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Wave, Sound, and Music


Music

Noise Noise sound contains so many harmonics randomly distributed throughout the spectrum that it doesn't have a perceivable pitch. Noise is a sound that is not periodic. That is, it contains random elements that cannot be described as a regular series of sine wave components. The name white noise is given to this sound: noise because of the lack of order in it, and white because it contains frequencies from all over the audible spectrum. Nevertheless, noise is extremely important in music. Most percussion instruments contain a great deal of noise. Radio static, rainfall, wind, thunder, jet exhaust, etc. are some examples of non-musical noise. Figure 12 shows the random amplitude of noise over an interval of time.

Figure 12 Noise

Speech Speech has a definite pattern such as the pronunciation of "will you ..." etc. (see Figure 13) -- but little regularity. Both speech and white noise contain transient sounds -- that is, air motion that doesn't repeat. The difference is that speech uses these non-repeating sounds in recognizable patterns, whereas white noise has no distinct patterns at all. In essence, speech is order without regularity. Alternatively, speech can be considered as a mixture of transient sounds and quasi-periodic sounds corresponding to consonants and vowels, respectively (a vowel is a sound in spoken language that is characterized by an open configuration of the vocal tract, in contrast to consonants, which are characterized by a constriction or closure at one or more points along the vocal tract). Singing emphasizes the vowels, which being quasi-periodic (see Figure 13), are tailor-made for musical creations. Speech tends to emphasize consonants much more than singing. Singers, especially operatic singers, are often very hard to understand because that type of singing requires a very heavy and unnatural concentration on the vowels.

Figure 13 Speech, Vowel, and Consonant [view large image]


Music When periodic air disturbances happen less than 16 times a second, we hear them as individual clicks, pops, or other events. An interesting thing happens, though, when those repetitions come faster than 16 times a second. There is a breakdown in the process because our nervous system cannot deal with hearing more than 16 individual events in a second, and begins to hear all of those disturbances as a single event -- a musical note. The faster the disturbance, the higher pitch we hear. Over the last few thousand years, we have been building some highly sophisticated devices that disturb the air at precisely controlled rates. We normally call these devices "musical instruments". Music has been defined as "ordered non-speech sound". There is a very close relationship between speech and the melodic and rhythmic elements of singing, which is just a slight modification of speech. In short, the amount of order and pattern we perceive in air disturbances determines whether we hear noise, speech, music, or anything in between. Sound patterns over a time interval for some musical instruments are depicted in Figure 14a.

Figure 14a Musical Patterns [view large image]

Melody is an universal human phenomenon, traceable to pre-historic times. The origins of melodic rendering have been sought in language, in birdsong and other animal sounds. The early development of melody may have proceeded from one-step voice inflections through combinations of such small intervals as minor 3rds and major 2nds to pentatonic patterns, (i.e. based on a five-note scale) such as found in many parts of the world. Melody can be defined as a series of musical notes arranged in succession and usually have a distinctive rhythmic pattern. Rhythm is an important element within melody because each note of the melody has a duration and larger-scale rhythmic articulation gives shape and vitality to a melody.

While the tones in melody are played one by one, music with richer feeling can be constructed by playing two tones together called "harmonic" as shown in Figure 14b. Western music often plays three tones together (called a triad) to create chords (three or more tones played simultaneously) for adding even more interesting variations. However, not all the tones added together produce the
Tones Dissonance same pleasing sound. Figure 14c shows that the perception of a chord as dissonant or consonant depends on the intervals (in semitones) between tones. In empirical tests, the dissonance reported by listeners is greatest when two musical tones are separated by one or two semitones etc. as shown by the red color regions in Figure 14c. It is the composer's job to resolve the dissonance and make the

Figure 14b Melodic and Harmonic Tones
[view large image]

Figure 14c Disson- ance [large image]

music satisfying, although some may deliberately create dissonant music against the tradition.

Figure 14d shows some more specific examples of harmony and discord (harmonic) tones by frequency ratio. A simple numerical
Harmonic Tones Harmony Beat ratio sound harmonious, while the more complex ones sound awful. Another way to check out the pleasing sound is through the beat frequency or beat wavelength. All the harmonic tones produce an integer (or with an additional 1/2) beat wavelength with respect to that of the fundamental as shown in Figure 14d. The same can also be verified with those mentioned in Figure 14b.

Figure 14d Harmony and Discord
[view large image]


Figure 14e Harmony Beat

Mathematically, the beat wave is the superimposition of two different waves of different frequency y1 = A sin(2f1t) (blue curve) and y2 = A sin(2f2t) (dark curve) as shown in
Discord Beat Figure 14e for harmony beat (assuming same amplitude A for simplification):
y = y1 + y2 = 2A {cos[2(f2-f1)/2]t} {sin[2(f1+f2)/2]t},
where f1 and f2 are the frequencies of the pair of tones. The condition for producing harmony beat is
f=(f2-f1)=f1/n or in term of wavelength = n1, where n is a positive integer. It seems that the human ears do not appreciate beat wavelength generated randomly violating this rule (Figure 14f).

Figure 14f Discord Beat


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