Triads are the basic harmonic structure in most musical styles. A triad is simply three different letter names played at the same time. Although there are many different possible combinations of notes to create triads, traditionally the study of triads is limited to four different structures. This lecture will discuss these four triadic structures plus a couple of others whose use have become quite common. Before getting into the lecture just a short mention about some terminology. The term 'chord' is often used in the discussion of harmony and sometimes this term is used interchangeably with the term triad. The term 'chord' is a more general term meaning two or more notes played as a harmonic structure. A triad is specifically a three note chord. All triads are chords yet due to the specific nature of triads, not all chords are triads. Although a chord is often a more complicated structure than a triad, it is common to refer to a triad using the term 'chord'.
Combining the first, third and fifth notes of a major scale creates the correct interval structure for a MAJOR TRIAD. Let's examine the intervals found in a major triad. Notice that the triad is created by stacking up the interval of a third upon another third. The stacking of thirds is basic to constructing triads. The lowest note of the triad is called the ROOT The other notes have logical names: The middle note is called the THIRD and the highest note is called the FIFTH.
Notice the interval structure of the triad:
All major triads have this structure. It is the "formula" for a major triad.
When starting on the fourth scale degree of a major scale and stacking up a couple of thirds you can create another major triad. The chord tones use the terms ROOT, THIRD and FIFTH as before, but in this case the root is F, the third is A, and the fifth is C. Another major triad can be created at the fifth scale degree of a major scale. The major scale contains three different major triads.
Hey, wait a minute what about the triads build on the other scale degrees, aren't they major triads also? This is the major scale isn't it?
No and Yes.
No, not all of the triads in a major scale are major triads but YES this is a major scale we are talking about. Let me repeat that idea: Not all of the triads in a major scale are major triads. Don't confuse a scale with a triad. A scale is a set of notes from which we can create several different triads. When using a major scale we can create 3 different major triads. This is important, let me say it once more. This time I'll use the word "chord" instead of "triad". Not all of the chords in a major scale are major chords. Of the seven different chords we can create from a major scale only three are major chords. These three major triads are built on the first scale degree, fourth scale degree, and fifth scale degree. You should MEMORIZE THIS. These are referred to as the 'Primary Chords' of the key. Often we use roman numerals to refer to chords. We refer to a chord built on the first scale degree as a "I chord". A chord built on the fourth scale degree is called a "IV chord", one built on the fifth scale degree is called a "V chord" and so on. (This type of naming system allows one to think in terms of chord progression formulas that can be applied to a variety of keys. This topic is introduced in our last lecture in this course.)
There are specific letter names also given to each chord but the roman numeral name reveals the chord's relationship to the key. Now, here is the same idea restated with roman numerals. In a major scale the I, IV, and V chords are major chords. This is true for every major scale on the planet earth. The I, IV and V chords in the key of C are C, F and G respectively. A capital letter is used to indicate a major triad (C = C major triad). Some systems use Cmajor, Cmaj or Cma. Sometimes CM. In the interest of brevity I prefer simply "C".
So if three of the triads are major, what are the other four? Now it gets good.
In addition to the major triad we will also examine the construction of the minor, augmented and diminished triads. First let's look at the triad built on the second scale degree, (the II chord in the key of C is rooted on D). This graphic, and several others in this lecture, show the notes spread across the page. This "broken chord" is called an arpeggio. It is common in music for a chord to be arpeggiated although it is usually a faster note value such as an eighth note or sixteenth note.
here is an analysis of the intervals:
This is called a minor triad. The "II chord" in a major scale is a Minor triad. This is true for all major keys. Really.
Notice that a minor triad has a minor 3rd from the Root to the Third. Conversely, a major triad has a major 3rd from the Root to the Third. Both have a perfect Fifth from Root to Fifth. Think about this for a while, this is handy information: Major triads have major 3rds from the root. Minor triads have minor 3rds from the root. Both have perfect fifths from the root.
Also of interest (to me anyway) is that major triads embody the interval of a minor 3rd (from the third to the fifth) and conversely, a minor triad embodies the interval of a major 3rd (from the third to the fifth). Cool, you get both types of thirds with either triad. It may not be apparent why that is useful but it means that many melodies of a major scale could be harmonized with both major or minor chords each with its own unique emotional effect. You would learn about that sort of thing in a later theory course, it's beyond this course so I'll move on.
So, are the rest of the triads also minor triads?
