keys held, which one can hear clearly. This is used also by composers in its works (z. B. Béla Bartók: Mikrokosmos, volume IV). With stringed instruments tones in the pitch of overtones can be produced by Flageolett Spielweise (see Flageolettton). To pressure at it the string with the grab hand only easily affected instead of it on the Griffbrett.

Usuallyovertones are noticed not individually, but they result in the sound of a clay/tone. In addition, there are humans, who can notice overtones clearly under certain conditions also without any assistance. This applies particularly with very stable tones like it for examplelong continuing tones of organ pipes.

Untertonreihen

theoretical is downward supplemented the overtone row by the Untertonreihe symmetrical to it, which results from frequency slicing. In nature there is not such Untertonreihe. Became practicalit so far only with the Trautonium, with the Subharchord and with the Untertongesang converted.

building of organs

The overtone row is particularly important also in the building of organs. By different organ registers, which produce individual in each case overtones, tone qualities can be produced practically syntetisch.

see also

• to Fourieranalyse
• vowel triangle, vowel trapezoid
• Flageolettton
• Psychoakustik
• difference tone
• building of organs
• tendency (music)

Web on the left of

• the Partialschwingungen a drum in animated graphics
• harmonious ones, Partialtöne, partial tones and overtones
• the partial clay/tone density and the partial clay/tone row

literature

• John R. Pierce, sound. Music with the ears of physics, spectrum, ISBN 3-8274-0544-0