Brass player here with a few months' worth of guitar ability. You're correct about the harmonics being at play, but the mechanism's a bit different.

To elaborate/review, your lips are the guitar strings in this equation, and naturally will behave much like a string on a chamber instrument or fretless guitar (as is obvious from "free buzzing" and mouthpiece buzzing). The length of the tubing then dictates which frequencies will resonate with your lips, meaning your lips will want to "settle" into something in harmonic resonance with that length of tubing.

The key difference here is that your lips themselves are basically "fretted" to the harmonics (though with practice you can bend that quite a bit), since the corners of your lips are moving (slightly; it's a short string!) in and out to go higher or lower (respectively), and since they'll want to vibrate at a harmonic (the vibrating metal and air impart a force on your lips for the same reason your vibrating lips impart a force on the metal and air, so it takes much more effort to buzz against that harmonic than it does to just ride it and keep that feedback loop going). Further, the mouthpiece itself is basically a capo in this context, so your lips are always "fretted" to the mouthpiece's constraints (this is a big part of the reason - if not the entirety of it - why trumpets have tiny mouthpieces and tubas have giant mouthpieces).

I suspect that if you were to replace the body of an acoustic guitar with a really long pipe, you'd see/hear similar dynamics at play: a string tuned or fretted to one of that pipe's harmonics will keep vibrating for a good while, and a string tuned/fretted to something else would stop vibrating sooner as the destructive interference sucks energy out of it. And the former would likely be much more audible than the latter.

I know HN frowns upon such meta comments, but thank you for this comment! Wonderfully clear exposition - I followed along completely with your comment and now have some level of understanding of harmonics and brass instruments where I had none before. This was a good day, I learned something today that I have long been curious about!

Your disclaimer "I know HN frowns upon such meta comments, but " was the only thing wrong w your comment. (Which I upvoted). As a guitar player and former trumpet player, I dug this tangent too.

Just to reiterate the other response to your comment, meta comments are often welcomed, especially when they are expressing thanks or gratitude.

Content-less comments that derail the conversation, comments that are needlessly inflammatory - these are the kinds of meta comments that are not wanted.

I don't play trumpet, but I think that is basically what is going on. You can do pinch harmonics on guitar, which silence certain harmonics or even the fundamental while retaining others. It sounds like changing mouth shape does a similar thing on trumpet.

edit: here's a fantastic video on pinch harmonics: https://www.youtube.com/watch?v=eTWxCdoyol0

Yes, that's exactly right. "Covering but not fretting" a string on the guitar will dampen the lowest harmonic because the full length of the string is unavailable for vibration [1]; frequency is one over wavelength (e.g. twice the frequency is one half the wavelength). You can pluck either side of the string when covering it to produce the same harmonic (neck side or body side).

On a trumpet, the embouchure will affect the frequency of the vibration of the air compressed in the tube, and simply drop out lower harmonics, as can be confirmed via spectrogram.

The same thing happens on a guitar, leetcrew I encourage you to try the spectrogram linked at that site with your guitar to note the effect [0].

[0] https://musiclab.chromeexperiments.com/Spectrogram [1] I am under the impression that the fundamental tone of the string requires the whole string-length to resonate, and if it is clamped, pinched, or otherwise muted all you will hear are resonant harmonics that can exist on smaller string segment lengths.

We need to compare this description with yellowapple above.

One of these is true but I’m not clear on whether this means actually both of them are true?

Yes, to first oder, a trumpet is a long tube with a standing wave, which works conceptually like a string (but with different boundary conditions). It's probably the player's imposed frequency hitting multiples of the lowest resonance frequency that leads to different tones.

Great video. In case it's not obvious, the different notes are purely a function of pick/thumb placement. The guitarist is not changing frets, but he seems unable to resist throwing in some vibrato :)

Yeah, on a trumpet you can play multiple notes with the same fingering. The set of notes you can play with a fixed fingering comes from the harmonic series. A bugle is essentially a trumpet with a fixed length of tubing, and famous bugle calls like Reveille and Taps all come from that harmonic series (and can also be played on a trumpet without varying the valves).

My understanding of how this works is that the length of the trumpet's tubing (at any given fingering) permits the air to resonate in standing waves only at one of the frequencies in a harmonic series. The player's lips can vibrate at any frequency on their own, but the big column of air inside the trumpet will essentially lock the column of air into vibrating at the closest frequency in that set.