Harmonizing the major scale (triads)


Recall, that an interval is the distance between two notes.

Recall, that the smallest interval in the western system we are using is the 1/2-step. It is the distance between to two adjacent frets.

Recall the following equivalencies:
a major third (3) = 4 half-steps
a minor third (b3)= 3 half-steps
a perfect fifth (5) = 7 half-steps
a diminished fifth (b5) = 6 half-steps

Let's look for a second at standard notation for music. The following is a treble clef, with letters written on the lines and spaces where those notes are written in the forms of whole notes (circles), half-notes (circles with an attached line and no flag), quarter-notes (filled in circles with lines but no flags), eighth notes (filled in circles with a line and one flag), etc.

      G 
|-F-----
      E 
|-D-----
      C 
|-B-----
      A 
|-G-----
      F 
|-E-----
      D 
 -C-

Recall, the major scale in the key of C is the notes C-D-E-F-G-A-B-C. The major scale's step pattern is WW1/2WWW1/2, and it's intervals (in numbers) are 1,2,3,4,5,6,7.

In standard notation, the C major scale:

|-------------------------------

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

Ok. So what are we discussing today? How to harmonize a scale in thirds. what the heck does that mean? Turning scales into chords and finding chords that will go with scales.

I'm assuming that you're familiar with the major scale, major chords, minor chords, diminished chords, and intervals in general. If not, feel free to refer back to the lessons on these. I will make this as clear as possible, but will not spend time rehashing these concepts. I'm also assuming a familiarity with keys. If you're still figuring keys out or haven't yet, you may find a transposition chart handy. there is a URL for one at the bottom of the page.

Ok. Looking backup at the staff those circles are whole notes, but for our purposes here they are place holders and do not represent any rhythm during this discussion.

Now, we will be harmonizing the C major scale in thirds. What does this mean? take the above scale, and stack it again on top of itself, starting with the 3rd note (E). So the 3rd note is stacked on top of the 1rst note, the 4th note is stacked on top of the 2nd note, etc. And we get:

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


We now have a list of intervals (3rds) built off the major scale. Analyzing these thirds we find that they are specifically:
C to E = 3
D to F = b3
E to G = b3
F to A = 3
G to B = 3
A to C = b3
B to D = b3
(you could have figured these out with a familiarity of keys, or by using a transposition chart, or by counting half-steps between notes)

Alright next we repeat the process taking the third note in the scale from the top note shown above (G) and stack the scale on top of the previous two, we get:

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

We could call these stacked thirds "superposed thirds". that would be a technical term, for when you have stacked thirds where the higher note of the bottom third is the lower note of the top (or next) third. In simpler terms, what we have just created is a list of chords, specifically triads. a triad is a three note chord. Analyzing the top notes (5ths), we find the following:
C to G = 5
D to A = 5
E to B = 5
F to C = 5
G to D = 5
A to E = 5
B to F = b5

Recall the following definitions of these chords:
major chord = 1,3,5
minor chord = 1,b3,5
diminished chord = 1,b3,b5

Now looking at the triads we just made we have:
C-E-G = 1,3,5 = major chord
D-F-A = 1,b3,5 = minor chord
E-G-B = 1,b3,5 = minor chord
F-A-C = 1,3,5 = major chord
G-B-D = 1,3,5 = major chord
A-C-E = 1,b3,5 = minor chord
B-D-F = 1,b3,b5 = diminished chord
(where each 1 refers to the bottom note of the respective chord)

So creating triads by stacking 3rds (in the key of C) we have the following chords:
C-Dm-Em-F-G-Am-Bo

Recall, that C-D-E-F-G-A-B-C are the notes in the major scale and that we can refer to chords in a relative context without reference to any specific key by using numbers to represent notes and roman numerals to represent chords (upper-case for major chords, lower case for minor chords, lower case with a circle in superscript for diminished chords).

So from C-Dm-Em-F-G-Am-Bo we get:
I-ii-iii-IV-V-vi-viio

And there you have it, the major scale (ionian mode) harmonized in thirds to give triads (basic 3-note chords)

Recall that the relative minor of C is Am, so the notes in the a minor scale (Aeolian mode) are:
A-B-C-D-E-F-G-A.
Stacking thirds again we get:
A-C-E = 1,b3,5 = minor chord
B-D-F = 1,b3,b5 = diminished chord
C-E-G = 1,3,5 = major chord
D-F-A = 1,b3,5 = minor chord
E-G-B = 1,b3,5 = minor chord
F-A-C = 1,3,5 = major chord
G-B-D = 1,3,5 = major chord

or Am-Bo-C-Dm-Em-F-G
It shouldn't be surprising that these are the same chords cycling through in the same order as above but starting on a different spot. But look at what happens when we take them and put them in roman numerals, we get:
i-iio-bIII-iv-v-bVI-bVII

So now you can see where some of our progressions come from. I-IV-V can be built off the major scale; i-iv-v can be built off the minor scale, etc. This gives us a basis to say that a certain scale fits over a certain progression , or that "progression x" is an ionian progression , etc.

If you're learning your modes, try to figure out what triads can be built off the other 5 modes (in roman numeral notation). I'll have the answer in a future lesson on modes.

This is really short for me, but I want theoryphobes to have time to digest this before moving on. Do not be illusioned, we're just scratching the surface of harmonizations, and harmonic structures. (Don't be down-heartened, there's only 12 notes to learn) Just a heads-up on future lessons. Next, 7th chords built off major/minor scales. then shortly- inversions, voicings, extended chords (9,11,13), altered chords, alternate harmonizations (secundal, quartal, etc.), harmonizing other scales and modes, other harmonic structures (add and sus chords, etc.), and alternate harmonization schemes - not necessarily in that order. But todays stuff is fundamental and necessary to understand why these things happen.

Feel free to ask questions. I'm hoping this will reinforce previous lessons, or give cause to fill in gaps.

Peace,
Chris Roberts


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 December 31, 2002.
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