Applications to the study of musical instruments

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A musical instrument is a system for producing one or more pleasant tones. Musical instruments are used by musicians to translate the symbolic notation of a musical composition into the corresponding sounds. A musical instrument consists of the combination of one or more resonant systems capable of producing one or more tones and mids to excite these systems that are under the control of the musician. We can consider the different types of musical instruments: string, wind, percussion and electric.

Musical instruments can be classified according to the categories that appear in the chart, according to the way the sound is produced. Each of these categories, in turn, can be subdivided into other more specific categories according to some characteristic. For example, stringed instruments can be subdivided into three subgroups according to the mode of string excitation: plucked stringed instruments rubbed stringed instruments and percussion stringed instruments.

General characteristics of musical instruments

The two characteristics of the music that is mainly a function of the musical instrument are tonal and dynamic. The tonal aspect depends on the height and timbre of the instrument. The dynamic aspect of the absolute intensity level produced by the instrument and the dynamic range or intensity range.

Musical instruments and voice produce fundamental frequencies and overtones of the fundamental frequencies. The structure of overtones is one of the characteristics that distinguish various musical instruments and voices. The height is generally determined by the fundamental frequency and the fundamental frequency range of the instrument. The timbre is the instantaneous acoustic spectrum of the instrument. The timbre envelops the frequencies and amplitudes of both the fundamental and the overtones.

The dynamic aspect of the music depends on the intensity. The intensity range of a musical instrument surrounds the absolute value of the highest and lowest intensity ranges and the resulting dynamic range.

The intensity and timbre of the sound produced by a musical instrument are also governed by the directionality pattern. This pattern refers to the sound output as a function of an angle to an instrument’s reference axis. In general, the directionality pattern is complex, in fact, it is a function of both the angle and the frequency.

The characteristics of attack, extinction, and stationary state and the duration of a sound produced by a musical instrument influence the tonal and dynamic characteristics of the sound.

String musical instruments

Vibrating a string is one of the oldest ways to produce a musical tone. The area projected by a string is quite small and therefore a vibrating string does not produce an appreciable movement of the air around it. For this reason, it is customary to attach to the string a resonance box (wide resonance), in order to increase the sound output. The box receives the vibrations of the strings through the support bridges and then transmits them to the amplified air.

Longitudinal and transverse vibrations can occur on the strings. Longitudinal vibrations are achieved by rubbing a tight string with a chamois in a longitudinal direction; the resulting note is intense but with an unpleasant timbre. The squeaks sometimes produced by string instruments in the hands of inexperienced players come from this type of vibration. However, when speaking of string instruments, it is usual to refer to transversal vibrations, in which each particle of the string vibrates in a plane perpendicular to the line of the string.

Wind musical instruments

Wind instruments are those that contain a gaseous volume capable of producing sound when conveniently excited. The sound body is the gas volume and not the container that contains it; the container has the important function of defining the shape of the gas volume but outside of this it influences relatively little on the sonorous phenomena.

The vibration of the columns of air contained in the sound tubes is due to the formation of a stationary wave. Therefore, the columns have nodes (null vibration) and bellies (maximum amplitude of vibration), equidistant from the previous ones. The distance between two nodes or two consecutive bellies is always half a wavelength. At the closed ends, nodes are always produced and at the open ends, bellies are usually produced. The excitation point cannot be a node, but it does not need to be a belly, being able to be in an intermediate point. It is not necessary that the openings of a tube coincide with the ends, these may be closed and there may be one or more openings in other parts of the tube.

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