Tertian harmony describes music and chords constructed with thirds. Based on the diatonic scale, and the basic concept of intervals, these thirds are either minor (an interval of 3 semitones) or major (an interval of 4 semitones). Tertian harmony forms the 4 triads of music as well as 8* of the most common seventh chords.
*There are 8 tertian seventh chords, but only 7 contain four distinct notes. We'll get to this later in our matrices.
A Closer Look At Tertian Harmony
A common way of describing tertian harmony is with the scale degrees of the Diatonic/Major Scale.
So let's look at the C Major Scale to get a better idea of what tertian harmony is:
What represents a third in this case?
A third interval is created in the diatonic scale with one note and another note 2 letter names above it.
In the case of C Major, E is the third of C (major since their interval is made of 4 semitones). If we take E as our next starting point, we'd have G as our third (minor as their interval is made of 3 semitones). So if C is our “first,” then D is our second, and E is our third. If we take E to be our first (Phrygian mode), then F will be our second, and G will be our third!
Playing C E and G together, we “stack” thirds. This is the basis of building chords with tertian harmony. This three note chord is called a triad. And more specifically a major triad.
By stacking three thirds starting on C, we'd have C E G B (C major seventh). This is called a “seventh chord.” It's referred to as a seventh chord because it has the seventh scale degree. In the case of C Major, our seventh scale degree is B, as we can see above.
We'll rewrite the diatonic C major scale in order of its thirds to better visualize how tertian chords are built:
- E is a third above C
- G is a third above E
- B is a third above G
- D is a third above B
- F is a third above D
- A is a third above F
- C is a third above A, completing the cycle
Looking deeper into the thirds, we can determine whether they are major or minor:
- E is a major third above C (4 semitone interval)
- G is a minor third above E (3 semitone interval)
- B is a major third above G (4 semitone interval)
- D is a minor third above B (3 semitone interval)
- F is a minor third above D (3 semitone interval)
- A is a major third above F (4 semitone interval)
- C is a minor third above A,(3 semitone interval) completing the cycle
So, now that we have a good idea of minor and major thirds, we can get into building chords with tertian harmony. We'll start with the most basic chords in music, the triads.
Let's Build Our Tertian Triads
Triads are built by stacking two thirds on top of one another. In the case of C Major, stacking C E G would give us a major triad; stacking D F A would give us a minor triad; stacking E G B would give a minor triad; so on and so forth. In other words, we play 3 notes: a root note; a third (minor/major) of that note; and a third of the third of that note (I may have just made it more confusing lol).
I like to use matrices to find out how many possibilities there are for tertian chords. In the case of triads, we have 2 possible options for third intervals (minor or major) and 2 intervals (3 notes) within the chord itself. Therefore, there are 2^2 = 4 different possibilities for triads. I have included the matrix below:
I find it to be easy to see the possible triads with the matrix, but I think it's equally, if not more, important to hear the possible triads! Here are audio clips of the four triads based on C:
C Diminished Triad: 1 ♭3 ♭5 – C E♭ G♭
C Minor Triad: 1 ♭3 5 – C E♭ G
C Major Triad: 1 3 5 – C E G
C Augmented Triad: 1 3 ♯5 – C E G♯
What do you think of the triads? The minor and major triads are much more common and much more consonant than the dissonant diminished and augmented triads. The diminished triad is dark and mysterious, while the augmented triad is almost too bright. The biggest reason for the consonance of the major and minor triads is the perfect fifth in the chord. And the diminished and augmented triads are dissonant because of their diminished and augmented fifth, respectively.
So it's fairly simple to think of the four triads: They're tertian, they have three notes, and there are only 4 possibilities!
taking tertian harmony one step further, we'll look into the tertian seventh chords.
Let's Build Our Tertian Seventh Chords
Tertian seventh chords are built by stacking 3 consecutive thirds together instead of 2. Seventh chords are 4-note chords with scale degrees 1 3 5 and 7, hence their name.
Most of the time, due to the popular use of the diatonic scale, seventh chords are tertian, but that is not always the case. In some scales the scale degrees can be spaced in such a way that their thirds are not major or minor (more on this later).
