Are all triads of a key, composed of notes in that original key?

Question

If you go through each note of a key, and create a triad with a root from each note. Are all the triads composed of notes exclusive to that original key?

For example, walking through F Major:

I - F Major Triad: F - A - C

ii - G minor Triad: G - B♭ - D

iii - A minor Triad: A - C - E

IV - B♭ Major Triad: B♭ - D - F

V - C Major Triad: C - E - G

vi - D minor Triad: D - F - A

viio - E diminished Triad: E - G - B♭

Now, each one of those notes bolded above are in the key of F Major. Does that stand true for every key?

Answer 1

Yes it does. In any key you have a "natural" set of chords. You are pointing out the triads but in fact you have an entire 7 note 13th chord, just the mode of that degree played in thirds.

Your formula can be extended to read.

I - I-Major Triad: 1 - 3 - 5

ii - ii-minor Triad: 2 - 4 - 6

iii - iii-minor Triad: 3 - 5 - 7

IV - IV-Major Triad: 4 - 6 - 8

V - V-Major Triad: 5 - 7 - 2 (9)

vi - vi-minor Triad: 6 - 8 - 3 (10)

vii - vii-diminished Triad: 7 - 2 (9) - 4 (11)

where the numbers 1 - 8 are the notes of the major scale, 9 - 13 are octaves of 2 - 6.

Minor keys, as pointed out in another answer, usually use the harmonic or melodic minor scale to get the leading tone to the root of the key. But the formula works if you just consider the degree numbers 1 - 8 to correspond to the notes of the scale you choose to use. For example, in harmonic minor the chords will be as follows. I will do it in A to be more concrete. A harmonic minor,

i - A min - (1 - 3 - 5) = (A, C, E)

ii - B dim - (2, 4, 6) = (B, D, F)

III - C aug - (3, 5, 7) = (C, E, G#) the 7th degree of harmonic minor is #

iv - D min - (4, 6, 8) = (D, F, A)

V - E mag - (5, 7, 9) = (E, G#, B)

VI - F mag - (6, 8, 10) = (F, A, C)

vii - G# dim - (7, 9, 11) = (G#, B, D)

Note that I'm treating 1 - 8 as an index set for the notes of A harmonic minor in order of appearance. So I don't say b3, or #7. In the formula for building a chord one usually uses the Major scale as the reference so a minor triad is always noted (1, b3, 5). I hope this does not cause confusion.

This formula will always get you the chords within a key but not the key of a chord sequence. D min can be in the key of A min, C maj, or D min, just to name a few. One needs many more bits of info to extract key from this.

Answer 2

Yes. The point of diatonic triads is that their notes are all contained within the key - diatonic.

There will be of course, other non-diatonic notes (chromatics) that will occur in many pieces, to add colour to the harmonies, but by definition, they will not belong to the key.

You ask about any key. That's a little too open. Do you mean any major key? If so, then a resounding yes! Then there's the 'grey' area of minor keys. My 'bible' - The Oxford Companion to Music - quotes 'the diatonic scales of major and minor,made up of tones and semitones (and in the case of harmonic minor scale, also an augmented second)'. I have no reason to counter that, although it's also believed by some that diatonic refers solely to notes from major keys.

So, believing that, I'd include minor keys in this answer. There have been questions regarding this discrepancy, may be interesting to peruse them.

Note that those notes not included within the term diatonic are called chromatic, as in the black keys on a piano, referencing key C major. (But not key C minor!).

Answer 3

They can be, they don't have to be especially as you dive deeper in harmony. In an intro to harmony, you'll build chords based off the notes in a major key, but then when you get into a minor key the harmony becomes more diverse.

In a slightly more advanced harmony class you will get into the concepts of secondary dominants, augmented 6th chords, and Neapolitan 6th chords along side of using chords outside the key to modulate all of those would quickly be outside your key.

Then as you learn specific genres and styles of music, you start viewing and building harmony in a manner that fits the styles. For example in blues if you go beyond triads, most of the chords are dominant 7ths even though for I7 and IV7 you take the 7th from outside the diatonic scales.

Harmony and chord construction is a huge topic that takes a while to study.

Answer 4

If you go through each note of a key, and create a triad with a root from each note. Are all the triads composed of notes exclusive to that original key?

Yes. Your question implies that the scale is built like F major, resp. C-major (wwhwwwh). In this case it doesn’t matter how many sharp or flats this key contains. The structure is always the same: the structure of the white keys of C - major, the model of the diatonic scale. The sharps and flats of your keys in question are key signs and not chromatic accidentals.

So the triads of all keys are built the tones of the scale of the respective key, (no matter of black or white keyboard keys).

Answer 5

For major keys, yes. All the chords belonging to the key consist of "notes in the key" or "notes of the key". These notes are often called the notes that are diatonic to the key, and the chords are often called the diatonic chords of the key. (The major scale is the diatonic scale starting from a certain point, so by sticking to the notes of the major scale, you are sticking to the notes of the diatonic scale).

For minor keys, it's a bit less certain exactly what is meant by notes "of the key". It's well-understood that in real-world pieces using minor keys, it's very common to go outside of the notes in the diatonic scale. That's why, as well as the natural minor scale (which is diatonic), we have the harmonic minor and melodic minor scale. Many people might consider that where the key is minor, "notes in the key" or "notes of the key" would include these notes too, and "chords of the key" could also contain these notes. That would make the answer to your question still 'yes', although it would be important to note that "notes of the key" here wouldn't mean only the notes native to the key signature.

Oddly, these considerations mean that when people talk about the notes diatonic to a minor key, it's not always clear what they mean - they don't always only mean notes in the diatonic scale (natural minor, in the case of minor keys)!

Answer 6

"If you go through each note of a key, and create a triad with a root from each note. Are all the triads composed of notes exclusive to that original key?"

Yes, there is a set of chords - you'll see them listed in every theory book, probably near the 'circle of 5ths' diagram - that can be made using just the diatonic notes - the 'notes in the scale'.

Good. Those are the plain vanilla chords. But so what? You're not restricted to using just them. Real music doesn't, except in very simple pieces (and there's nothing wrong in being simple). Using other ones MAY imply a change of key or a new 'temporary tonic' but doesn't have to.

C, Dm7, G7, C. Strictly diatonic.

C, D7, G7, C. OK, a brief tonicisation of G, I suppose. But still 'in C'.

C, C7, F, Fm, C, G7, C. The cliche 'Saints go marching in' ending. You REALLY want to analyse that as a temporary tonicisation of F, then a 'borrow' from C minor? Can't we just enjoy the voice-leading and let them be chromatic chords 'in C'?

PLEASE stop looking for theory rules. Look at real music. Describe what happens. THAT'S real 'theory'.