What is the value in analysing chords as if they were made up of stacked triads?

Question

To my ears chords each have their own quality and how they sound (and what feelings they might evoke) depends on the context. In general plain majors are strong/simple while minors are sad, but add2 chords or 6th chords can be even sadder than triads with a minor 3rd, depending on what comes before and after and what everyone else might be playing. It’s not quite as simple as Cohen’s Hallelujah but he had the key to the basics.

There is some discussion about chords with more than 3 notes being ‘made up’ of overlapping triads, or in the case of 6+ note chords perhaps non-overlapping triads. An example: Is a “minor Seventh Chord” basically just a combination of a “minor Triad” and its Relative “Major Triad”?. What is the value in this? Does it help us choose and/or construct chords which evoke predictable responses in the listener?

I usually think that power chords (root-5th) are not really chords - we might as well call a 4th or any interval a chord. The usual triads (major and minor) are fundamental while anything else is just notes added for extra color, or to serve the harmonic movement or melody, or just ornament (with or without a note from the basic triad omitted). So is there any reason why we might need to notice that a m7 chord is a pair of overlapping triads from two scales? Does this kind of analysis explain how someone hears something like the minor major 7th chord? Are not perceptions of chord value mostly a matter of acculturation, of what sounds good or right in the specific context? What’s missing if we start with the two basic triads and then talk only about adding extra notes, or suspending a note, or voicing an inversion?

This might look like a bunch of different questions but it is really just one question about the analysis of chord construction - and how this is affected by context.

N.B. This is not a question about the ‘stack of thirds’ view of chord construction (see e.g. What is the "stack of thirds" in chord theory?). It is about triads and overlapping triads.

Answer 1

In functional harmony, I don't think it's particularly useful to analyze Cm7 as a Cm + Eb polychord, or to feel that it implies two different scales. But a C + D polychord could be a different matter. Yes, be open to all ways of dissecting a chord! Is a “minor Seventh Chord” basically just a combination of a “minor Triad” and its Relative “Major Triad”? But in mainstream functional harmony, I doubt a polychord approach will be useful.

This is much the same question:

is-a-minor-seventh-chord-basically-just-a-combination-of-a-minor-triad-and

Answer 2

What is the value in analysing chords as if they were made up of stacked triads?

This forms the basis of functional harmonic theory, which holds that C/E has the same tonal function as plain old C (i.e., with C in the bass). Of course they don't actually sound the same, but they are certainly similar, and for the most part you can use them in the same place in a chord progression. For example, both of these are common functional progressions:

• C - Dm/F - G7 - C
• C/E - Dm/F - G7 - C

Before Jean-Philippe Rameau published this theory in the first half of the eighteenth century, the chords that we today call C and C/E were considered distinct. Rameau's theory simplified certain elements of music theory.

To identify the "true bass" of a chord such as E-G-C, you stack the pitches in thirds and find that it is C. Similarly, if you have a D in the bass and F, G, and B above, you stack in thirds and find that it is what we now call a G7 chord.

I don't think Rameau went as far as ninths, since ninths were invariably non-chord tones, typically suspensions. But a couple of centuries later, people began to extend the principle to ninths and more. In doing so they have somewhat lost touch with Rameau's original purpose; for example, the chord C-E-G-A in Rameau's world is a minor seventh chord in first inversion, but nowadays it is also known as C (add 6) or C13 (with the seventh, ninth, and eleventh omitted).

In my opinion, it doesn't make sense to call it a first-inversion seventh chord if it doesn't function as one, i.e., if the sixth is there for added color, for example on the tonic chord. But I also find the approach where you conventionally omit some of the thirds to be rather disingenuous. Is there any analytical benefit to a 13th chord with 7th, 9th, and 11th omitted rather than just "add 6"? I haven't found any.

Answer 3

There really is not much value to thinking of chords this way other than anecdotally or as a different way of visualizing them, or if it helps in conceptualizing or executing things from a players point of view.