Let's examine each one. Built on the third scale degree we have a triad that matches the minor formula (the III chord in the key of C is rooted on E).
The III chord in a major key is a minor triad. In all of the major keys the III chord is minor.
We already covered the IV and V chords, they're both major.
On to the VI chord (the VI chord in the key of C is rooted on A).
It checks out as a minor triad. The VI chord in every major key is a minor triad.
One more to go the VII chord (the VII chord in the key of C is rooted on B). Let's look carefully.
Hmm, it's neither a minor triad nor a major triad. You can probably deduce that this one is the "Diminished triad". The VII chord of every major key is a diminished triad.
These are all the triads in a major scale. We call these the "diatonic chords" of the key. Notice the following pattern. Every major scale embodies these triads in this exact order. It is worth memorizing. I'll wait while you stare at this for a moment.
| I | II | III | IV | V | VI | VII |
| Major | Minor | Minor | Major | Major | Minor | Diminished |
Chant the mantra:
Major, Minor, Minor, Major, Major, Minor, Diminished.
When using roman numerals many people use upper case to indicate a major triad and lower case to indicate minor triads. Additionally, upper case with a '+' sign indicates an augmented triad and lower case with a 'o' indicates a diminished triad. Although I have not used this system, you should be aware of this system because many music theory books use it. Here is how the major scale triads would look using this system:
| I | ii | iii | IV | V | vi | viio |
| Major | Minor | Minor | Major | Major | Minor | Diminished |
In addition to using roman numerals, each scale degree has a name. If you want to fill your brain with more info, memorize this also. Even if your brain is full, at least memorize the names for the I, IV and V chords. The names tonic, subdominant and dominant are commonly used and you should become familiar with their meaning.
| Tonic | Supertonic | Mediant | Subdominant | Dominant | Submediant | Leading tone |
| I | II | III | IV | V | VI | VII |
| Major | Minor | Minor | Major | Major | Minor | Diminished |
There is still one more basic triad: the "Augmented triad". It is not diatonic to a major scale but it is diatonic to both the harmonic and melodic minor scales as a III chord. Using the above mentioned system, the augmented triad would be indicated like this: III+, an upper case roman numeral with the '+' symbol. While this system is common, I generally do not use it for my own work. I won't use it in this lecture. Well actually, I guess I just did. Just keep it in mind, if and when you see this system somewhere else.
Here is the formula for the Augmented triad:
It is easy to create an augmented triad by starting with a major triad and then raise the fifth one half step. The first measure below shows the notes of a C major triad, the second measure shows a C augmented triad.
Another way of creating an augmented triad is to start with a minor chord and lower the root one half step. The first measure below shows the notes of a D minor triad, the second measure shows the Db augmented triad.
There are several other combinations of three different tones that could be (and are) used to create music. Two of the more common of these additional structures are called "sus chords". The sus4 chord replaces the third of the triad with a fourth. As an example, the Csus4 chord contains the notes C, F and G. It is used in Rock, Jazz, Classical, Pop, Country, Hi-Hop, pretty much anywhere good music is found. Keep in mind that although these triads have been shown in arpeggiated form, they can also be played as a block chord (all notes at the same time).
Another is the sus2 chord. The sus2 chord replaces the third with the second. A Csus2 chord contains the notes C, D and G. It is a common replacement for a major triad in some styles. U2 and The Police used it alot. Bruce Hornsby likes it. It is fairly common, it should be a part of every contemporary musician's harmonic vocabulary.
We've already discussed the triads within a major scale. I'll show the diatonic triads in major again.
| I | II | III | IV | V | VI | VII |
| Major | Minor | Minor | Major | Major | Minor | Diminished |
Now let's examine the triads in the minor scales.
For natural minor the diatonic chords are as follows:
| I | II | III | IV | V | VI | VII |
| Minor | Diminished | Major | Minor | Minor | Major | Major |
The order of the triads is different form the order in the major scale. You might notice however that there are 3 major triads, 3 minor triads and 1 diminished triad, just like in major. Upon closer examination you will see that the order is related to the order of the triads in major yet it starts at a different place. Let me explain. In major the order of triads is Major, Minor, Minor, Major, Major, Minor and Diminished. You can create the order of the minor triads by starting on the last Minor and continue to the Diminished then jump back to the beginning and finish it off in order.
The order of triads in a major key:
major minor minor major major minor diminished
(start here
to create the order
for nat. minor)
the order of triads in natural minor
|----- the first five triads in major ------|
minor diminished major minor minor major major
pretty cool, huh? we'll revisit this kind of idea next week with modes.
