Harmonics

Japanese: 高調波 - こうちょうは（英語表記）harmonics

When any periodic waveform with a frequency (frequency) of f is expanded into a Fourier series, it can be decomposed into sine wave components of integer multiples of the fundamental frequency f . In this case, sine waves other than the fundamental frequency are collectively called harmonics, and the wave of the fundamental frequency is called the fundamental wave. The components with frequencies of 2f and 3f are called the second harmonic and third harmonic, respectively, and the component with nf ( n is an integer of 2 or more) is called the nth harmonic. When a sine wave signal is applied to an electrical system with nonlinear characteristics, harmonic components of that frequency, called distorted waves, are generated. Sounds caused by resonance phenomena such as musical instruments are also created by the synthesis of waves with frequencies that are integer multiples of each other. In this case, the fundamental wave, which is the lowest frequency, is called the fundamental tone, and the harmonic components are called overtones or harmonics. The interval up to twice the frequency is called an octave.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

周波数 (振動数 ) が f である任意の周期波形をフーリエ級数に展開すると，基本周波数 f の整数倍の正弦波成分に分解できるが，このとき基本周波数以外の正弦波を総称して高調波と呼び，基本周波数の波を基本波という。周波数が2 f ，3 f の成分はそれぞれ第2高調波，第3高調波，nf ( n は2以上の整数) の成分は第 n 高調波という。電気信号では非線形特性をもつシステムに正弦波信号を加えるとひずみ波と呼ばれるその周波数の高調波成分が発生する。楽器などの共振現象による音も，互いに整数倍の関係にある周波数の波が合成されてできている。このとき最も低い周波数である基本波を基本音，高調波成分を倍音，あるいはハーモニックスと呼ぶ。なお，2倍の周波数までの間隔をオクターブという。

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