When a C chord is dissonant
Updated: Feb 8
I was once on a Zoom call with a bunch of other piano teachers. We were talking about how we introduce chords to young students. One very nice teacher told me about a keyboard method book that teaches the G chord and C chord in the same unit. Makes sense, I thought, as they are fifth related, and I start seeding fifth relations to my students as soon as possible.
But then she told me that the book introduces G and C chords like this:
She told me this, and I plastered a smile on my face. But inside I was screaming. Because introducing a C chord like this presumes that the notes G-C-E are the same in any order. But a C chord in 2nd inversion might be an instance when a C chord is dissonant, because what's in the bass counts.
Of course, I can understand that introducing these two chords like this has some advantage of staying in the same hand position, and no doubt, this is the thinking behind the methodology. I can imagine that some pragmatic soul would say that this makes it easier for a beginner piano student to play a G-C-G chord progression, and who can tell the difference?
But it is precisely this kind of teaching that ensures that the student can't hear the difference! It suggests that we think of chords as these 3-note blocks that sound alike, and we don't concern ourselves with (or hear) different voicings. A C-E-G chord is the same as an E-G-C chord is the same as a G-C-E chord. It's all C, and I suppose it's reassuringly major and on all the white keys.
But did you know that sometimes a C chord is dissonant?
The key to understanding harmony in the classical style (in any style really) is to pay attention to voicing. And none more so than what is in the bass!
What's in the bass counts.
When we talk about "voicing", we have to think about the obvious reference here - that every note in a chord is a voice. And voicing refers to how we distribute those voices across the range of an instrument. So let's undo our original chord blocks and distribute each note of each chord over a wider space.
The bass note, G, is moved down an octave. The top two notes of the chords are up an octave. The bottom part is the bass; the middle part is the alto; and the top part is the soprano. The first chord, G, is in root position. That is, the root of the chord (G) is in the bass. Acoustically, this is significant.
Think of the bass note as a resonator
Time for a spot of acoustics. Think of the bass note as a resonator. When the G sounds, what you're actually hearing is G (the fundamental) plus a series of overtones (called the harmonic series).
The fundamental is the strongest sounding tone in the harmonic series with each subsequent overtone becoming weaker. The octave (G) and the perfect 5th (D) are the strongest overtones resonating above the fundamental. This is why perfect octaves and perfect 5ths are so consonant - and why they are called "perfect". The third of the G chord (B) is the 5th note in the harmonic series, the 4th overtone above the fundamental, so still fairly consonant. This partly explains the consonance of a major chord in root position.
But if we look for the notes of the C chord above the G (so C and E), they are nowhere to be found in the first 12 notes of the harmonic series. In fact, C is number 21 and E is number 27. This means that these notes (C and E) resonate to a much lesser degree with the fundamental note (G) than the notes of the G chord (B and D).
It might be helpful to think of this in terms of a vibrating string rather than as notated pitches.
When the bass string is struck (on a piano) or plucked or bowed (on a stringed instrument), the fundamental vibrates at the full length of the string as well as at other points along the string - halfway (1st overtone) - 1/3 of the way (2nd overtone) - 1/4 of the way (3rd overtone), etc. You can see this vibration if you look inside a piano. The lower strings visibly vibrate when activated without the damper, and you can see multiple points of vibration all along the string.
Sometimes a 4th is a dissonance
So since the C and E in our C chord -
- are so high on the overtone series of G, they hardly resonate with the fundamental - i.e. the G in the bass. Where B and D strongly resonate with the fundamental and are a strong part of that sound world, the C and E are not.
And so - if your C chord has a G in the bass, it might be dissonant. Before you roll your eyes and click off, let me qualify that.
Consonance and dissonance is not just a scientific concept. It is also a cultural one. Dissonance in the 21st century is quite different to almost anything we could produce on a piano, because we now receive so much of our sound and music through electronic media. This puts our concept of dissonance in a whole other sound-based universe in which there exists no chords. Probably all chords sound great to us. This is also a personal thing, so I can't speak for you.
