What's the secret of high frequency harmonics?
Posted: Tue May 09, 2017 9:19 pm
The question is very interesting. Let's set the scene first. We all know that sounds have more or less harmonics and that different waveforms result from the mixture of harmonics and levels.
The third harmonic will have 3x the frequency of the fundamental (which is the first harmonic). Now let's assume we want to generate a sawtooth. The 3rd harmonic will also have 1/3rd the level of the fundamental. I can continue bulding my waveform with these simple rules.
But, if I want a perfect sawtooth while playing at 220 Hz, I would need to add all harmonics of the audible range. I did the math for you.
That's a total of 100 harmonics if we assume 22.05 kHz to mark the upper end of the audible range (220, 440, 660, 880, etc.).
Ok. But now I play at 1600 Hz.
This time it's only 13 harmonics (1600, 3200, 4800, 6400, etc.).
Yet it's still a sawtooth and clearly recognizable as such. Why is that? We lose information, but the waveform stays intact. I don't understand it.
The third harmonic will have 3x the frequency of the fundamental (which is the first harmonic). Now let's assume we want to generate a sawtooth. The 3rd harmonic will also have 1/3rd the level of the fundamental. I can continue bulding my waveform with these simple rules.
But, if I want a perfect sawtooth while playing at 220 Hz, I would need to add all harmonics of the audible range. I did the math for you.
That's a total of 100 harmonics if we assume 22.05 kHz to mark the upper end of the audible range (220, 440, 660, 880, etc.).
Ok. But now I play at 1600 Hz.
This time it's only 13 harmonics (1600, 3200, 4800, 6400, etc.).
Yet it's still a sawtooth and clearly recognizable as such. Why is that? We lose information, but the waveform stays intact. I don't understand it.