overtones. That’s the musical term for the waves like sin 3x and sin 5x in the earlier formula for the triangle wave. Overtones add color to a note by adding in multiples of the fundamental frequency. In addition to the sine wave at 440 cycles a second, a synthesized triangle wave includes a sine-wave overtone at three times that frequency (3 × 440 = 1320 cycles per second). That overtone is not as strong as the fundamental sin x mode. Its relative amplitude is only 1/9 as large as the fundamental, and the other odd-numbered modes are even weaker. In musical terms, these amplitudes determine
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