For now, let's look at the possibilities of our tertian seventh chords. We have 2 possible options for third intervals (minor or major) and 3 intervals (4 notes) in a seventh chord. Therefore, we have 2^3 = 8 different possibilities for seventh chords. I have included them in the matrix below:
And here they are in audio:
C Full Diminished Seventh Chord:
1 ♭3 ♭5 ♭♭7 – C E♭ G♭ B♭♭
C Half Diminished Seventh Chord:
1 ♭3 ♭5 ♭7 – C E♭ G♭ B♭
C Minor Seventh Chord:
1 ♭3 5 ♭7 – C E♭ G B♭
C Minor Major Seventh Chord:
1 ♭3 5 7 – C E♭ G B
C Dominant Seventh Chord:
1 3 5 ♭7 – C E G B♭
C Major Seventh Chord:
1 3 5 7 – C E G B
C Augmented Major Seventh Chord:
1 3 ♯5 7 – C E G♯ B
C Augmented Augmented Seventh Chord:
1 3 ♯5 ♯7 – C E G♯ B♯
*Note that the Augmented Augmented Seventh has a ♯7. This is enharmonic (sounds the same) as a perfect octave! For this reason, it's rarely considered a seventh chord, and instead as an augmented triad.
What do you think of the (7) tertian seventh chords? There's a lot of colour and inner consonances/dissonances, making them interesting choices in chord progressions!
Recap On Tertian Triads And Seventh Chords
So now we know how to build triads and tertian seventh chords. It's interesting to note that as we stack thirds, the variation in our scale degrees expands. We have one root (the note the chord is based on); either a minor third or major third; a diminished, perfect, or augmented fifth; and a double-flat, minor, major, or augmented seventh.
In other words, we have more variety the further away our scale degree is from 1:
- first – one option – 1 (the root of the chord)
- third – two options – ♭3 or 3
- fifth – three options – ♭5, 5, or ♯5
- seventh – four options – ♭♭7, ♭7, 7, or ♯7
This raises a big question:
Can we use non-diatonic scales and thirds based on their scale degrees to build tertian chords?
Tertian harmony has been explained to me using the scale degrees of the major scale, but the major scale doesn't even include all the triads and only 4 of the *7 tertian seventh chords.
We can find these tertian chords in other heptatonic scales based on their scale degrees. And we find even more of these tertian chords with enharmonic scale degrees. For example, if we take the Harmonic Major Scale's 1 3 ♭6 7, we have an augmented major seventh chord, since ♭6 is enharmonic to ♯5.
With our options for scale degrees, we could write out a seventh chord with scale degrees 1 3 ♭5 7. This particular chord has the intervals (in order) of a major third, diminished third, augmented third. According to scale degrees, these are indeed thirds, but they are not exclusively minor and/or major. This may be a ridiculous example, but it poses perhaps a better question:
Are tertian chords based on thirds of scale degrees, or only by true minor and major third intervals?
Tertian chords are built by stacking only minor thirds (3 semitone intervals) and/or major thirds (4 semitone intervals) regardless of what the scale degrees tell us the “thirds” are. The scale degrees are simply a useful reference when harmonizing a scale into chords. We are really only concerned with the sound of the intervals when building tertian chords, rather than written scale degrees. Here are some examples of triads with “improper” scale degrees:
- 1 ♭3 ♯4 is a diminished triad (♯4 is enharmonic to ♭5)
- 1 ♯2 5 is a minor triad (♯2 is enharmonic to ♭3)
- 1 3 ♭6 is an augmented triad (♭6 is enharmonic to♯5)
Another reason for my answer is that these non-tertian scale degree combinations just aren't that common in western music. I like using exotic scale and modes, so I think about these things. But if we take the most common heptatonic scales (Major, Melodic Minor, Harmonic Minor, or Harmonic Major) we'll see that not even 1 of their combined 28 modes contains a non-tertian triad or seventh chord by looking at their scale degrees.
It's only when we start introducing two consecutive semitones in our scales that tertian harmony does not coincide with our scale degree framework. Shout out to the Double Harmonic Major and Enigmatic Scales 😉
At the end of the day, it's all about what the chord sounds like, and tertian chords sound great! We hear them all the time in western music.
I hope this sheds some light on tertian harmony and tertian chords. So much music is based on tertian harmony that you most likely already knew it! I know I used it almost exclusively until I started delving into music theory. It's fun to put these chords into words and to see all the possible outcomes of stacking minor and major thirds.
As always, thanks for reading and for your support!