Acoustics

(Grk., audible). The study of how sound is produced. A note can be produced in many different ways: common among musical instruments are a vibrating string (as on a guitar or violin), the air inside a pipe (the pipe of an organ), a stretched membrane or head (a drum), or a vibrating bar or piece of metal (a bell or vibraphone).

For stringed instruments, the actual note produced depends on the string's overall length and how tightly it is stretched; if the thickness and tautness of a string remain the same, the frequency of vibrations decreases with its length. If a string is set in motion with a greater force so that the amplitude of its vibrations is increased, then the resulting sound becomes louder without changing the pitch.

Panpipes consist of a group of reeds arranged in a row, and the player blows into the end of a reed to play a note. Using your knowledge of acoustics, which pipe do you think plays a lower note: the short, thin one on the right end or the long, fat one on the left end?

The longer, thicker pipe would sound a lower note because of the shape of the air column.

The length and width of an air column determines the note it produces. For example, a long, fat organ pipe produces a lower pitch or note than a short, thin one.

In drums, the smaller and tighter the membrane, the higher the pitch. That's why kettledrums have a deeper tone than tambourines, for example.

In bells, the larger and thicker the bell, the lower the note.

Each string or air column naturally divides itself into component parts to produce overtones, or PARTIALS. Theoretically, each complete vibration produces also two vibrations of 1/2 that of the sounding body, three vibrations of 1/2 that of the sounding body, and so on; these partials have the potential to be audible.

The range of audible sounds for the human ear is between 16 and 25,000 cycles per second (cps), a cycle being one complete vibration of an oscillating string. Dogs hear sounds far above the human range; high-pitched whistles, inaudible to humans, are used by handlers to summon them.

For more than 2,000 years theorists have wrestled with this problem: 12 perfect fifths on the keyboard of the piano (or any instrument built on the tempered scale) is supposed to be identical to seven octaves. But this is an impossible equation, because two to the seventh power does not equal 3:2 to the 12th! Therefore, the acoustic perfection of the perfect fifth was sacrificed in order to fit twelve 3:2s into the compass of seven octaves; a similar adjustment was made in other intervals.

When the piano tuner tunes a "perfect fifth," it is actually slightly narrower (flatter) than a "pure" 3:2. Violinists and players of other string instruments, however, tune their strings in nontempered perfect fifths. If a violinist plays a fifth on the open strings and the piano accompanist plays the same fifth, a disagreeable discrepancy results.

It was not until the late CLASSIC period that acousticians finally abandoned all hope of reconciling the pure harmonic series with practical instruments, and EQUAL TEMPERAMENT became generally accepted.

Generally, the simpler the fraction produced by the divided string, the more musically pleasing is the interval created by the overtone. When a string is divided into two (V2, or 2:1), the note that is heard is one octave higher than the original tone. Other commo n intervals are the perfect fifth (2/3, or 3:2), the perfect fourth (3/4, or 4:3), and the major 3 third (4/5, or 5:4). This theoretically infinite group of intervals comprises the HARMONIC SERIES of intervals.

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