But this is precisely my point. We live in a world where we regard chords as one thing - a harmonious collection of three or more pitches played simultaneously, or at least conceived of as a collective. The trouble with this is that we still make and listen to music that had a conception of harmony where a fourth is a dissonance that must resolve. And this had some relationship to the overtone series.
Try this easy listening experiment
We are not so far gone in our electronically-based universe that we can't relate to this idea. In fact, it can be very easy to demonstrate through exploration of different voicings of a chord. You don't have to get fancy - play a root position C chord in closed position in the right hand -
- and try out different notes from the chord in the left hand - root, 3rd, 5th. Close your eyes, and listen deep into the sound.
How does each one sound to you? Do they sound the same? If not, how do they sound different?
I do this with students all the time. It's fun to explore this idea. It's also a kind of ear training that clues us in to the difference between root position, 1st inversion and 2nd inversion chords. Don't despair if hearing these differences does not come naturally to you at first. If you struggle to hear the bass note, try singing it. In fact, try singing each member of the chord as you play it, starting from the bass. It's worth developing this kind of "three-dimensional" hearing, because if you can't hear the difference between these three chord positions, there is a lot of music that you aren't fully perceiving.
Figured bass and the 6-4 -- 5-3 progression
I've been putting together a Figured Bass Handbook in the last few weeks, so this issue is very much on my mind. So many people tell me they don't understand figured bass.
Figured bass is actually a very simple concept. It is a bass line annotated with numbers and symbols that indicate intervals above each bass note.
[Note - Don't get me wrong - the concept is simple, but the execution of that concept (especially as a continuo player) is more involved and requires a good deal of training.]
Back to our chord voicings:
Here I've added a lower middle part (tenor) on the Gs an octave above the bass. The first bass G has an octave above it (G), a 3rd above it (B) and a 5th above it (D). We can disregard octaves in this, so the figured bass for the first and third chords is 5-3.
The default figured bass for that root position G chord is - nothing. Technically, it is 5-3, because there is a 3rd and a 5th above the bass. But in practice, a composer who uses figured bass wouldn't bother to write in these figures. They are considered the default - the "home" position - no need to indicate, because all is well and completely consonant.
The figure for the C chord in 2nd inversion (wtih the 5th of the chord - G - in the bass) is 6-4.
This is because there is a 4th (C) and a 6th (E) above the bass (G). (Notice that the bass note is not always the root of the chord!).
Let's reverse these two chords.
Notice that we don't have any sharps or flats in the key signature, so let's think of this in the key of C major. If we're thinking in the key of C, then we can see that the dominant (scale degree 5) is in the bass (G). The C chord is labelled I (because it is built on scale degree 1 - C), and the G chord is labelled V (because it is built on scale degree 5 - G).
This chord progression - I 6-4 --> V 5-3 - is quite famous in classical music and usually moves to the root position I.
It creates a grand closure in the form of a perfect cadence at the end of a section or movement of music. (Notice that I revoiced the chords, swapping tenor and alto parts. I couldn't help it - this sounds better. :-) )
If you want to really hear the effect of the I 6-4 chord, go listen to a Classical or Romantic era concerto. (I love Mozart piano concertos and recommend one of those.) At the end of the first movement, right before the soloist plays the cadenza, the orchestra works its way up to a I 6-4 chord, and then there is a grand pause. The I 6-4 chord needs to resolve to V 5-3. It is not settled in any way, and some might call that a dissonance. So the orchestra creates a big sense of expectation by pausing on I 6-4, and we lean forward on the edge of our seats (literally or figuratively). Cue the soloist, who at the time would have shown off their amazing improvisational skills by executing technical fireworks and dazzling thematic cartwheels in their own made-up cadenza. Now, many soloists play cadenzas that have been written down. Either way, most cadenzas end with a trill on a note of the V chord, under which the orchestra obligingly re-enters on V. This is followed by a great big final cadence and a resolution to the root position I chord. In this case, C is now consonant.
This progression features two C chords, but the voicing of these chords changes their sound and their function in the progression. And that's because...
What's in the bass counts. It colours everything we hear above it.
So whether you're a listener - a player - a composer/arranger - an improviser - a teacher, pay special attention to what is in the bass. If you do, you'll start to hear in glorious sonic technicolour!