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Comment by ttt0 | Hacker News Reader

> Spectograms of each note will also make it strikingly clear that there is a dominant frequency invoked and overtones (harmonics)

It's not even about which frequency is dominant. I'm not an expert on psychoacoustics from the "sciency" side, but basically our brains can figure out the fundamental note based on the harmonics alone, even if we don't hear the fundamental frequency itself. De-emphasizing the fundamental frequency is sometimes used in synthesis just to create an interesting sound, but most notably this phenomenon is heavily relied on in modern heavy bass electronic music and down-tuned metal. A really common trick is to distort the bass track, so it can be still heard even if speakers can't reproduce that frequency, as distortion generates more harmonics. I don't mean distortion in literal sense, but in audio effect sense, so effects like saturation, overdrive, fuzz, clipping, etc.

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Being able to “hear” a fundamental when it’s not there in a spectrogram but the upper harmonics are is known as the missing fundamental and has been known and studied for over 100 years. It seems likely that the auditory system is not only doing a spectral breakdown of sounds (like an FFT) but also something like an autocorrelation of the signal. That autocorrelation will recover the fundamental as long as enough harmonics are present

> but basically our brains can figure out the fundamental note based on the harmonics alone, even if we don't hear the fundamental frequency itself

I guess this is valid for trained musicians. For me, I can't possibly identify the same note in different instruments, as all these sound very different to me.

The only thing I seem to be able to do is to identify a song based on the very first second or two. Because they are different sounds, not just notes.

Very interesting, since the artificial “ghost” note is at a lower frequency, would they essentially become an “undertone” ?

No, not really.

The fundamental is always the lowest frequency. All overtones are some (almost always integer, or _nearly_ integer) multiple of that.

Undertone is something different, but I never explored that concept and what could it be useful for, so I can't really explain it

Not an undertone, it's fundamental frequency. Harmonics/overtones follow a very specific pattern:

https://en.wikipedia.org/wiki/Harmonic_series_(music)

...so in most cases there isn't really any ambiguity on what the actual fundamental frequency is. The best way to demonstrate it is probably with a high-pass filter (aka. low-cut filter). High-pass filter allows only higher frequencies to pass through, or in other words it cuts out lower frequencies. On the example below you can hear that as the lower frequencies are getting removed from the signal, it's still the same note:

https://www.youtube.com/watch?v=50lRE2Bgag0

I wish the filter sweeps were slower, but that's the best example I could find

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