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6.2.2 Bass Note: Power in the Hierarchy of Chord Notes
Here’s what happens. In a chord, whichever note occupies the bass note position with respect to the other chord notes will carry more harmonic weight by virtue of its necessarily more powerful (loud) fundamental and overtones (i.e., compared with the fundamentals and overtones of the higher-pitched chord notes).
In fact, the bass note of the chord (triad) with respect to the other two notes wields so much power over the sound of the chord that the distribution of the other two notes doesn’t really matter.
For example, in first inversion, the order of the notes could be either E, G, C or E, C, G. The chord will still have a characteristic “first inversion” sound (in this example, the sound of “the chord C Major with E in the bass”).
In the context of a scale, every note is unbalanced to some degree, with respect to either scale degree 1 or 1 (8). Except, of course, scale degrees 1 and 1 (8) themselves, with respect to each other. So, having an unbalanced chord note (third or fifth) in the bass position (as is the case with first and second chord inversions) creates a certain amount of disturbance in the sound of the chord, despite the absence of dissonant intervals.
To a hear a completely balanced, completely stable, completely consonant triad, you have to play it in root position.