For example, if you have a wave that happens once a second, a wave that happens twice a second is harmonious, or a "Harmonic". That is because they both can have a synchronous start and end at the same time- and the wave that happens twice a second has another start and stop in between.
Natural waves in nature are Sinewaves- gentle tides and ebbs, like riding on a swing with a gentle change in direction at the top of the back, fast at the bottom, and gentle change at the top of the front.
Squarewaves are sharp changes in direction with no time in between.
Harmonics are a multiple of the fundamental frequency. 20KHz is the second harmonic of 10KHz (10 x 2), 30Khz is the 3'rd harmonic of 10KHz (10 x 3), and so forth. Even numbered harmonics are call Even-Order Harmonics (the 2'nd, 4'th, 6'th, etc.), and odd numbered harmonics are called the Odd-Order Harmonics (3'd, 5'th, 7'th, etc.)
Mathematically, a Squarewave is the composite of an infinite number of progressively shorter odd-order sinewaves. If you add together the Fundamental (1'st), 3'rd, 5'th, 7'th, 9'th, and more to infinity of a pure Sinewave, you will get a pure Squarewave.
Comparing a Sinewave to a Squarewave of the same peak to peak amplitude, a Squarewave contains more power than the Sinewave.
Here is the composite of a 10KHz Sinewave and a 30KHz Sinewave:
And the composite of 10KHz, 30KHz, 50KHz, and 70KHz Sinewaves:
You can see the shape getting closer to square, and if all odd-order harmonic waveforms are added in, the waveform would be a Squarewave.
Looking at the power of Sinewaves vs Squarewaves, the Spectrum Analyser shows the power of a pure 10KHz Sinewave:
Next shows the power of the 30KHz Sinewave added to the 10KHz Sinewave:
And, the 30KHz, 50KHz, and 70KHz Sinewaves added to the 10KHz Sinewave:
Adding an infinite number of odd-order progressively shorter Sinewaves will change the shape of the waveform to a perfect Squarewave, and the Spectrum Analyser would show an infinite number of power points at odd-order frequencies.
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