Text: MUSICAL SOUND. An aural sensation caused by the rapid periodic motion of a sonorous body. In contrast, noise is an aural sensation due to nonperiodic motions. These observations, originally made by Helmholtz, may be modified slightly so that the frequencies of vibration of the body fall within the limits of hearing: 20 to 20,000 Hz. This definition is not clear-cut; there are some noises in the note of a harp (the twang) as well as a recognizable note in the squeak of a shoe. In other cases, it is even more difficult to make a distinction between music and noise. In some modem "electronic music," hisses and thumps are considered a part of the music. White noise is a complex sound whose frequency components are so closely spaced and so numerous that the sound ceases to have pitch. The loudness of these components is approximately the same over the whole audible range, and the noise has a hissing sound. Pink noise has its lower frequency components relatively louder than the high frequency components. The attributes of musical sound and their subjective correlates are described briefly. The number of cycles per second, frequency, is a physical entity and may be measured objectively. Pitch, however, is a psychological phenomenon and needs a human subject to perceive it. In general, as the frequency of a sonorous body is raised, the pitch is higher. However, pitch and frequency do not bear a simple linear relationship. To show the relationship, a pitch scale can be constructed so that one note can be judged to be two times the pitch of another and so on. The unit of pitch is called the mel, and a pitch of 1,000 mels is arbitrarily assigned to a frequency of 1,000 Hz. In general, it is observed that the pitch is slightly less than the frequency at frequencies higher than 1,000 cycles, and slightly more than the frequency at frequencies less than 1,000 Hz. Pitch also depends on loudness. For a 200 cycle tone if the loudness is increased the pitch decreases, and the same happens for frequencies up to 1,000 Hz. Between 1,000 and 3,000 Hz pitch is relatively independent of loudness, while above 4,000 Hz, increasing the loudness raises the pitch. A rapid variation in pitch when the variation occurs at the rate of from two to five times per second is called vibrato. The pitch variation in mels may be large or small but the rate at which the pitch is varied is rarely greater than five times per second. Violinists produce vibrato by sliding their fingers back and forth a minute distance on a stopped string. A variation in loudness occurring at the rate of two to five times a second is called tremolo. Singers often produce a combination of tremolo and vibrato to give added color to their renditions. Like frequency, intensity is a physical entity defined as the amount of sound energy passing through unit area per second in a direction perpendicular to the area. It is proportional to the square of the sound pressure, the latter being the rms pressure over and above the constant mean atmospheric pressure. Since sound pressure is proportional to the amplitude of a logitudinal sound wave and to the frequency of the wave, intensity is proportional to the square of the amplitude and the square of the frequency. Sound intensity is measured in watts per second per square centimeter and, since the ear is so sensitive to sound, a more usual unit is microwatt per second per square centimeter. By way of example, a soft speaking voice produces an intensity of .1 micromicrowatt/cm2 sec, while 1,500 bass voices singing fortissimo at a distance 1 cm away produce 40 watts/cm2 sec. Because of such large ranges of intensities, the decibel scale of intensity is normally used to designate intensity levels. An arbitrary level of 10-16 watts/cm2 sec is taken as a standard for comparison at 1,000 Hz. This is very close to the threshold of audibility. At this frequency, other sound levels are compared by forming the logarithm of the ratio of the desired sound to this arbitrary one. Thus log I/10-16 is the number of bels a sound of intensity I has, compared to this level. Since this unit is inconveniently large, it has been subdivided into the decibel one-tenth its size; 10 log I/10-16 equals the number of decibels (dB) the sound has. A few intensity decibel levels are listed: dB Quiet whisper 10 Ordinary conversation 60 Noisy factory 90 Thunder (loud) 110 Pain threshold 120 While intensity levels can be measured physically, loudness levels are subjective and need human subjects for their evaluation. The unit of loudness is the phon, and an arbitrary level of 0 phons is the loudness of a 1,000-Hz note which has an intensity level of 0 dBB. Sounds of equal loudness, however, do not have the same intensity levels for different frequencies. From a series of experiments involving human subjects, Fletcher and Munson in 1933 constructed a set of equal loudness contours for different frequencies of pure tones. These show that for quiet sounds (a level of 5 phons) the intensity level at 1,000 cycles is about 5 dB lower than an equally loud sound at 2,000 cycles, for 30 cycles about 70 dB lower, and at 10,000 cycles about 20 dB lower. In general, as the intensity level increases, loudness levels tend to be more alike at all frequencies. This means that as a sound gets less intense at all frequencies, the ear tends to hear the higher and lower portions of sound less loudly than the middle portions. Some high fidelity systems incorporate circuitry that automatically boost the high and low frequencies as the intensity level of the, sound is decreased. This control is usually designated a loudness control. That entity which enables a person to recognize the difference between equally loud tones of the same pitch coming from different musical instruments is called timbre, quality, or tone color. A simple fundamental law in acoustics states that the ear recognizes only those sounds due to simple harmonic motions as pure tones. A tuning fork of frequency f, when struck, causes the air to vibrate in a manner which is very nearly simple harmonic. The sound that is heard does, in fact, give the impression that it is simple and produces a pure tone of a single pitch. If one now strikes simultaneously a series of tuning forks having frequencies f (the fundamental), 2 f, 3 f, 4 f, 5 f, etc. (overtones), the pitch heard is the same as that of the single fork of frequency f except that the sound has a different quality. The quality of the sound of the series can be changed by altering the loudness of the individual forks from zero loudness to any given loudness. Another way to alter the tone quality is to vary the time it takes for a composite sound to grow and to decay. A slow growth of an envelope even though it contains the same frequencies makes for a different tone quality than one which has a rapid growth. The difference in quality between a b-flat saxophone and an oboe is almost entirely due to the difference in growth or decay time. A fundamentat theorem discovered by the mathematician Fourier states that any complicated periodic vibration may be analyzed into a set of components which has simple harmonic vibrations of single frequencies. If this method of analysis is applied to the composite tones of musical instruments, it is seen that these tones consist of a fundamental plus a series of overtones, the intensity of the overtones being different for instruments of differing timbre. Rise and decay will also differ. The reverse of analysis is the synthesis of a musical sound. Helmholtz was able to synthesize sound by combining sets of oscillating tuning forks of various loudness to produce a single composite steady tone of a definite timbre. Modern synthesizers are more sophisticated. Electrical oscillators of the simple harmonic variety are combined electrically and then these electrical composite envelops are electronically modified to produce differing rise and decay times. A transducer changes the electrical composite envelope into an acoustical one so that a sound of any desired timbre rise and decay time can be produced. An alternate way to produce similar effects is to use an oscillation known as the square wave. When this is analyzed by the method of Fourier, it is shown to consist of a fundamental plus the odd harmonics or overtones. Another kind of oscillator, a sawtooth wave, when analyzed, is shown to consist of the fundamental and all harmonics--even and odd. A square wave or a sawtooth wave produced by an appropriate electrical oscillator can be passed through an electrical filter which can attenuate any range of frequencies of the original wave. This altered wave can later be transformed into the corresponding sound wave. In this way sounds having a desired rise and decay time, plus the required fundamental and overtone structure, can be made as desired.

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