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In key signature of C major the notes used are CDEFGABC and I came to know that in Chord signature become C Dmin Emin F G Amin Bdim and C. D is major second and A is major sixth interval but it is Amin chord . F is minor, but it become major chord why?

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There are two facts here, that are separate, but you've mixed them. The intervals, between any two notes, are what they are. So - C>D= maj2, C>E=maj3, C>F=perfect4, C>G=p5, C>A=maj6, C>B=maj7. Those represent the space in between the lower and upper notes.

The chords built on the notes from any scale, C in your case here, have a root note, and a third and a fifth. C itself is CEG, Dm is DFA, Em is EGB, F is FAC, G is GBD, Am is ACE and Bo is BDF. All those chords are diatonic and as such, only contain notes from that scale.

Two separate bits of theory that are quite confusing to beginners - you're not alone! Try very hard not to 'fill the gaps' in the theory you know with your own 'theory'. It's easy to do, but see the problems it causes!!

Not sure what your last bit means.

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You are mixing two things here. The interval to the note in the scale, and the triad that is formed from a note using the scale.

D is major second and A is major sixth interval

These are intervals from the root note C. This does not say anything about the chords formed from these notes. So A is a major sixth above C, but the A chord formed with notes in the C major scale is an A minor (A C E).

Similarly, D is a major second above C, but the D chord formed is D minor. F is a perfect forth, and forms a major chord.

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Major chords and major intervals are very different concepts and independent of each other.

A major interval is an interval that is the larger of two typical distances for given degree. For example, a major third is 4 semitones in distance from a given note while a minor 3rd is 3 semitones in distance from a given note.

A major chord has a specific definition based on the notes contained within it. The note contained within a major chord form the intervals of a major third and perfect fifth. For example, a C major chord had a major 3rd which is E and a perfect 5th which is G in it.

So are these two definitions in mind we can see that in C major, A is a major 6th while the chord built off of it is a minor chord due to the intervals contained within the chord.

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F is the 4th note of C major, its interval above C is known as a Perfect 4th. ANY note in a major scale is a major interval above the tonic, except that the "major" 4th and 5th have a special name - "perfect". We'll get to why later!

Yes, some of the triads are major, some minor, one is diminished.

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I'd like to add that major intervals become minor intervals on inversion and vice versa. C to E is a major third, and E to C is a minor sixth.

The quality of chords depends on the quality of the third when the chords are written as stacks of thirds. C-E-G is C-major, E-G-C is major.

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I will rephrase your question in a way that I think will highlight what the conundrum is for you.

In the key of C major why is the A natural above C natural the interval of a major sixth while the diatonic seventh chord rooted on that same A natural is a minor seventh chord?

The apparent trouble for you is that in one situation the A is involved with some minor quality, but in another situation it is involved with a major quality.

I think you need to understand when to analyze intervals literally versus theoretically. You may be just starting to study music theory. If so, the best thing to do is just walk you through the whole analysis involved.

When any interval is examined it should be done literally as written or played. You did not show notation, nor gave a recording, so we have to read your question carefully...

In key signature of C major ... A is major sixth interval

You did no say it explicitly, but your implication is an A natural above a C natural. Let's put octave numbers on those pitches to make things clear: C4 with an A4 above. That interval is indeed a major sixth, because any interval C to an A above is a sixth, and when in encompasses nine half steps that sixth will be major, and that holds regardless of any key signatures or whatever chord the two tones might be found in.

On the other hand, the quality of chords comes from the various chord tones in relation to the chord's root regardless of in what octave the various tones appear. From low to high, CEGA, EGAC, GACE, and ACEG are all minor seventh chords with A natural as their root. To examine the chord quality any voicing of that chord should order the tones by ascending thirds and disregard octaves. So, we would say the root is A the C is the chord's third, the E is the chord's fifth, and the G is the chord's seventh. The specific qualities of those intervals are minor third, perfect fifth, and minor seventh. Those specific intervals above a chord root make a minor seventh chord.

So...

  • The interval between any two pitches is taken literally from what is written or played.
  • The quality of chords, and that chord's internal interval structure, are theoretically taken relative to the chord's root.

Now, the next part needs to be said, but it might be a bit confusing.

Let's say there is a chord C4 G4 A4 E5. We arrange those pitches by thirds, without octave numbers, and get ACEG. The chord is an A minor seventh chord. We can simultaneously talk about the C of the chord being both the third of the chord, the lowest pitch, the bass, and the chord root. We can also say A is the root and again the C is the chord's third, and the C provides (theoretically) the third of the chord. We can also say the portion of the chord C4 and A4 is a major sixth.

All of those qualities and relationships described get a little complicated, but all those statements are correct. You just need to be careful when switching between descriptions of theoretical chord roots and chord tones and descriptions of literal intervals.

All of this will be true regardless of any key signature. An Am7 chord is the same in terms of interval relations, literally and theoretical, whether is found in C major, A minor, F sharp major, etc. etc.

If this is a lot to take in all at once, just give it time, eventually you will get it.

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