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By 'keys contain' I mean in the normal rules of choosing what chords 'fit' within a given key, since of course you can put just about any chord anywhere if you try hard enough!

Is there a shortcut where you can take any major or minor chord and list the keys this chord could belong to, then narrow it down to keys containing two chords, etc?

10

"What keys contain both E and Am"... "By 'keys contain' I mean in the normal rules of choosing what chords 'fit' within a given key"

Strictly speaking, (perhaps surprisingly) the answer is: none. That is, if you only allow chords from the diatonic scales, without chromatic alteration, then there is no scale that contains both of these chords. Below, I will show you why this is, and what common alterations allow them both.


"...is there an easy trick to determine this?"

Absolutely! Just look at the Circle of Fifths. In the image below, I'm actually using a segment of the infinite Line of Fifths, since it works exactly the same, but will help you to pick the correct spelling for black keys.

This image works like a slide-rule. Beneath the line of fifths are two colored rows: the top for major keys, and the bottom for minor keys. Slide the colored part left or right, along the line of fifths, until the tonic column (I or i) lines up with the desired major/minor key. The roots of all other chords can now be read off the chart. Note that the orange chords (IV, I, and V) are major, the blue chords (ii, vi, and iii) are minor, and the funky yellow chord (vii°) is diminished.

If you're in the minor key (second colored row), the only things that change are the roman numerals associated with the chords (you add 2 or subtract 5), but the pattern of 3 majors, 3 minors, and a diminished stays the same. This gives you VI, III, and VII as major chords; iv, i, and v as minor chords; and ii° as a diminished.

Chords in the line of fifths

As you can see, there's no way to slide it so that A is minor (blue) and E is major (orange). That means that in order to get both chords, we must chromatically alter one of them. We could pick a key containing an E minor chord, then alter it to be major, or we could pick a key with an A major chord, then alter it to be minor. (In the keys of D major/B minor, we'd have to alter both chords, since we'd have both an A major and an E minor).

However, there is an extremely common technique in the minor key, which is to raise the third of the v chord by a half step, which makes it a major chord (V). Note that the third of the v chord is also the seventh scale degree, so raising this note by a half step places it just under the tonic, creating a "leading tone" which wants to resolve to the tonic. This variant of the scale is called the Harmonic Minor. In the graph, this would be equivalent to replacing the blue "v" in the second row with an orange "V". In this case, you can see that you could have an A minor chord (i) and an E major chord (V) in the same scale: A harmonic minor.


Although the harmonic minor is an extremely common technique, it is not the only possible way to alter chords to get both E and Am together. By moving the colored portion around to different keys that contain both E and A, you can find what alterations are required to get them both. Here's some alternatives:

  • In C major, you'd be replacing iii with III, which causes it to act as a secondary dominant of vi (V/vi). This is quite common to do.

  • In G major, you'd be replacing vi with VI, which causes it to act as a secondary dominant of ii (V/ii). This is a bit less common.

  • In D major and D minor, you'd be replacing ii (or ii°) with II, which causes it to act as a secondary dominant of v (V/v). You'd also need to replace the V chord (which occurs naturally in D major, or in the altered D harmonic minor) with v. Making a dominant chord minor is a less common technique (at least in classical music), and it has the effect of weakening the sense of tonality, and increasing the sense of modality.

  • In E minor, you'd be replacing i with I (making the tonic a major chord), which might be used as a "Picardy Third" at the end of a piece, or to modulate to the parallel major.

  • In A major, you'd be replacing the I with a i (the reverse of the above) which can be used to modulate to the parallel minor.

  • In E major, you'd be replacing IV with iv. This minor subdominant tends to have a melancholy sound to it, and is good in chromatic passages leading up to a cadence. This is another common technique.

  • 1
    I'd add D major and D minor. In both case the E is on the IInd degree and serve as a secondary dominant to the Vth degree (namely, Am). Am is a minor dominant for Dm without the leading tone while Am in the key of D is an altered dominant. – András Hummer Dec 29 '14 at 10:48
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    Very nice answer. It may be helpful to clarify the statement "to raise the seventh scale degree in a v chord". I find that a lot of times people get confused when we talk about scale degrees in conjunction with chord tones and chord names (7 of V is 4 of the scale type of thing). It is clear to me what you mean but I think further clarification will prevent followup questions and provide more thorough understanding. As a not to the OP, the function of V in a minor key has a few implications that would probably be best asked in another question and likely has already been asked by someone else. – Basstickler Dec 29 '14 at 19:31
  • @Basstickler Good point! Better? – Caleb Hines Dec 29 '14 at 20:31
  • That is an excellent clarification! I love the slide rule as well. It spells out one of the things I would have included in my answer, which is that any given key (not modal) will have a naturally occurring 1/4/5 that are all major or minor (depending on being a major or minor key). – Basstickler Dec 29 '14 at 20:38
  • Does anyone know where a slide rule like this can be found online (not a physical version, just baked into a website), or a mobile app? – tarun Dec 30 '14 at 18:14
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Am and E are both found in the key of A minor.

The easiest way to find out what key the chords fit best is to figure out the relationship between the root of the chords. For example in this case E is a Perfect 5th away from A. In any key the dominant will be built a perfect 5th away from the tonic. In a minor key even though the dominant is naturally minor, it is very common to make it major to lead back to the tonic chord.

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    To add to Dom's answer, the term for changing the V chord in the fashion described above is called musica ficta. – jjmusicnotes Dec 29 '14 at 1:42
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I would say a good way to figure this out if you have two chords or any number of chords is to lay the notes out in alpha order. For Am and E this would look like this: Am (ACE) and E (EG#B) would be ABCEG#.

The next step is to determine which major or minor keys have those notes.

Here's another example, what key or keys fits best for the chords Am, Dm, Bb? Am = ACE Dm = DFA Bb = BbDF

Lay them out in alpha order: A Bb C D E F

The only note we're missing is some sort of G. By looking at the notes, it seems we're in a flat key. We have Bb, which is the first flat in the order, therefore F major is a contender. Since we have an E and no Eb, we can have at most 1 flat, therefore F major is the only option.

In general, use your knowledge of key signatures to help you. Scales and chords go hand-in-hand.

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The answer is no, because as you wrote:

By 'keys contain' I mean in the normal rules of choosing what chords 'fit' within a given key.

... what you are describing is the term "diatonic," which means only the notes that are contained within a key's signature.

A quick way to notice this is that the chord E major has the note G#, and the only keys that note can fit in, diatonically, are A, E, B, etc. (as well as their respective relative minors). But none of these keys will diatonically allow C-natural, which is necessary for the A-minor chord! :)

Caleb's chart above is very helpful, BTW.

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