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So I made this frequency spectrum analyzer and tested various instruments playing a certain note. There doesn't seem to be any problem with the 'equalizer'. However, I found the spectrum for trumpet rather unusual.

Trumpet Spectrogram

So the fundamental frequency isn't the one with the highest intensity. Higher harmonics (1.5kHz to 2.5kHz range) harmonics have a much higher contribution to the sound.
Keeping in mind all the frequency ranges are of the same size, I couldn't think of any possible explanation other than this being a characteristic thing for trumpet, which makes me wonder if people perceive the note to be that of the first/second(or whatever in 1.5-2.5kHz range) harmonic or the fundamental frequency?
Also attaching spectrum for saxophone for the same note:

Saxophone spectrum

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  • do you get the same results (i.e. a non-fundamental freq not being loudest) regardless of what note you play? is it the same for the entire range of the instrument?
    – b3ko
    Jun 4, 2018 at 15:57
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    Can you tell us which note you were playing to produce the first graph?
    – jdjazz
    Jun 4, 2018 at 18:38
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    It would definitely be more insightful if you looked at a proper spectrum instead of those broad-filtered bars. This can be done with any half-decent software nowadays (free or otherwise – Audacity, Reaper, Python script...).
    – leftaroundabout
    Jun 5, 2018 at 9:24

2 Answers 2

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Excellent find! Trumpet, as well as the acoustically similar trombone, are very peculiar instruments when it comes to physics. They are cylindrical tubes closed at one end, so they should have a fundamental wavelength that's 4x the length of the tube, and then only generate odd overtones. Look at clarinet for an instrument that actually obeys this1.

But trumpet clearly plays a full overtone series, except for a fundamental that's apparently missing. And if you measure the actual tubing length to see what the fundamental should be, something screwy is clearly going on.

The answer is that the tube of metal does want to produce only odd overtones, but the design of the mouthpiece and bell wrangle the overtones into a full overtone series. See here for details.

This means that the trumpet actually does not produce its fundamental at all! You hear only the 2nd and higher harmonics, and your brain fills in the missing fundamental. It's not actually there.

The trumpet uses this psychoacoustic effect innately, but it has been intentionally used in a few other areas as well. Organists will play a set of notes that imitates an overtone series, which causes the unplayed fundamental to seem to sound. And a few modern saxophonists have learned to use multiphonics (singing through the instrument while playing) to do the same, called Tartini tones.

1The clarinet has a body length that's approximately the same as a flute or soprano sax, but plays significantly lower. Then, when you add the register key, the instrument jumps up a twelfth instead of an octave (to its third harmonic).

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    WTF : Wow, Trumpet is Fun!
    – Eric Duminil
    Jun 5, 2018 at 6:48
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    Nice introduction of the physics, but it's not really true that the trumpet doesn't produce the fundamental at all, is it? The mouthpiece is quite nonlinear and generates the “impossible” frequency through intemodulation between the overtones. For sure, the loud blaring character of trumpet&trumbone is largely down to the effect you describe though. But I find the reference you link a bit obscure, it would be nice to see some research that actually shows plots of the acoustic impedance along a trumpet's length and computed eigenmodes.
    – leftaroundabout
    Jun 5, 2018 at 8:46
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    To add to this, the same trick is often used in pop music for the bassline. Many playback sources (e.g. mobile phone speakers or cheap headphones) cannot handle those low fundamental frequencies, so at the mixing/mastering stage it is common to use techniques (distortion or pitch shifting, for example) which add higher harmonics to make the bassline seem to exist. Conversely, some instruments such as bass guitar produce more harmonics than fundamental, and it is common to add that fundamental using a sine-wave synth for better playback on systems that can handle those lower frequencies.
    – Graham
    Jun 5, 2018 at 12:57
  • You confuse the fundamental of the note being played with the fundamental of the instrument. It is true that a B-flat trumpet can hardly produce the fundamental (Bb2), but if you play Bb3, then the fundamental of that note will certainly exist. I also doubt your explanation in general. While the fundamental is hard to produce, it is certainly possible, and it becomes flat, not sharp. On flugelhorn, it is a perfectly good note. Trombonists might even be required to play it. Conversely, on natural trumpet, even the second harmonic is hard to produce.
    – sbares
    Jun 9, 2018 at 8:20
  • "but if you play Bb3, then the fundamental of that note will certainly exist." -- No it won't. Look at a spectrum analyzer, it's not there. " While the fundamental is hard to produce, it is certainly possible," -- it's a pedal tone, you're forcing a vibration through the instrument that isn't a natural resonance. "On flugelhorn, it is a perfectly good note." -- flugel is a conical instrument and obeys different physics. "Trombonists might even be required to play it." -- trombone is able to make pedal tones sound better.
    – MattPutnam
    Jun 9, 2018 at 15:24
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here might be your answer:

https://physics.stackexchange.com/questions/246020/is-it-possible-for-a-harmonic-to-be-louder-than-the-fundamental-frequency/246023

It is not uncommon for some of the higher harmonics to have a larger amplitude. Take a look at the frequency spectrum of a trumpet for example. Trumpet Frequency Spectrum

enter image description here

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