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I recently noticed a pattern between the Primary (I IV and V) Chords and Secondary (II III VI VII) chords as they are further harmonized in 3rds all the way to 13ths.

Starting with the basic triads and arranging them into a chart, I broke down note counts in the two chord categories and got this chart:

enter image description here

Then I noticed that the secondary chords taken together, are opposite to the primary chords, in that any note that only appears once in the primary chords, appeared twice in the secondary chords, and any note that shows up twice in the primary chords taken together, shows up only once in the secondary chords, taken together.

As the harmonization continues in 3rds, the notes in each chord category that increase with each degree of harmonization are opposite in the Primary category as opposed to the Secondary category:

enter image description here

I noticed how under the primary chord category, the counts for the notes A, D, and E were added to, and in the secondary chord category the counts for the notes C, F, G, and B were increased. This pattern was present through each step of harmonization in 3rds: 7ths, 9ths, 11ths and finally in the 13ths pictured above.

Is this pattern important in understanding something to do with why the I, IV and V chords ARE primary chords, and the II, III, VI, and VII chords are secondary?

P.S: I'm not sure if "Primary" and "Secondary" are the right terms to describe the 'I IV V' chords versus 'II III VI VII' chords. Sorry for any misunderstandings.

P.P.S: I know it isn't appropriate to upload pictures if the post wouldn't be clear without them, but posting these photos of the charts I made was the only way I could get the formatting right.

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    In RN, caps are used for majors, while lower case represents minors. ThusI ii iii IV V vi viio. Check out tertiary chords.
    – Tim
    Jun 21, 2018 at 8:22
  • Given that the ii-V-I chord progression is so common, swap IV and II. Do you get the same results?
    – Dekkadeci
    Jun 21, 2018 at 10:58
  • @ Dekkadeci I haven't had the opportunity to swap chords in 3rds, but I did try different chords in 2nds, 4ths, and 5ths. I found that so long as each of the 7 notes in the chosen key appeared at least once in the 3 chosen chords, then the pattern held. Please see my comment on ttw's answer below.
    – Pattern Man
    Jun 21, 2018 at 16:08
  • @Dekkadeci The ii is a viable substitute for the IV and vice verse. Whether or not you get the same result depends on voicing. In fact a major 6 chord and its relative minor 7 are identical (enharmonic). The maj and min chords in a key all pair this way, (I, vi), (IV, ii) and (V, iii).
    – user50691
    Jun 26, 2018 at 21:31

1 Answer 1

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It's a counting argument. There 7 chord roots and 3 notes per chord giving. The most equal partition of 3 is 2 + 1 so some notes occur in 2 chords and some in 1. All these patterns are a consequence of laying out chords in thirds. Primary and Secondary are the correct names. Thus if a secondary chord is made into a dominant seventh type by sharpening the third and adding a minor seventh (at least in the major scales, these are names "secondary dominants." Example, D7, A7, and E7 in the key of C.)

A minor scale will show a similar pattern with the change being that the sharpened seventh is used for the V and vii chords. (The VII chord makes the minor mode a bit less symmetrical.)

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  • It seems you're correct, ttw. This holds out even for harmony in 2nds, 4ths, and 5ths. Each one gets the same result. An aside: I don't know what primary chords or secondary chords are in anything other than 3rds, so I chose chords to use based on the results of the primary chords having all 7 notes, collectively. This pattern remains, no matter which chords are chosen, so long as all 7 notes are present at least once.
    – Pattern Man
    Jun 21, 2018 at 1:27

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