A chord’s sound quality and function come from the root and the relation of the notes stacked above the root more than the fact that say, a Cm7 chord has both a Cm and an Eb triad in it. You can say that both those chords have a similar function because they share 2 of 3 notes but in the end the Bb note is heard as the b7 of C, not the 5th of Eb. There are many ways to think of chords such as overlapping triads, stacked thirds, pairs of 5ths, etc. but in the end relating all the notes of the chord to the root is really best.

Answer 4

I wouldn't call it analysis - I see it more as a way of looking at chords which in some situations might be useful or practical.

Jazz pianist would quite often think about the chords in terms of left and right hand and would voice them as non-overlapping triads and there is even a special polychord notation for piano where chords are written as left hand chord and right hand chord separated by a horizontal line.

I found it very useful for jazz comping to know how to spell out the upper structures of more beefy chords like 11,13 etc as a simple upper structure triad.

It could be summed up as a practical way of memorizing upper structures and their relations but for proper harmonic analysis probably not so useful.

Answer 5

In my opinion, the primary value of trying to find a stack-of-thirds interpretation for a chord is to get a simple chord symbol name for it. It's a very condensed way of writing down harmony. For analyzing the harmonic changes of a piece, it helps in some situations and genres but not all, as noted in the other question about stacks-of-thirds. The question is about stacks of triads, not thirds. But because of the definition of triad, a stack of more than two thirds is also inevitably a combination of triads, so the questions aren't completely separate.

Other values in seeing stacks-of-thirds and finding triads in them are in arranging and jazz style soloing. For example a guitarist can choose to play only the so-called upper structure triad of a ninth chord, leaving out the root and the third. Or if there is only a written C major triad, it can be deliberately turned into a C9 chord by adding a G minor triad. It can make a band's overall sound more open, less muddy, and maybe more interesting, if chord voices are split among instruments, and knowing about stacks of thirds helps in doing that. If guitars don't play the low notes, it can avoid some muddiness. Soloists can use the same principles as well.

If you happen to have, say, chord samples of only triad chords, you can use them as components for making thicker chords. G minor + F major in the next octave creates a Gm11 chord. Bb major + F major = Bb maj9.

A bass player can turn a C major chord into an Am7 by playing an A bass note. Or a Steely Dan chord by playing an F, but that's not a stack of thirds.

Answer 6

...In general plain majors are strong/simple while minors are sad, but add2 chords or 6th chords can be even sadder than triads with a minor 3rd...

I think you are mixing up analysis of chord with analysis of melody.

Indeed context matters. That includes hinting at Leonard Cohen's song Hallelujah and mentioning add2 and "6th chord" to discuss pop style.

Many, many pop music song books use add2, 6, etc. to reflect non-chord tones that occur in a song's melody. In my experience, many of those non-chord tones are not used in the recorded accompaniment part of the song. In other words, such tones shouldn't be construed as chord extensions, nor as some kind of non-triadic tone, but are clearly melodic tones.

If I understand your question correctly, in a situation such as a Dadd2 chord, you want to know why harmony analysis would look at that chord as stacked thirds, which by definition ignores the add2, and identifies the chord as D F# A, rather than identifying all the purported chord tones of D F# A plus the added E? Why do that when the E is important to the music?

Assuming a lot about the context this Dadd2 occurs in, the simple answer is the E is part of the melody and not part of the proper chord. If the chord occurred in a passage like D(add2) E7 | A, the harmony analysis is really just concerned with the root progression of IV V | I. The E might come into play in the melody, perhaps something like F# E over D(add2) to E D over E7 to C# over A, where the first E over D(add2) is a non-chord tone anticipation to the E over E7.

Harmonic analysis primarily is looking for chord roots and defining chords as stacks of third is what makes that possible (the chord root is the bottom tone of the stacked thirds.)

The add2, add6, etc. non-chord tones are not ignored in a good analysis of a song. They are just analyzed as melodic aspects rather than harmony.

In my opinion I think it's bad when songbooks use chord labels in the way I describe, because in my scenario, the chord is really just a simple triad D, and Dadd2 is a muddle of chord performance instruction combined with melodic non-chord tone identification. Nevertheless, that is what many songbooks do.