Why is it that no matter what arrangement or inversion of notes are presented to me, I can quickly find the root? Is it training or is there a mathematical answer? If you play C E G or E G C or G C E, I always find the C quickly because it sounds "right". What explains this?

  • Most likely, as (presumably) a bass player, you are expected to, and usually do, play the root note of a chord before anything else. It's what we bassists do, at least in popular music. That apart, the most stable sounding triad will have the root at its base, so making it easier to hear, even if it actually is somewhere else, your ears move it. There's also the phenomenon that the strongest harmonics are root octave and fifth, then root root double octave, which makes the root note stand out slightly. – Tim Dec 18 '18 at 10:45
  • Are you talking about reading from staff notation, or if the letters are written in the alphabet, or aurally identifying the root? – Michael Curtis Dec 18 '18 at 17:55

In each of these voicings, C is the resultant. For instance, C4–E4–G4 can be seen as the 4th, 5th and 6th overtone of C2. For, G3–C4–E4, they're the 3rd, 4th and 5th overtones of the same C2, whereas E2–G2–C3 are the 5th, 6th and 8th overtones of C1. (In 12-edo temperament, they're not exactly the overtones, but pretty close.)

So for major chords, it's really not surprising that we hear it this way. For minor chords it is a bit surprising however, because here the fundamental is not a (readily audible) resultant of all three notes, regardless of inversion. It is however (obviously) still a resultant of the fundamental and fifth, below which the minor third can then be construed as a dropped major third.

  • ...I've never heard of that as an explanation... why, then, do the minor chords get recognised justas easily? What about other chord types? – user45266 Dec 19 '18 at 5:04
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    It's worth mentioning that minor chords only started to be recognised as fully cabable tonics in the Baroque era; in the Renaissance a Picardy third was pretty much obligatory even if the melody was in minor mode; the minor chord was considered to not clearly enough point to the fundamental. Some people argue that C4–E♭4–G4 can also be interpreted as the 16th, 19th and 24th overtones of C0, but I don't think much of that – that's so high in the harmonics that it becomes pretty arbitrary. – leftaroundabout Dec 19 '18 at 10:22
  • However, the maj7 chord (which is considered very consonant in Jazz, and a common final chord) can definitely be interpreted with resultants: C4–E4–G4–B4 are the 8th, 10th, 12th and 15th overtones of C1. – leftaroundabout Dec 19 '18 at 10:24

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