Lesson 17: Chords and Roman Numerals

We studied all about tonic and dominant triads in Lesson 15. You learned that a triad is a three-note chord in which there exists a root, 3rd and 5th. Here is a 'C' triad, made up of three notes, a 'C', 'E' and 'G':

  

In this triad, the bottom note is the root (1), the middle note is the 3rd, and the top note is the 5th. We know this to be true because if we start on the bottom note and start counting upward from 1, the 'E' in the middle would be '3', and the 'G' on the top would be '5'.

If we look at the structure of this triad, we would see that it is a major triad. Here is why: In each triad there are two intervals to consider:

1- The outer interval
2- The bottom interval

The outer interval is a 5th: if you start on 'C' and count upward until you hit the 'G', you will have counted to 5. What kind of 5th is it? Ask yourself that question, "Is the upper note in the major scale of the bottom note? (Is there a 'G' in a 'C-major' scale?) The answer is yes, so this is a perfect 5th. Now for the bottom interval. This interval is a 3rd. If you start on 'C' and count upward until you hit the 'E', you will have counted to 3. What kind of 3rd is it? ("Is there an 'E' in a 'C-major' scale? The answer is yes) This is a major 3rd. So now we have determined that this triad is comprised of a major third on the bottom, with the outer interval being a perfect fifth. This makes it a major triad:

Hear the perfect 5th:     Hear the major 3rd:     Hear them together:  

Although we dealt only with tonic and dominant triads in Lesson 15, we can actually build triads on any note of a scale. Here is a C-major scale:

  

We can build triads on every one of these notes, using the notes of the scale as the root of each triad. Here's what it looks like:

  

Now we need to examine each triad to determine whether they are major, minor, or something else. We already know that the first triad, built on 'C', is major. That's why there is a '+' underneath it.

Let's take a look at the second triad, the one built on 'D':    Again, the outer interval is a 5th, and it is a Perfect 5th (Yes, there is an 'A' in a D-major scale). The bottom interval is a 3rd, but it is a minor 3rd (No, there is no 'F' in a D-major scale. There is an 'F#', and so this interval is actually a minor 3rd.) This triad is a minor triad. Minor triads have a minor 3rd on the bottom, with an outer interval of a Perfect 5th:

  

If you keep going through the major scale and examining the triads that are built on each scale tone, you will see that except for the triad built on the 7th note (the 'B' in a C-major scale), they are all either major or minor triads. Here's what we come up with (Major chords are indicated with a '+' sign, minor chords with a '-' sign):

  

Now for that triad built on the 7th note. It has an outer interval of a 5th, but you can see that it is actually a diminished 5th (No there is no 'F' in a B-major scale... there's an 'F#', so this 5th is diminished). The bottom interval is a 3rd, and a quick examination will tell you that it is a minor 3rd. Any triad which consists of an outer interval of a diminished 5th and a bottom interval of a minor 3rd is called a diminished triad:

  

A diminished triad is different from a minor triad by the fact that a diminished chord has an outer interval of a diminished 5th: the minor triad has a perfect 5th.

Here is an important table of information. Study it carefully:

We can use Roman Numerals to describe all of these triads. We did this in Lesson 15 when dealing with tonic and dominant chords. For example, in the triads shown above, the note 'C' is the first note of the C-major scale. Therefore, we assign the number '1' to that chord. When describing chords using numbers, it is traditional to use Roman Numerals. It is also traditional to use upper-case letters for major and augmented chords, and lower-case letters for minor and diminished chords. Here are the triads of a C-major scale, properly numbered:

  

Now you can see that we can identify triads by their Roman Numeral. In C-major, the C-major chord is a I-chord. The D-minor chord is a ii-chord. The E-minor chord is a iii-chord, etc. Which chord is the vi-chord? Answer: the A-minor chord. This process works, of course, in any key. The vi-chord in F-major is a d-minor chord. The iii-chord in D-flat major is an F-minor chord, etc.

As you know, each scale degree, whether we are dealing with major or minor, has a technical name associated with it. We can apply these technical names to the triads that are built on them. For example, the first note of a scale is the tonic note. If we build a triad on the tonic note, it is called a tonic triad. You already know that from Lesson 15. The supertonic note is the second degree of the scale. The triad built on the supertonic note can be called the supertonic triad, and so on. Here is the subdominant triad of G-flat major:      The submediant triad of C-major:     The supertonic triad of F-major:    Simple, isn't it?!

There is one other type of triad, which will show up in the building of triads on the notes of harmonic minor scales. It is the augmented triad. An augmented triad consists of an augmented 5th as an outer interval, and a major 3rd as a bottom interval. Here is one:

  

So here are the four types of triads, in a nutshell:

TYPE OF TRIAD:	DESCRIPTION:	WHAT IT SOUNDS LIKE:
MAJOR:	Outside interval is a Perfect 5th; bottom interval is a Major 3rd
MINOR:	Outside interval is a Perfect 5th; bottom interval is a Minor 3rd
DIMINISHED:	Outside interval is a Diminished 5th; bottom interval is a Minor 3rd
AUGMENTED:	Outside interval is an Augmented 5th; bottom interval is a Major 3rd.

(In one school of thought it is customary to place a small 'o' after the 'vii' to indicate that the triad is 'diminished'. Similarly, some musicians place a "+" after an augmented triad. This course will not require any such indication. You will be required, however, to indicate the quality of a triad with such symbols as an exercise, as a way of indicating that you understand the structure and quality of a triad.)

Armed with your knowledge of triads, and how to determine quality (major minor, augmented diminished), place the Roman Numeral underneath each triad shown above. Then indicate the quality of each triad by placing a "+" for major, "-" for minor, "o" for diminished, or "X" for augmented underneath each Roman Numeral. Get your teacher to check your answers, or click here.

• Define the following: major triad, minor triad, augmented triad, diminished triad.
• Determine the quality of an interval by examining the outer interval and the lower interval.

Assign a Roman Numeral to a triad.