The scale degrees in minor also have names. The names are the same as the ones in major with the exception that in the natural minor scale the VII chord is referred to as the Subtonic chord (not the Leading Tone chord). In the harmonic and melodic forms the name Leading Tone is used instead of Subtonic because the 7th note is different in those forms compared to natural minor. So, what is the difference between subtonic and leading tone? A leading tone is one half step below the tonic, a subtonic is a whole step below the tonic. Now you know, but do you care? One of the reasons I prefer using roman numerals instead of the names is that with roman numerals all of the forms refer to this chord as a VII chord. I like consistency. I'm well aware of the differences in the minor forms but l like keeping the same symbols for the chords of the different minor forms.
| Tonic | Supertonic | Mediant | Subdominant | Dominant | Submediant | Subtonic |
| I | II | III | IV | V | VI | VII |
| Minor | Diminished | Major | Minor | Minor | Major | Major |
Here are the triads in C natural minor.
For harmonic minor the diatonic chords are as follows:
| Tonic | Supertonic | Mediant | Subdominant | Dominant | Submediant | Leading tone |
| I | II | III | IV | V | VI | VII |
| Minor | Diminished | Augmented | Minor | Major | Major | Diminished |
Here are the triads in C harmonic minor. A natural sign is needed to raise the 7th scale degree. Notice the III chord is augmented.
For melodic minor the diatonic chords are as follows:
| Tonic | Supertonic | Mediant | Subdominant | Dominant | Submediant | Leading tone |
| I | II | III | IV | V | VI | VII |
| Minor | Minor | Augmented | Major | Major | Diminished | Diminished |
Here are the triads in C melodic minor. A natural sign is needed to raise both the 6th and the 7th scale degrees to create the melodic minor form. Once again the III chord is augmented.
Are you curious why we don't have harmonic and melodic minor key signatures? Me too. I've seen a piano piece by Bela Bartok that uses a harmonic minor key signature of Bb and C# to indicate D harmonic minor. Does that ring a bell? This is not common however. Generally the only minor key signatures used are the traditional natural minor signatures and any needed changes are made with accidentals. One reason may be that in minor keys it is common to use more than one of the forms in a composition so you would have to use accidentals regardless of what minor key signature was used.
The first MIDI file plays the triads in ascending order up one full octave: I II III IV V VI VII I. This is the same as the Major scale graphic shown in the previous section. Then it plays the chords in descending order: I VII VI V IV III II I.
Open MIDI file
Open mp3 file
Play file
The second MIDI file uses the same pattern but this time the pattern is applied to the three forms of Minor: Natural Minor, Harmonic Minor, Melodic Minor. Use the graphics from the previous section to see the triads in ascending order.
A change in sound is made to each minor form so that it is easier to hear the different forms of minor. The natural minor triads are played using a string sound, the harmonic minor triads are played using an organ sound and the melodic minor triads are played using a voice sound.
Open MIDI file
Open mp3 file
Play file
So far we have seen and heard the chords in "Root Position". Root position refers to the Root being the lowest note of the chord. It is possible to use either the third or the fifth of the triad as the lowest note of a chord. These are called inversions.
First inversion
A "first inversion" triad has the third of the chord in the bass (the lowest note). Notice the spacing of the notes, there is an interval of a third on the bottom and an interval of a fourth on the top. The interval of a sixth spans the outside notes. Any of the triad types can be inverted.
They're are two ways of indicating an inversion with symbols. The traditional way uses arabic numbers along with roman numerals. The numbers 6 and 3 represent the intervals of a sixth and a third which are found in a 1st inversion triad. As an abbreviation, the number 6 alone is used. When the number 6 is attached to a roman numeral it indicates that a specific chord within the scale system is in 1st inversion. Example, I6 and V6, indicate that the tonic chord is in 1st inversion and the dominant chord is in 1st inversion.
A second way to indicate the inversion is with Chord symbols. These letter names are sometimes called "Pop chord symbols" because this system of chord notation is included in sheet music of popular music. The letter name of the chord (described earlier) is followed by a slash then another letter indicating the name of the bass note. As an example, the symbol C/E indicates a C major chord (remember, a capital letter alone means major) with the note E in the bass. This notation does not tell if this is first inversion, it merely tells you that some note other than the root of the chord is in the bass. As it turns out the example "C/E" IS in first inversion but this same notation can be used for many different comibinations of chords and bass notes. I refer to this type of chord notation as the "Chord/Bass" symbol.
