How to analyze chords when you only have a dyad?

I am doing a piano course and come from studying harmony as triad chords in songwriting on the guitar. In the piano course they teach you chords but then you get a lot of cases where the left hand just plays two notes. Most of the time, I find myself trying to figure out which triad the two notes come from so I can see how it fits in with my current understanding of chord progressions and chord theory as that is what I am used to. For example, here is a piece I am currently learning how to play

when I see this, I immediately think Cm, Ab, Bb, Gm

Is it wrong to see these dyads as implied simplified triads? How can I learn about harmony if there is only a dyad instead of the whole triad? I like to know what I am playing as opposed to just reading and playing so I always ask, what key am I in? What is the melody doing? etc etc.

No it's not wrong, it's one way to handle the situation. But two notes are just two notes.

By trying to play other notes over the existing ones, listening and analysing your feelings you can test the situation. To explore the harmonic possibilities, try adding or removing notes. What can you make it be?

But the question should be "how to analyze harmonic possibilities", not how to analyze chords. Because (a) you don't really have chords to begin with, and (b) even if you had chords, they wouldn't be the whole harmony.

The harmonic context in your mind consists of things like what you consider to be a probable home note, and what intervals you expect to hear around it. These probabilities can be manipulated even with single notes, just not in such a powerful way as with chords. But even if you have three of four note chords, it still leaves something to imagination. Chords are not the same thing as total harmony. Where is the line between implicit and explicit harmony?

If you play a C major chord, do you imagine a C Ionian or Lydian or Mixolydian or what? How about if you play a C major chord and then an individual F# note?

Why do you need to "analyze"? Are you going to make an arrangement and want to keep the original feel intact? Or are you going to make a variation? Play a solo? Where is this "analysis" going to.

Yes, you should think about the implied harmony. Don't get hung up on the terminology of dyad, triad, chord. A basic definition of chord is three notes, but that is more properly a triad. A chord is just an abstract harmonic idea that doesn't need a specific number of tones. Your question deals with understanding two-part harmony where you can even have seventh chords with only two notes! Ex. `G` with `F` above in `C` is an incomplete but unmistakable `V7` chord! When analyzing two-part harmony you end up mentally filling in the missing, implied voices.

I like to think about the tendency of chord inversions to decide how incomplete chords could be understood and then the voice leading possibilities.

When you see a fourth the implication is a second inversion chord or a suspension. Either check to see if the fourth above moves like a suspension or fill in the missing third. Basically fourths get special handling so the options for the full harmony are a bit restricted in that sense.

A plain third is ambiguous. It could be the root and third of a root position chord, or it could be the third and fifth of a first inversion chord.

From those options try the possibilities.

Consider the implications for chord qualities when choosing the third voice and ask whether you are trying to hew to conventional harmony. In conventional harmony diminished chords often act as dominants or passing chords, and augmented chords are fairly rare.

Regarding conventional harmony think about voice leading and root progression. Two voices moving by step is roots by descending fifth, the "strong" progression. One voice moving by step is roots by descending third, a less strong but common progression. Three voices moving contrary to bass is root by descending/ascending step, not so common except for `IV V`. Those aren't the only movements, just essential ones.

So, from your example: the first thing I thought was the fourths doesn't move like a suspensions so treat them like a second inversion chords. Don't worry about their qualities of major/minor yet. The important thing is to start with knowing their roots which are `C` and `Bb`.

Next, try harmonizing the thirds as either root position or first inversion chords. For these you don't really need to worry about chord quality, because you are adding either a perfect fourth or perfect fifth above the potential root and so the thirds of the potential chord will already be determined.

The two example below are how I completed the chords. I added the third voice in the treble the bottom bass clef is just to show the resulting chord roots...

The first uses roots by descending thirds and a harmonic sequence between the two bars. Descending thirds isn't the strongest progression, but the first and last chord are `Cm` and `Gm` outlining a root relationship by fourth/fifth. There isn't a proper dominant, but it certainly outlines a basic `C` minor tonality.

The second uses roots all by descending fifths and also the harmonic sequence. I used `E` natural for the first chord, because then the two sequential pairs are dominant to tonic movements, like `Fm: V i | Eb: V I` or `Eb: V/ii ii | V I`.

As @LawrencePayne says there isn't one "right" way to complete the harmony. consider the options and take whatever suits your purpose. My first example could be a good pop progression where eschewing the tonic is common. The second is super conventional for classical style, so conventional it has a nickname, "the fonte."

Yes, it's fine to infer a triadic chord progression, but there's not enough information to say what the 'right' answer would be! (Seeing the melody as well would doubtless narrow down the choices.)

Why C minor? There's an open key signature, so my first thought would have been C major. But C minor is possible.

Ab is possible for the second chord. Fm would have been a little nearer to home - the subdominant chord with one note modified (Ab would have been the submediant with two notes modified). Then B♭ and G are reasonable suppositions (have you omitted a ♮ from the last B?) but far from the only possibilities.

Better, perhaps, to treat this piece as an exercise in piano PLAYING rather than a harmony lesson.

• Considering the first chord, don't powerchords tend to strongly sound "major", thanks to the major third being more prominent in the overtone series than the minor third? Though, I mean, a melody played over this could clearly complete the triad into either major or minor so who cares.
– user70370
Jul 29 '20 at 16:28
• @Taschi - Nah, power chords sound neutral enough that chord progressions involving exclusively them can easily sound like they are in minor keys. G5-Db5-Ab5-G5 sounds like it's in G minor to me and that I'd fill in the chords as Gm-Db-Ab-Gm, for example. Jul 30 '20 at 11:10
• @Laurence, you could be right to treat this as a piano playing excercise but if I wanted to learn about composing a piece like this one, how can i not learn it? Jul 30 '20 at 14:58
• Learn your composing from material that can be more surely analysed. But also learn that it's OK to have music that can't be! Jul 30 '20 at 15:05

Just let 2 notes be 2 notes. Not everything has to be a chord or have a chord in it. Why try and find an implied harmony? The permutations can be endless. There are so many places you can look to analyze harmony if that’s what you want to do. If this is part of a piece whatever harmony that may exist there will present itself eventually later in the piece. Musicians (myself included) can sometimes get a little carried away with looking at all the nuts and bolts rather than stepping back and saying: “Hey, that’s a nice car!”

• not if you want to build a car Jul 30 '20 at 14:55
• I love analyzing music but there’s analysis and there‘s speculation and if 2 notes is all you have it’s the latter. That’s fine but it’s not analysis. Jul 30 '20 at 17:22