22

Source: Prof. Bruce Taggart (PhD in Music Theory, U. of Pennsylvania), 58 s of his Coursera video.

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.

  • 9
    It isn't true. It depends on the listener, the acoustic, the voicing of the chord, the instrumentation, ... – user207421 Apr 16 '17 at 4:48
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    Yet, it is normally the top part that carries the tune. Consider some SATB arrangements, who has the tune: the soprano or the bass? – badjohn Apr 16 '17 at 6:37
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    I don't like the way he phrased it. Psychoacoustically, the lower the note, the harder it usually is to discern its pitch. So that seems to contradict his statement except when the bass note is high enough. That said, the lowest sounding note is of special importance when the brain is docoding the overall sound, which is probably what he is talking about, I just think he choose words poorly to summarize the concept. – Todd Wilcox Apr 16 '17 at 12:28
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    Possible duplicate of Why is bass note so important in harmonic analysis of music? – leftaroundabout Apr 16 '17 at 15:44
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    With a root+fifth(+optionally, octave), a listener may often hear a non-existent note an octave below the root, due to the "missing fundamental" illusion. Probably part of the reason why heavy metal sounds so "heavy", it makes extensive use of such chords ("powerchords") – Mark K Cowan Apr 16 '17 at 20:05
18

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".

  • 2
    Some good summary from here: dspguide.com/ch22/2.htm and the section prior. Consider, even just listening to someone speak: what we hear as the pitch is the lowest tone. All the other tones (harmonics/overtones) that accompany the fundamental are wrapped into the perception and heard as "timbre" not as separate notes. Main exception, Tuvan throat singing where individual "notes" (harmonics) are amplified and pop out. I don't know that the bass is always heard "most distinctly" but it has a huge (arguably the largest) affect on what we perceive to be the tonality or tone center. – Phil Freihofner Apr 16 '17 at 3:31
  • When you talk about 'fundamental frequency', it sounds like you're talking about the "fundamental frequency of a chord", rather than a single note. Are you talking about some kind of 'implied' fundamental that the listener would perceive based on the superset of overtones present? – topo Reinstate Monica Apr 16 '17 at 6:51
  • Yes, the notes we layer on to the main note of a chord are adding relative harmonic overtones to the fundamental frequency (lowest or slowest frequency). What we hear as "consonance" are notes that resonate at simple integer relationships (like adding an octave or 2:1 ratio). Unless you are playing a sine wave, the notes we add to a chord are usually already represented in the main note, adding them makes them more present in the harmonic stack. If you change the lowest note, then the brain perceives the stack compared to that fundamental. I'm remembering this from Physics of Music class... – Alphonso Balvenie Apr 16 '17 at 17:49
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    " the notes we layer on to the main note of a chord are adding relative harmonic overtones to the fundamental frequency" - it's important to note (ha ha) that some of the overtones of the higher notes these may not be overtones of the lowest note in the chord, though. This is true even of a root position triad; the third and fifth may have overtones that (together with those in the root) suggest a note below those in the chord. So we still can't say that quoted idea - that 'The lowest note of a chord is the most important one'- is really true. – topo Reinstate Monica Apr 16 '17 at 19:27
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    @topo morto True, I was answering more to why Prof. Taggart would be making that statement. It is definitely an over-simplification of the concept. If you read the transcript the statement is sort of a filler while he's explaining inversions. – Alphonso Balvenie Apr 17 '17 at 18:23
9

It's that guy's opinion. Many would say the top note stood out more. Others might consider the root most important (if not most audible) no matter what the inversion. It's certainly not an established fact.

  • In the absence of another melody part, the top and bottom notes would both stand out. In the presence of another melody part, however, the top note of the chord part would stand out less than the bottom one, because the melody would distract attention from the upper chord-part node. – supercat Apr 16 '17 at 21:04
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    A very simplistic rebuttal not backed up by any evidence in itself. See the other answers for more information. – Lightness Races with Monica Apr 18 '17 at 1:07
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    A simple rebuttal is all that's necessary to an off-the-wall claim, not backed up itself with any evidence. If someone says 'the sky is green!', 'no it isn't!' is sufficient rebuttal. If they have evidence of special circumstances where it may appear green, let's hear it. – Laurence Payne Apr 19 '17 at 13:59
  • Your case is that since the question has no documented support that means your answer does not need documented support? If the phenomenon mentioned in the question were not real, studied, documented, and well-known by many of the users here, the question would have gotten comments similar to your answer. The fact in question is a fact, it's not "one guy's opinion". The simplest but not at all only factor is masking, which is a consequence of the structure of the basilar membrane which gives preference to lower frequencies over higher simultaneous frequencies. – Todd Wilcox Jun 16 '17 at 21:49
8

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!

  • A related phenomenon is the missing fundamental: most people to will perceive the pitch of a note as the "bottom" of the corresponding harmonic series even when that specific frequency is absent. This phenomenon occurs (among other places) in the notes of timpani, tubular bells, and in the pedal tones of brass instruments. – Michael Seifert Apr 17 '17 at 13:52
3

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.

0

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.

-1

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.

