Sound spectrum

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In musical acoustics, sound spectrum refers to the frequency spectrum of sounds resulting from the number and strength of resonating overtones of a sound.

Frequency spectra of different types of musical instruments

Musical instruments can be divided into two categories:

  • Melody leading musical instruments:
The human ear can assign a pitch to these sounds . Periodic vibrations are often an essential part of these sounds . The perceived pitch corresponds to the fundamental frequency of this oscillation. The frequency spectrum of periodic oscillations is a line spectrum , whereby the lowest frequency corresponds to the fundamental frequency ( fundamental tone ) and the other frequencies are integer multiples of the fundamental frequency ( overtones ).
The human ear often cannot assign a pitch to these sounds. Many of these sounds are characterized by non-periodic or stochastic sound processes. The frequency spectrum of these sounds is a continuous spectrum or a line spectrum in which the frequencies involved are not in integer relationships to one another.

Musical instruments can also be divided into the following groups based on the type of vibration excitation:

  • One-dimensional transducers:
With these instruments, vibrations can only propagate along one path. These include, for example, stringed instruments (the string swings up and down, vibrations can only propagate along the string) or the singing voice and wind instruments (a column of air swings up and down the pipe, vibrations can only propagate along the pipe). In the case of one-dimensional oscillators, the path over which the oscillations can propagate is predetermined. At the end of the line (clamping points of the strings, pipe end) no more movement is possible, here the oscillation amplitude is zero. In the case of the fundamental oscillation, the entire string or column of air vibrates in phase. In addition to the fundamental vibration, only those vibrations are stable that are at rest at the clamping points of the string or at the end of the tube. However, this only applies to frequencies that are integral multiples of the fundamental oscillation. Other vibrations are not stable here, because they would require, for example, that a string can still move at a clamping point, this is severely restricted by the construction.
  • Multi-dimensional transducers:
With these instruments, vibrations can spread over a surface. These include, for example, drums , cymbals, but also bells . Vibrations can propagate in different directions on a membrane or a metal jacket. The excited frequencies depend on the material, shape and dimensions of the vibrating body. Here, too, there are restrictions on the possible vibrations (the vibration amplitude is zero at the restraint of the eardrum). But even with these restrictions, a multitude of different waveforms is possible. In this way you also get a line spectrum with a drum, but the frequency lines are no longer in the ratio of small whole numbers to one another. There are so many oscillation possibilities in pools that there is more of a continuous, noise-like spectrum. In the case of bells, one tries to limit the vibrations to relatively few frequencies by means of the shape. Even if the frequencies are not in the ratio of small whole numbers to each other, a bell oscillation comes close to a periodic oscillation.

Frequency spectra of real musical instruments

Sound spectrum of a baritone with the sung vowel u

With real musical instruments, the frequency spectrum cannot be described by the principles of vibration excitation alone (e.g. as periodic vibration).

More complicated frequency relationships between fundamental and overtones

In real musical instruments, the fundamental and overtones do not always vibrate exactly in relation to each other in small whole numbers. This phenomenon is called inharmonicity . One of the reasons for this is that the body of the musical instrument is also stimulated to vibrate. In wind instruments this results in z. B. slight changes in the tube length, with stringed instruments changes in the vibrating string length. However, the primary factor in overtone shifts in string instruments is the flexural strength of the string material used. This can lead to slightly different vibration conditions for overtones than for the fundamental frequency. A slight deviation of the overtone frequencies from multiples of the basic frequency can lead to the formation of beats , which contribute to the individual sound character of the instrument and z. B. associated with the piano with "warmth" and "liveliness" of the sound.

Non-periodic portions

In the case of real musical instruments, in addition to periodic vibrations (e.g. of the string or air column), non-periodic components or noise components are also added. Examples of this are striking noises in string instruments and blowing noises in wind instruments and organ pipes. So z. B. a broadband stimulation when striking a string. Vibrations outside the vibration modes of the string (fundamental tone and overtones) are not stable and are strongly damped, while the harmonic vibrations of the string (fundamental tone and overtone) are very stable. This means that after a few tenths of a second the impact noise has subsided and only the periodic oscillations remain.

The non-periodic components can, however, have an impact on the sound impression. (You would hardly recognize the sound of a panpipe without the air noise that occurs when you blow it.)

Spectral changes in the tone course

The sound and spectrum analyzes illustrate the vowel formants as frequency ranges with increased intensity.

In many musical instruments, the frequency spectrum of this tone changes when a tone is played. The individual harmonics of a periodic oscillation build up at different speeds at the beginning of a tone. In addition to the short-term impact or blowing noises, this leads to the frequency spectrum of a musical tone changing significantly at the beginning. In the stable state, the individual harmonics are attenuated to different degrees, so that there are continuous changes in the frequency spectrum even when the sound fades away.

The spectral changes that occur when a string or the air column vibrates are often formative for the sound of a musical instrument. If you fade out the first tenths of a second, many musical instruments can hardly be identified.

Frequency changes

In addition, the frequency of a tone can change while it is being played. There are periodic frequency changes (e.g. vibrato on flutes) or non-periodic frequency changes (e.g. on the piano the pitch is slightly higher when you hit it than when it fades out, see also stretching (music) )

See also

literature

  • Jürgen Meyer: Acoustics and musical performance practice . Edition Bochinsky, series: Textbook series Das Musikinstrument, Frankfurt, 1999, ISBN 3-923-63901-5

Web links

Individual evidence

  1. ↑ Miriam Noemí Valenzuela: Investigations and calculation methods for the sound quality of piano tones . Herbert Utz Verlag, 1998, ISBN 978-3-89675-343-4 ( google.de [accessed on May 24, 2016]).