Harmonizing the Diatonic Scale

Some people refer to it as "harmonizing the major scale" but I don't want to be too specific since we can harmonize any mode of the diatonic scale.

So what does it mean to harmonize you may ask. Well, it sounds a little complicated but it is just so amazingly simple. But first I have to introduce the concept of triads. A triad (or trichord) is a three note chord that can be stacked in thirds. This means that you start with the root, for example C. Then the next note above the root will be a major or a minor third, for example E which is a major third to C. The next note would be a minor third to E, which is a G. The note G is also what we call the fifth to the C. This is the C-major triad C-E-G. A C-minor triad would thus be C-Eb-G where Eb is a minor third from C and G is a major third from Eb, but G is still a fifth above C.
Interestingly if you take two minor thirds in a row you will get a diminished triad, e.g. C-Eb-Gb, and if you take two major thirds in a row you will get a augmented triad, e.g. C-E-G#.

These are the four basic triads:

Name         Interval steps   Formula   Example
Major        3-m3             R-3-5     C-E-G
Minor        m3-3             R-m3-5    C-Eb-G
Diminished   m3-m3            R-m3-d5   C-Eb-Gb
Augmented    3-3              R-3-a5    C-E-G#


Where "3" is a major third, "m3" is a minor third, "d5" is a diminished fifth (flattened fifth) and "a5" is an augmented fifth (sharpened fifth).


Furthermore, the names minor and major triads derive their names from the third and the diminished and the augmented triads derive their names from the fifth as can be clearly seen in the Formula column.


Understanding these triads are crucial! If you develop an ear for these triads then you will much more easily be able to distinguish colorations of these chords, e.g. dominant (7:th) chords, 9:th chords, 11:th chords etc. This is how chords normally are structured.


Now, I will extend these triads to include another third to construct another tertian or ladder of thirds with one extra note. Since the chord contains four notes it is generally referred to as a tetrad. Here I show the four tertian tetrads that you can construct:


Name             Interval steps  Formula    Example    Example name
Dominant 7:th    3-m3-m3         R-3-5-b7   C-E-G-Bb   C7
Major 7:th       3-m3-3          R-3-5-7    C-E-G-B    Cmaj7
Minor 7:th       m3-3-m3         R-m3-5-b7  C-Eb-G-Bb  Cm7
Half diminished  m3-m3-m3        R-m3-d5-b7 C-Eb-Gb-Bb Cø7 or Cm7b5

As you see, at this point the naming convention is a bit illogical. This was very frustrating to me but after a while I came to accept the convention. For me it is like the convention of the direction of current in electrical circuits, it is not logical that the current goes in the opposite way as the electrons wander but it just happened to be like that. Maybe there is a reason behind it but it is currently beyond me. When it comes to a major 7:th it is the 7:th that is "major" but when it is a minor 7:th it is the 3rd that is "minor". I don't have a better suggestion for naming though so this will have to do. :)

Furthermore, if you would construct the other four combinations of stacked thirds you would get the following tetrads:

• m3-m3-3 = R-m3-d5-7 = m/maj7 add♭5. (♭5 = d5. A very dissonant chord).
• m3-3-3 = R-m3-5-7 = m/maj7 (nice when used properly. I.e. Cm-Cm/maj7-Cm7).
• 3-3-m3 = R-3-a5-7 = 7♯5 (a nice jazz chord to "land on").
• 3-3-3 = R-3-a5-R = augmented triad.

Nuff said. The four triad colorations above have a very interesting property as you will see now. I will give you a task to solve! Hurray! Please don't cheat by looking further down in the blog post.

Task 1: Take the C-ionian mode ("C-major scale") C-D-E-F-G-A-B-C and chose only every other note, and only chose 4 notes. Write the 4 notes down (e.g. C-E-G-B) and move on to the next note D. Do the same with D and chose notes from the next octave in the mode when appropriate. Write down all chords for each corresponding note in the C-ionian mode listed above.

Task 2: For every chord you wrote down you should analyze what kind of chord it is. Is it a major 7:th? A half diminished perhaps? Write the name of the chord for every such chord (e.g. Cmaj7).

I hope you didn't cheat. :)

You should end up with the chords:

Name     Notes    

Cmaj7    C-E-G-B

Dm7      D-F-A-C

Em7      E-G-B-D

Fmaj7    F-A-C-E

G7       G-B-D-F

Am7      A-C-E-G

Bø7      B-D-F-A


Wow! Ain't this cool?
See the beautiful patterns? The notes lining up vertically in such a lovely way.
This is the harmonization of the C-ionian mode.

What is more interesting is that you can harmonize the D-dorian, the E-phrygian, the F-lydian, the G-mixolydian, the A-aeolian and the B-locrian in the exact same way (or in any key for that matter). It is just a matter of starting the progression above in another position!

I encourage you to play these chords on your instrument to hear the harmonization at work.

What is really cool about knowing all this is that you can very easily harmonize just about any song you listen to (if it is a simple pop song, jazz songs involve a little more work. Note that this theory is not applicable to atonal/"12-tone" music). Simply start with the tonic chord. Decide what key the song is in (I will explain a method for this in a later article). Then identify what mode it is. Is it major or is it minor (or is it phrygian? dorian? etc). Then just harmonize it and you will see that the chords will fit. There is only one thing more you need to know, and it is the concept of progressions. I will talk about this later. But for now, if you hear a song in C-major, then try play the first chord (Cmaj7) then the fourth chord (Fmaj7) and then the fifth chord (G7). Or simplify them by playing C, F, G7. At least now you know where the chords stem from!

Good luck!