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    Downvoted for being utterly incomprehensible! – Laurence Payne Apr 16 '17 at 10:07
  • All overtones 'mesh' with all other overtones. 'The first overtone of the fundamental is lready higher than all fundamentals' is meaningless. 'Overtones of the fundamental are more tightly spaced that the overtones of the higher notes' is simply false, and 'neverthess' is a non sequitur, as is 'and thus dominate ...' The 'resulting grid of harmonics' is determined by the chord's position (root or inversion), not by 'the harmonic root of the chord'. The final sentence contradicts both the quotation in the question and the remainder of the answer. Answer is complete nonsense. – user207421 Apr 16 '17 at 10:11
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    @EJP it's not complete nonsense, though I agree that it's not phrased particularly comprehensible. But I think this answer says more or less the same as I did in this other question (of which this question is IMO a duplicate). – leftaroundabout Apr 16 '17 at 15:50
  • @leftaroundabout could be a duplicate, although this question seems to be more about why we are perceiving the lowest note as important, or what it is that we are hearing, I think making the question more related than duplicated. – Alphonso Balvenie Apr 16 '17 at 18:02
  • @leftaroundabout OK, it's not complete nonsense, but the intelligible parts of it are incorrect. The non sequitur and internal contradiction are nonsense by definition. – user207421 Apr 16 '17 at 18:07
-1

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.

  • A rectangular signal is actually an example of a signal with a particularly strong overtone content (in particular, very high-reaching harmonics), i.e. a signal with relatively little energy in the fundamental. – leftaroundabout Apr 16 '17 at 15:47
  • No. What is your reference? I got your point, are you trying to say "if we have 2 waves with the same energy and one of which is rectangular, rectangular will have the least energy on the fundamental?" Well it doesn't change the "fact" that the fundamental component is the greatest. Fourier constant for the fundamental frequency is 4/pi, which is greater than 1, even greater than the wave itself. – b.g. Apr 16 '17 at 16:11
  • Well, the square wave maximises total RMS energy, hence it's just overall the loudest signal you can have for given amplitude. Yes, it also has a very strong fundamental, but that's not the reason it sounds so loud – if you apply a lowpass filter to a square wave, especially if the fundamental is in the bass range, it will appear to get much quieter, although the amplitude in fact increases, because so much of that energy is actually in the overtones. Most other signals, e.g. triangle, sine-FM signals, acoustic instruments, are more dominated by the fundamental frequency than a rectangle is. – leftaroundabout Apr 16 '17 at 21:13
  • ...Anyway, I fail to see where you're getting with this entire point. Yes, in most signals, the fundamental is stronger (amplitude-wise) than any of the overtones. But how has that any bearing on how loud the lowest note in some arrangement is heard? If you mix trumpet and bass flute, then both may individually have the strongest amplitude in their respective fundamental, but that changes absolutely nothing about the fact that each trumpet note as a whole is louder than anything the bass flute can ever hope to produce. – leftaroundabout Apr 16 '17 at 21:13
  • @leftaroundabout You are correct that square waves have a lot of harmonics, but they have half the number of harmonics present as saw waves, so they are not the most complex waveform. And sawtooths are often perceived as louder because of their rich spectra. Remember, RMS energy/power is not directly related to loudness, frequency content/spectrum is very important (as famously noted by Fletcher and Munson). And square waves are mostly fundamental. The overtones are lower energy. See: goo.gl/images/MTn78X – Todd Wilcox Jun 16 '17 at 21:52
-4

This is how chords are played.

Mu band director uses the analogy of a sound pyramid-- the lower instruments are told to play louder, and the higher instruments to back off a bit. This lets the harmony sound balanced instead of"top heavy."

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    That is dependent on the acoustics in the room, the numbers of players, others' hearing. I don't think it's particularly accurate. – Tim Apr 16 '17 at 6:00
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    Seriously? Never encountered this before. In my experience its usually the other way around. – JimM Apr 16 '17 at 8:45
  • @JimM no, actually it's true. The lowest note is best heard because it is strongest – bass instruments are generally capable, helped by their bigger size, to produce much stronger amplitudes than corresponding treble instruments. Even so, they don't necessarily sound louder, due to Fletcher-Munson. A violin usually sounds louder than a cello, though that can produce stronger amplitudes and generally needs to do so as well, to make the mix sound balanced. Of course it still needs to be properly dosed – double basses may occasionally overpower violins. – leftaroundabout Apr 16 '17 at 21:23
  • This is how chords are played. Not completely true, on guitar you can play chords with the highest note first, and lowest last, also called an upstroke – rock-on Apr 17 '17 at 10:39
-4

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.

  • I use a tuning where the fifth string is the lowest; if I strum an lower-position A chord, it will come out as A-E-e-a-c#'-e'. The voicing is equivalent to an A/E chord in standard tuning E-A-e-a-c#-e except for the sequence of the first two notes, but I find the E much more noticeable in the the Standard tuning A/E than in my A chord. – supercat Apr 16 '17 at 21:02
  • I didn't vote -1. I think that your answer is perhaps applicable to some instruments, and the sequence in which pitches arrive at the ear can play a definite role in determining which is heard more noticeably, but for many instruments lower notes are prominent even when higher notes would be heard slightly first (e.g. on a pipe organ, if multiple keys are played simultaneously, the shorter pipes will usually speak more quickly). – supercat Apr 17 '17 at 14:58
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    Marshal - we have a "Be Nice" rule her, so please moderate your tone in future. – Doktor Mayhem Apr 18 '17 at 7:45

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