musical acoustics

musical acoustics [′myü·zə·kəl ə′kü·stiks]

(acoustics)

That part of acoustics which is relevant to the composition, performance, and appreciation of music, including the physical characteristics of sounds that may be heard as music, laws governing the action, design, and construction of musical instruments, and the effects of musical sounds upon listeners.

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Musical acoustics

The branch of acoustics that deals with the generation of sound by musical instruments, the transmission of sound to the listener, and the perception of musical sound. A main research activity in musical acoustics is the study of the way in which musical instruments vibrate and produce sound. The most common way of classifying musical instruments is according to the nature of the primary vibrator, into string instruments, wind instruments, and percussion instruments. The vibrations of a plucked string, a struck membrane, or a blown pipe can be described in terms of normal modes of vibration. Determining the normal modes of a complex vibrator is often termed modal analysis. Much of the progress in understanding how musical instruments generate sound is due to new methods of modal analysis, such as holographic interferometry and experimental modal testing. See Interferometry, Mode of vibration, Vibration

In the case of most percussion, plucked string, and struck string instruments, the player delivers energy to the primary vibrator (string, membrane, bar, or plate) and thereafter has little control over the way it vibrates. In the case of wind and bowed string instruments, however, the continuing flow of energy is controlled by feedback from the vibrating system. In brass and reed woodwinds, pressure feedback opens or closes the input valve. In flutes or flue organ pipes, however, the input valve is flow-controlled. In bowed string instruments, pulses on the string control the stick-slip action of the bow on the string.

Four attributes are frequently used to describe musical sound: loudness, pitch, timbre, and duration. Each of the subjective qualities depends on one or more physical parameters that can be measured. Loudness, for example, depends mainly on sound pressure but also on the spectrum of the partials and the physical duration. Pitch depends mainly on frequency, but also shows lesser dependence on sound pressure and envelope. Timbre includes all the attributes by which sounds with the same pitch and loudness are distinguished. Relating the subjective qualities of sound to the physical parameters is a central problem in psychoacoustics, and musical acousticians are concerned with this same problem as it applies to musical sound.

Sound pressure level is measured with a sound level meter and is generally expressed on a logarithmic scale of decibels (dB) using an appropriate reference level and weighting network. From measurements of the sound pressure level at different frequencies, it is possible to calculate a subjective loudness, expressed in sones, which describes the sensation of loudness heard by an average listener. Musicians prefer to use dynamic markings ranging from ppp (very soft) to fff (very loud). See Decibel, Sound, Sound pressure

Pitch is defined as that attribute of auditory sensation in terms of which sounds may be ordered on a scale extending from low to high. Pitch is generally related to a musical scale where the octave, rather than the critical bandwidth, is the “natural” pitch interval.

Timbre is defined as that attribute of auditory sensation in terms of which a listener can judge two sounds similarly presented and having the same loudness and pitch as dissimilar. Timbre depends primarily on the spectrum of the sound, but it also depends upon the waveform, the sound pressure, the frequency location of the spectrum, and the temporal characteristics of the sound. It has been found impossible to construct a single subjective scale of timbre (such as the sone scale of loudness); multidimensional scales have been constructed. The term “tone color” is often used to refer to that part of timbre that is attributable to the steady-state part of the tone, but the time envelope (and especially the attack) has been found to be very important in determining timbre as well.

Another subject relating to the perception of music is combination tones. When two tones that are close together in frequency are sounded at the same time, beats generally are heard, at a rate that is equal to their frequency difference. When the frequency difference Δf exceeds 15 Hz or so, the beat sensation disappears, and a roughness appears. As Δf increases still further, a point is reached at which the “fused” tone at the average frequency gives way to two tones, still with roughness. The respective resonance regions on the basilar membrane are now separated sufficiently to give two distinct pitches, but the excitations overlap to give a sense of roughness. When the separation Δf exceeds the width of the critical band, the roughness disappears, and the two tones begin to blend.

Pythagoras of ancient Greece is considered to have discovered that the tones produced by a string vibrating in two parts with simple ratios such as 2:1, 3:2, or 4:3 sound harmonious. These ratios define the so-called perfect intervals of music, which are considered to have the greatest consonance. Other consonant intervals in music are the major sixth (f₂/f₁ = 5/3), the major third (f₂/f₁ = 5/4), the major sixth (f₂/f₁ = 8/5), and the minor third (f₂/f₁ = 6/5). Why are some intervals more consonant than others? H. Helmholtz concluded that dissonance (the opposite of consonance) is greatest when partials of the two tones produce 30 to 40 beats per second (which are not heard as beats but produce roughness). The more the partials of one tone coincide in frequency with the partials of the other, the less chance of roughness. This explains why simple frequency ratios define the most consonant intervals. More recent research has concluded that consonance is related to the critical band. If the frequency difference between two pure tones is greater than a critical band, they sound consonant; if it is less than a critical band, they sound dissonant. The maximum dissonance occurs when Δf is approximately 1/4 of a critical band, which agrees reasonably well with Helmholtz's criterion for tones around 500 Hz.