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I asked a similar question yesterday in regards to the major scale:
Can the I IV V chords hamonize any major scale melody?

And the general consensus was: YES they can.

Now I'd like to ask the same question for the natural minor scale. The primary chords of the natural minor are i iv v. But from my experience these chords can't harmonize all natural minor melody. It seems like it's the i, VII, and something else. So what three chords in the natural minor scale can harmonize any natural minor melody, if its not the primary ones?

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The question—and answer—are actually the same.

In major, you have seven scale degrees, and the I, IV, and V chords cover all seven scale degrees.

In minor, it's exactly the same. You have seven scale degrees, and even though scale-degrees 3, 6, and 7 are lowered from the major, those seven scale degrees are still covered by the i, iv, and v chords. i includes scale-degrees 1, 3, and 5; iv includes 2, 4, and 6; and v includes 5, 7, and 2.

But note that the seven scale degrees could also be exhausted by the i, iv, and VII chords. But using these chords will likely push you towards the relative major, since those chords create a circle-of-fifths progression of viiiV that would really want to move to I.

And, as the answers in your other question say, just because these chords exhaust the given scale degrees does not mean that your harmonization is guaranteed to be musical. Nor does it guarantee that every aspect of the progression will be syntactically correct according to the style you're attempting to emulate.

And, before you ask: the same is true for harmonic minor, and for melodic minor (although you'd have both major and minor forms of the IV and V chords), and for modes, as well.

  • I haven’t looked at the other question and answer, but one thing that’s not mentioned in this answer is that it’s possible to effectively harmonize with a melody note with a chord that doesn’t contain that note. The easiest way is if the melody note combined with the chord forms a seventh chord, but sometimes fourths and ninths work also. All that is to say that each of the three chords can potentially cover more than three notes. Certainly in a major key the V chord can go well with the fourth scale degree, forming a V7 chord. – Todd Wilcox Apr 7 '18 at 19:13
  • @ToddWilcox True enough; perhaps it was wrong to assume the OP meant triads! – Richard Apr 7 '18 at 19:20
  • What I meant wa that the iv chord doesn’t just cover scale degrees 2, 4, and 6. It can also work with the 3rd scale degree and maybe the 5th and 7th degrees. And similarly with the i and v chords. – Todd Wilcox Apr 7 '18 at 19:30
  • @ToddWilcox Agreed. I just assumed OP was asking only about triads and not added sevenths, ninths, etc. – Richard Apr 7 '18 at 19:31
  • You’re not understanding me. The iv triad in the harmony (not a 7th chord) can be played effectively with the 3rd scale degree in the melody. Triads don’t only harmonize their chord tones. A triad can go with more than three different notes. – Todd Wilcox Apr 7 '18 at 21:28
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When you say "i" do you mean the "I" key made minor or the relative minor of I, which is vi, treated as a minor one (i)?

Of course the vi, ii, iii forms a I, IV, V for the relative natural minor key. In fact the format is the same:

ii is a fourth up from vi

iii is a fifth up from vi.

Example, Amin, Dmin, and Emin, for the one, four and five in Amin and are the vi, ii, and iii chords of C maj.

(1) It is not typical that songs written in minor keys stay natural. If you want to create the cadence in a minor key you really need a leading tone. The leading tone in a minor key is present in the Harmonic minor scale (and the Melodic minor scale too, with the sharp 6th etc). With this in place you convert the iii chord (the v of your minor) to a major chord. Again, Amin, Dmin, E7. This allows you to create the movement E7 --> Amin which has a similar "feel" as G7 --> Cmaj. The 3 of the V chord is the 7th of the key.

Another interesting relation is the relative minor-major relation between pairs in the progressions. (I, vi), (IV, ii), (V, iii). These are "substitutions" for each other, c6 = A-7, F6 = D-7, G6 = E-7 all are in the same key.

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