6th Chords: Is it just me...

[Km7]

I didn't have the intention to sound in black and white.
In first inversion, the chord (as a separate entity) loses some of its purity and strenght. In tonality, to some degree, it also loses its functional power, but the context is also important.
Traditional theory and analysis actually have several flaws and the understanding of inversions is one of them - relating the inverted chord to the original form of the chord, which has a different structure.
And the system of inversion appears to work for the tertian harmony, but becomes unstable and collapses in quartal harmony, for example.

[Toxikator]

that's because quartal/quintal harmony have different analytical methods.

The understanding of inversions is fairly good, I'd say. No one is denying the difference in tonal quality but the reality of it is that the FUNCTION almost never changes, excluding certain extremely weak intervals like the I64 (which is used transitionally). In virtually EVERY circumstance, the first inversion does nothing to weaken function, and in many cases actually strengthens it (see N6 for an example).

[nuffink]

Traditional theory and analysis actually have several flaws and the understanding of inversions is one of them - relating the inverted chord to the original form of the chord, which has a different structure.

Yes, absolutely. In acoustics a sound is defined in terms of it's fundamental and harmonics, because the fundamental is exactly that - fundamental to the sound. Only in harmonic theory are we asked to accept that the root is of prime importance even if it's not in the bass. Well I don't believe that and it's certainly not how I hear chords.

[Toxikator]

The reason we are "told to do so" is BECAUSE of the harmonic series! The nature of overtones is that octaves are strong; so strong, in fact, that in many cases two notes are indistinguishable if they are played an octave apart. When two notes of a consonance or dissonance interact, the relative placement of the octaves is not of a particular importance since the overtone interaction is duplicated across octaves. Playing E-G-C sounds different from playing C-E-G, yes, but the notes all tend in the same melodic and harmonic directions.

[nuffink]

The reason we are "told to do so" is BECAUSE of the harmonic series! The nature of overtones is that octaves are strong; so strong, in fact, that in many cases two notes are indistinguishable if they are played an octave apart. When two notes of a consonance or dissonance interact, the relative placement of the octaves is not of a particular importance since the overtone interaction is duplicated across octaves. Playing E-G-C sounds different from playing C-E-G, yes, but the notes all tend in the same melodic and harmonic directions.

Really.

[Sascha Franck]

Only in harmonic theory are we asked to accept that the root is of prime importance even if it's not in the bass. Well I don't believe that and it's certainly not how I hear chords.

I think we need to look at things a bit more differentiated here.

For instance, if you take a "pure chord", let's say E-G-B-D it'll defenitely sound like an Emin7. Fine.
But, as soon as there's a G root note below it, we will perceive the same chord as a G6.

So, generally spoken, the perception of whatever chord inversion is strongly depending on the musical context.
Even the chord from above could still sound like an Emin7 when the bass was doing, say, some E-G-B-G walking or whatever line. You wouldn't change the chord symbol to G6 on the second quarter or wherever.

Then there's another problem which may lead to a whole different perception of chords: The socalled "low interval limits". I don't have any exact figures in mind, but building up a major chord on, say, the major third, is only working to a certain degree. As soon as the major third (our lowest note) is getting below whatever frequency, things will start to sound sort of messy and our perception will probably be that now the major third became the root, with the entire chord sounding somewhat unclear (in this case as a min/b13 chord).

However, from an arrangement point of view, such as in arranging for, say, a 4-part horn section (read: There's always a bass below it, taking care of the root notes), inversions hardly ever change anything regarding the function of a chord.

Really, it's all about the context.

[Adaerus]

Traditional theory and analysis actually have several flaws and the understanding of inversions is one of them - relating the inverted chord to the original form of the chord, which has a different structure.

Yes, absolutely. In acoustics a sound is defined in terms of it's fundamental and harmonics, because the fundamental is exactly that - fundamental to the sound.

Right, but also in psycho-acoustic terms there is no difference between a sound that has it's fundamental and the same sound with its fundamental removed. Meybe there is a quality change but still the sound keeps its pitch and the overall timbre.

I would agree that the base note is important since that is what the ear, well actually the brain, counts as a fundamental for a given chord but the inverted chords will create intervals that do not correspond to the expected structure of the root chord according to the base note so they become unstable.

[Toxikator]

The reason for the low interval limit is also the harmonic series; the harmonic series has a good deal of dissonances as it increases (since we hear logarithmically but it is built linearly), so the lower notes are going to have more prevalent high harmonics. By contrast, high notes will have high harmonics outside the human threshold of hearing; plus, the nature of many "high notes" is that they're built from shortened or shrunken strings compared to their low counterparts, causing a decrease in the volume of certain high harmonics (why high piano keys have no dampers and sound very percussive).

