Triads


Music can be thought of as being made up of melody, harmony, and rhythm.

Harmony is the part of music of a particular instant in time and how more than 1 sounding body interact with each other. To make that simpler harmony is how 2 or more pitches sound together at the same time.

Chords are harmonic structures of 3 or more notes. Those minimum 3 notes are generally required to be distinct (octaves and enharmonic notes would not count with dtermining if a structure was a chord or not).

Triads are 3 note chords (Dyads are 2 note harmonic structures, tetrads are 4 notes, etc.).

We consider 4 basic triads that are fundamental to understanding the modern music we hear, and the tonal context in which it occurs. they are: major triad, minor triad, diminished triad, and augmented triad. (We will not consider the legitimacy of other possible triads at this time).

Triads from stacked 3rds
We recall from our intervals that
a M3 = 4 semitones (4 half-steps), and
a m3 = 3 semitones (3 half-steps)

What happens if we stack (superpose) 2 intervals of a 3rd? We create one of the 4 triad types.

ex. take the M3 from C to E and stack a minor 3rd from E to G on top. This creates a C major triad. And any major triad can be reduced to the form:

minor 3rd                    G
--------- = major triad      E = C major triad
major 3rd                    C

Stacking other combinations of 2 stacked 3rds (superposed) creates the other triad types.

In general,

major 3rd                    G
--------- = minor triad  (m) Eb = C minor triad
minor 3rd                    C

minor 3rd                          Gb
--------- = diminished triad  (o)  Eb = C diminished triad
minor 3rd                          C

major 3rd                       G#
--------- = augmented triad (+) E = C augmented triad
major 3rd                       C

We note that these structures are basically the same as their chord counterparts. We typically use the chord names (Am chord rather than Am triad) in practice, and generally use the term triad in our theory classrooms. The term chord is much more broad than the term triad, and has less restrictions. Understanding the much more restrictive idea of the triad establishes a foundation to understand other chords and harmonic structures.

Looking at the triads/chords from a set-theoretic point-of-view, we define by intervals the four triads as:
major = 1,3,5
minor (m) = 1,b3,5
diminished (o) = 1,b3b5
augmented (+) = 1,3,#5

Connecting chords to scales
We can create chords from scales by stacking the scale in 3rds.
Stacking the major scale in 3rds gives.

|--------------------------|
|                       O  |
|--------------------O-----|
|                 O     O  |
|--------------O-----O-----|
|           O     O        |
|--------O-----O-----------|
|     O     O              |
|--O-----O-----------------|
      O
 --O--
  M3 m3 m3 M3 M3 m3 m3 M3
   1  2  3  4  5  6  7  8(1)

Stacking again gives:

                        O
|--------------------O-----|
|                 O     O  |
|--------------O-----O-----|
|           O     O     O  |
|--------O-----O-----O-----|
|     O     O     O        |
|--O-----O-----O-----------|
|     O     O              |
|--O-----O-----------------|
      O
 --O--
  m3 M3 M3 m3 m3 M3 m3 m3
  M3 m3 m3 M3 M3 m3 m3 M3
  C  Dm Em F  G  Am Bo C
   M  m  m  M  M  m  o M
  I ii iii IV V vi viio VIII(I)

We can represent the triads by Roman numerals. An uppercase numeral is a major chord (triad), a lowercase numeral is a minor triad, a lowercase numeral with a degree sign after it is a diminished triad, and an uppercase numeral with a plus sign is an augmented triad (there are no augmented triads in the example above).

So if we had a I-IV progression (such as C-F) we could see it as a major scale progression, and possibly create a melody from the major scale to go along with it.

Looking at the 3 minor scales we considered (natural minor, harmonic minor, and melodic minor) we see they can be harmonized to create the following triads:

Natural minor

|--------------------------|
|                       O  |
|--------------------O-----|
|                 O     O  |
|--------------O-----O-----|
|           O     O     O  |
|--------O-----O-----O-----|
|     O     O     O        |
|--O-----O-----O-----------|
      O     O
 --O-- --O--
      O
 --O--

  M3 m3 m3 M3 M3 m3 m3 m3
  m3 m3 M3 m3 m3 M3 M3 M3
  Am Bo C  Dm Em F  G  Am 
   m  o  M  m  m  M  M  m  
 i iio bIII iv v bVI bVII viii(i)

Harmonic minor

|--------------------------|
|                       O  |
|--------------------O-----|
|                 O     O  |
|--------------O-----O-----|
|           O     O     O  |
|-------#O----#O----#O-----|
|     O     O     O        |
|--O-----O-----O-----------|
      O     O
 --O-- --O--
      O
 --O--

  M3 m3 M3 M3 m3 m3 m3 m3
  m3 m3 M3 m3 M3 M3 m3 M3
  Am Bo C+ Dm E  F  G#o Am 
   m  o  +  m  M  M  o  m 
 i iio bIII+ iv V bVI viio viii(i)

Melodic minor

|--------------------------|
|                       O  |
|--------------------O-----|
|                 O     O  |
|--------------O-----O-----|
|           O     O     O  |
|-------#O----#O----#O-----|
|    #O    #O    #O        |
|--O-----O-----O-----------|
      O     O
 --O-- --O--
      O
 --O--

  M3 M3 M3 m3 m3 m3 m3 m3
  m3 m3 M3 M3 M3 m3 m3 M3
  Am Bm C+ D  E  F#o G#o Am 
   m  m  +  M  M  o  o  m 
 i ii bIII+ IV V vio viio viii(i)

Scales can be defined by the type of triad built off their root note. The major scale is a major scale because you can build a major triad off the root note (it contains I). The minor scales above all minor scales because they contain a minor triad off the root note (i).

Triad Inversion
Like intervals, triads can be inverted by moving one of the notes past the other into a different octave.

The triads created above are all in "root postion". Moving the root note above the 3rd and 5th, we have the "1st inversion" (the 3rd is in the bass). Taking the 1st inv. and moving the 3rd up an octave we have the "2nd inversion" (the 5th is in the bass).

C major triad

|-------------------|
|              O    |
|-------------------|
|        O     O    |
|-------------------|
|                   |
|--O-----O-----O----|
|                   |
|--O-----O----------|
      
 --O--
Root    1st   2nd
position inv  inv

Next lesson is on Form and Style.

Peace,
Christopher Roberts
snglstringtheory@aol.com


How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

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Last updated May 8, 2003
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