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Confirmation and Modification

toothed wheel, middle C, air stream, air blast, octaves

Sounds can be produced at a desired frequency by different methods. Sirens emit sound by means of an air blast interrupted by a toothed wheel with 44 teeth. The wheel rotates at 10 revolutions per second to produce 440 interruptions in the air stream every second. Similarly, hitting the A above middle C on a piano causes a string to vibrate at 440 Hz. The sound of the speaker and that of the piano string at the same frequency are different in quality, but correspond closely in pitch. The next higher A on the piano, the note one octave above, has a frequency of 880 Hz, exactly twice as high. Similarly, the notes one and two octaves below have frequencies of 220 and 110 Hz, respectively. Thus, by definition, an octave is the interval between any two notes whose frequencies are in a two-to-one ratio.

A fundamental law of harmony states that two notes an octave apart, when sounded together, produce a pleasant-sounding combination. Other combinations of notes can also be pleasing. Physically, an interval of a fifth consists of two notes, the frequencies of which bear the arithmetical ratio 3 to 2, and a major third, the ratio 5 to 4. Fundamentally, the law of harmony states that two or more notes sound pleasant when played together if their frequencies bear small, whole number ratios; if the frequencies do not bear such ratios, the intervals are dissonant. On a fixed-pitch instrument, such as the piano, it is not possible to arrange the notes so that all of these ratios hold exactly, and some compromise is necessary in tuning.

Article key phrases:

toothed wheel, middle C, air stream, air blast, octaves, octave, revolutions, Sirens, interval, Hz, piano, interruptions, compromise, frequencies, tuning, intervals, teeth, ratio, pitch, definition, speaker, Sounds, notes, means, quality

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