The reason why inversions (especially in the lower ranges) can lead to different sounds is because of overtone relationships.

if you voice a CMaj chord in root position in close voicing (CEG) you get these overtones:

C-E-G-C-E-G-B-C-D-E-G-Ab (first 12, bolded indicates reinforcement). There are strong percieved dissonances between the 7th and 8th partials and the 11th and 12th partials (roughly a half-step between each).

In EGC voicing:

E-G-C-E-G-B-C-D-E-G-Ab-B (first 12). The dissonances come earlier on in the series and the chord tones are not as reinforced early on as they are in the root position voicing. This is what gives the chord its characteristic "unstable" quality; the more you invert it (if you were to put the G in the bass, this effect is even more exaggerated) the less reinforced the chord is harmonically. However, notice that both inversions, though they had a different order and doubling, shared all of the same partials. This is true right up until around the 16th partial, where a very slight shift occurs... but after that, the intervals are very similar again. This is the reason why, functionally, the chords are considered to be the same; though the chord is not reinforced as strongly and there are more harmonic inconsistencies in certain inversions the basic harmonic features are still the same.

Not only that, but when you consider harmony in the context of a scale, the resolutions don't change based on voicing. In CMajor, the note G has a strong overtonal relationship to the tonic, the note "b" has a melodic tendency toward the tonic, the note D is uncomfortably between two notes of the tonic chord, and the note F has a melodic tendency toward the note E in the tonic chord. That's why GBDF tends toward CEG. Regardless of WHERE these notes are, they have the same harmonic dissonance and are resolved by the same melodic and harmonic motions; F to E, B to C, D to either C or E, and presumably G stays put (but can also bounce to C). The F won't have a different tendency if the D is above it as opposed to below it.

[nuffink]

For instance, if you take a "pure chord", let's say E-G-B-D it'll defenitely sound like an Emin7. Fine.
But, as soon as there's a G root note below it, we will perceive the same chord as a G6.

That's it in a nutshell. EGBD sounds like a minor chord (with tension) and GBDE sounds like a major chord (with tension). Yet conventional theory suggests that they are functionally equivalent. Not to me. Although they clearly both function well, one's fundamentally minor, the other major.

[Km7]

@Toxikator, that's why I said that the context is important.
EDIT: Indeed. In bass, the dissonant intervals are more dissonant mainly because of the ATH and we hear more overtone conflicts.
@Adaerus, yes. The Tartini's combination tones.
But it seems that those natural things are not used and explored widely enough in traditional theory. Something with which I have been always unsatisfied. I was deeply interested in those things and explaining how music works - at the beginning, thinking and analyzing myself, explaining melodic and harmonic forces, tendencies, etc. Then I started to familiarize myself with the theories of Paul Hindemith and found similarities between his and my own understanding and approach, which bringed me satisfaction and even deeper interest, so I dived deeper into his theories in order to adjust and expand my view. For anyone who is interested in those things I would sincerely recommend his book "The Craft of Musical Composition". I have never been so satisfied and in agreement with any other theorist. These techniques of understanding and analysis are suitable for all kinds of music - Bach, Schoenberg, etc.

[Toxikator]

For instance, if you take a "pure chord", let's say E-G-B-D it'll defenitely sound like an Emin7. Fine.
But, as soon as there's a G root note below it, we will perceive the same chord as a G6.

That's it in a nutshell. EGBD sounds like a minor chord (with tension) and GBDE sounds like a major chord (with tension). Yet conventional theory suggests that they are functionally equivalent. Not to me. Although they clearly both function well, one's fundamentally minor, the other major.

But understand, too, that once you get into 7th and extended chords the rules which govern tertian harmony tend to break down. That's why jazz analysis makes special note of inversions ("slash" chords): when dealing with that many tones the order gains importance. The analysis which asks us to "accept that the root note is the important one" is a primarily TERTIAN analysis.

[nuffink]

You do know that "tertian" refers to the intervals involved (thirds) an not the number of notes, do you?

[Km7]

P.S.: And, to be clear, I apologize if have created the impression that (to me) the inversion completely changes the function and resolution of the chord. I am not talking in black and white, but just about "clouding", so to speak. Toxikator's explanations are of course right. If we don't resolve voices according to the scale tendencies (which are acoustically explainable with the overtone series and the combination tones as well) thus forming chord progressions, we would weaken and eventually escape the tonality.

[Toxikator]

OOP! You're right Nuffink. I mean to say "triadic", my bad.

[Watto]

They have their own unique sound, that's for sure - I've really been getting into 6th chords