Second inversion
We can flip the chord around one more time to create the "second inversion". A second inversion triad has the Fifth of the chord in the bass. The spacing changes to a fourth on the bottom, and third on top and a sixth between the outside notes.
Using traditional classical notation the numbers 6 and 4 are used to indicate second inversion. This is because of the sixth and the fourth intervals measured for the bass note. These numbers are attached to roman numerals to indicate a chord in 2nd inversion. The 6 is usually placed above the 4 as shown below.
| IV | 6 4 |
This symbol means the subdominant chord (the IV chord) is in 2nd inversion. Of course, the letter name of the chord will be different in each key. In the key of C this means the IV chord (F major) has its fifth (the note C) in the bass. In the Key of D the IV chord is G and its fifth (the note D) would be in the bass. The roman numeral system is not tied to any specific key, therefore, before you can discuss any specific chord letter names, you must first give a key context. The term "IV chord" begs the question "In what key?".
The traditional roman numeral system with a specific key context can always be translated into a Chord/Bass symbol. Here are some examples using both 1st and 2nd inversion.
| I | 6 | In the Key of C this mean C/E - In the key of G this means G/B - In the key of F this means F/A |
| IV | 6 4 | In the Key of C this mean F/C - In the key of G this means C/G - In the key of F this means Bb/F |
The spacing of the notes of the chord is known as the "voicing". We have been examining close voicing chords but they can be spread out to create open voicings. The standard open voicing is created by moving the center note up one octave. This technique can be applied to any inversion.
This is shown in both treble and bass clefs.
It is common to use a four voice texture when studying harmony. If the prevailing chord structure is a triad, then three of the voices take the Root, Third and Fifth and the remaining voice will double one of the chord tones. The most common note doubled is the Root, however doubling either the third or fifth is possible.
The following MIDI file uses a standard chord Progression using a minor scale. The first three chords are from natural minor, the fourth chord is from harmonic minor. This short harmonic idea is played using a variety of inversions and voicings. You probably have heard several songs that use this type of chord progression, its been around for centuries. The progression is played seven times through. The first time in root position/close voicing, the second time in root position/open voicing, the third and fourth time use 1st inversions both in close voicing and open voicing. The fifth and sixth are using 2nd inversion first with close voicing and then with open voicing. The last repetition is in a four voice texture with the bass doubling the root of each chord. Notice that the bass is moving in the opposite direction of the upper three voices. This type of voiceleading is known as "contrary motion" between the bass and the upper voices. Contrary motion is a common voiceleading practice.
Music education has some funny traditions. One such tradition is a type of indoctrination regarding parallel fifths. Parallel fifths occur when two voices which are a perfect fifth apart move in the same direction and the exact same distance. "Serious" music theory books from the last century tell you it is wrong and sounds bad. For reasons unknown to me, traditional music theory education has held on to that idea. What do you think, there are parallel fifths in 6 of the following 15 measures. Can you tell which ones? Do they sound bad compared to the other measures? The measures that contain parallel fifths are 1,2,3,4,7 and 8. I think the notion of parallel fifths being undesirable is silly. Of course I was brought up on Rock & Roll and that style has plenty of parallel fifths so I'm quite used to the sound.
The chord progression in roman numerals is I - VII - VI - V, the key is A minor (mixture of natural and harmonic).
Open MIDI file
Open mp3 file
Play file
Other Reading:
Required Test 12 and Midterm 2 are in the Quizzes area.
Below is a sample from the tests for this week. This IS NOT the actual test but instead a short example from the test so that you can get an explanation of how to take it and the "look and feel". To take the real test you must go to the Quizzes area.
Below are several triads shown in arpeggiated form. Analyze the intervals of the triads and determine the quality (major, minor, augmented or diminished) of the triad. Click on the button next to the correct quality for each triad.
In the 1st example, the root (F#) to the 3rd (A#) is a Ma3. The root (F#) to the 5th (C#) is a P5. It is a major triad.
In the 2nd example, the root (D#) to the 3rd (F#) is a Mi3. The root (D#) to the 5th (A) is a d5. It is a diminished triad.
In the 3rd example, the root (G#) to the 3rd (B) is a Mi3. The root (G#) to the 5th (D#) is a P5. It is a minor triad. The third menu is set to the correct answer.
   
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What is the quality of the above Triad? |
What is the quality of the above Triad? |
What is the quality of the above Triad? |