The lowest note of a chord is the most important one. It's the one that the listener hears most distinctly.
Why is the above true? I know no physics: please keep answers simple.
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The answer lies in the realm of Psychoacoustics and/or Music Psychology. I studied a little of this in Audio Engineering, and from what I remember it has to do with how our primary auditory cortex in the brain processes vibration pulses that we hear as a tone.
Lower tones are given more "weight" than higher frequencies, especially when determining what the "Fundamental Frequency" is. I'm not sure why, but I know testing has been done on the subject.
Additional harmonic tones added to the chord can help the brain recognize the fundamental. This is likely why putting the chord pitch in the bass note is so effective. The 5th, being harmonically related can also work and not mask the perception of the fundamental. Putting the 3rd in the base can cause confusion about which frequency the fundamental is.
You can try this yourself on a keyboard: play a root position C chord in the right hand, and play a low C in the bass with it. Then switch the low note to a G and listen to the difference. Finally put a low E in the bass and you will hear how the chord doesn't sound as "C ish".
It has to do with overtones and how our brain processes signals.
When a source of a sound has overtones, there is a mathematical relationship between each of the frequencies of the tones. If you understand the relationship, you can simplify your processing by breaking it apart into a single frequency and an encoding of the relationship of the overtones.
As it turns out, the most natural frequency to choose is the lowest frequency in most cases. Why? Well it's in a unique position to describe the sequence the best. Consider a vibrating string example, where I choose to think about the string as a single note and some harmonics -- but I choose different fundamental frequencies. In the first column I pick the lowest frequency, and in the second I pick the third (an arbitrary choice):
Frequencies: 400 800 1200 1600 2000 2400 ... multiplex of 400 multiples of 1200 400 1 1/3 800 2 2/3 1200 3 1 1600 4 4/3 2000 5 5/3 2400 6 2
As you can see, the math looks a lot simpler if we consider the fundamental frequency of the note to be the lowest frequency! This particular example is for a string, which is different from, say, an open pipe, but the story is the same. The equations are simply more natural if you think about the lowest frequency.
Our brains are smart little processors. They figured this out billions of years ago, before we were even mammals! So when you and I hear things, we naturally hear this decoupled pattern: we hear the "fundamental frequency" defining the note and we hear the "character" of the sound as a separately encoded set of information regarding the overtones.
An interesting breakdown of this model occurs with throat singing. Best known in Tuvan throat singing, this is a way to sing two notes at once. The technique is a brilliant abuse of this processing that our brain does. In virtually all real instruments, the most power (i.e. energy transmitted, in a scientific sense) comes in the lower frequencies, closer to the fundamental. In throat singing, one carefully adjusts the shape of the mouth to highlight one harmonic, making it resonate far more than the others. When the listener processes this, their brain sees a sound that doesn't fit into their usual model, which assumes that for single sound source there will be less and less power in each of the overtones. It then makes the assumption that there is not one sound source but two! Thus, when we hear Tuvan throat singing, it sounds like they are singing both the bass line and the whistling melody at the same time. In fact, they are singing one note, but with a brilliant and tricky precision that causes us to invent a new "lowest note" in our own head to carry the melody with!
This is a complex issue encompassing the way that the listener is attuned to sounds, musical culture (eg western or South Asian), tonality, the effect of an individual's audiogram characteristics (eg high frequency hearing impairment), the loudness of the instruments and the way they are being played and the difference between harmonic progressions and counterpoint.
Each musical note sounds with a lot of overtones, so the overtones of lower notes mesh with the fundamentals and the overtones of higher notes. In a three-note chord, the first overtone of the fundamental is already higher than all fundamentals. Nevertheless, the overtones of the fundamental are more tightly spaced than those of the higher notes and thus dominate the lower part of the spectrum, partly blending with the fundamentals and overtones of the higher notes. However, the resulting grid of harmonics is determined by the harmonic root of the chord which may or may not be its lowest note depending on the inversion of the chord. In the case of chord inversions, the lowest note is not as dominant as in the case of chords in root position.
The bass or lower notes are perceived at the center of the inner ear. Weather in the harmonic partials of a note or as part of a bass line, as in a chord progression, for example, the lowest note seems "more rooted" or "more fundamental". Some of the other issues mentioned in other answers here may still apply as in the case where the fundamental harmonic partial of a note is not present, the ear/mind infers it, but these are not why the bass is so important and structural. The perception of the harmonic partials of a note are also affected by the fundamental perception of the bass, but coincidently, in natural sounds, the lowest harmonic partial typically happens to be the loudest, as well as the one all other harmonic partials are whole number multiple of. Could the inner ear have evolved to what it is because all harmonic partials are whole number multiples of the lowest frequency one? It seems possible. The fact remains that the bass line is key and logically more restricted than other parts.
In the book "this is your brain on music", Mr Levitin talks about an experiment where sounds whose fundamental ( =lowest ) frequency is deliberately erased are played to both animals and humans. As a result, a circuit in our cortex have filled the missing frequency, the output of the brain circuit had the same vibrations with the original unmodified sound. And we animals could not tell the difference. So coming to your answer; it's our evolution that gave it. But if you'd like to know, in electrical electronics engineering, when a rectangular signal is converted into frequency components, I.e. Fourier transform, it has the highest amplitude component in the lowest frequencies. Your answer may have something to do with the music we listen to may be imagined as rectangular signals, whose frequency transform has highest amplitude at the lowest frequencies. https://en.m.wikipedia.org/wiki/Sinc_function or the sounds we listen to have sinusoidal similarities or every musical interaction (echo etc) may be considered as derivation or integration operation, where sinusoidal waves doesn't change shape and frequency but others decay and thereby lowest sinusoidal wave is the remnant. I just made up after the Wikipedia reference.
My opinion, the prevalence of guitar in the last 100 years means a lot of chords, the lowest note sounds first usually because chords are strummed downwards usually.
Maybe consider sound energy may be higher with lower notes.
Of course chord harmony is a different case, the listener may hear notes that fit or ones that stand out.