Theory: Why is it a D major and not F sharp major or A major?
If there are #F , A, D notes in a chord why is it called D major and not F# or A ?
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Because a D major chord is by definition built with the notes D, F# and A.
These three notes form a D major triad and can be re-arranged to form different inversions of the same chord.
In other words, the D does not necessarily have to be the lowest note. The following are all inversions of a D major chord:
D F# A root inversion
F# A D first inversion
A D F# second inversion
An F# major chord, on the other hand, is built from the notes F# A# and C#. Therefore the notes you provided could not be called an F# major chord.
An A major chord is built from the notes A, C# and E. Therefore the notes you provided could not be called an A major chord.
Someone could come up with a different name for a chord with a D, F# and an A in it, but most musicians upon seeing these three notes (in any order) are going to interpret them as a D major chord (particularly in isolation as in this example.)
What you just described is a D major chord in its first inversion.
rest: D-F#-A -Dmajor chord
first inversion: F#-A-D -still a Dmajor
second inversion: A-D-F# -still a Dmajor
Amaj consists of A-C#-E and F#maj consists of F#-A#-C#
Chords are normally named after the lowest, or root, note in the chord. In the case of the D major chord, the D string gives it its name.
What we call the root of a major triad is, to a great extent, determined by the root's harmonics. The note D has as its lower harmonics D an octave above, A a perfect twelfth above, D two octaves above, F? a major 17th above, A a perfect 19th above, D three octaves above, and so forth. By comparison, the corresponding lower harmonics of F? are F?, C?, F?, A?, C?, F?... and those of A are A, E, A, C?, E, A...
Do you see a pattern here? The roots of the triads are what they are because the other notes reinforce them, and, to a certain extent, are subsumed by them. The stacking by thirds became a convention and allowed minor triads to be built by analogy with the major. (Minor thirds are much higher in the overtone series, and thus less powerful than major thirds, but the fifth of the chord still reinforces the root.)
Edit: In answer to your comment, you asked why it is the way it is, which is a very different question than how you recognise it in a score. It's very possible that the answer I gave to your original question wasn't technical enough.
If you want to recognise the root of a triad, stack the notes you encounter in a chord in thirds (leaving out octave or unison duplicates), so that you have a third from the lowest note to the middle note, a third from the middle note to the top note. If the lower third is major, you have a major triad; if it is minor, you have a minor triad. (The exceptions are if both thirds are major, you have an augmented chord; if they are both minor, you have a diminished chord.) In all cases, the lowest note is the root. Examples:
Chords are named by stacking the notes in thirds (moving up and down octaves is necessary) if possible. Then the lowest in the stack of thirds is the root. Thus, C-E-G, G-E-C, E-C-G, E-G-C, are C chords. There may be a question about whether the chord being examined is a real chord or just some passing simultaneities; that's usually easy to tell by looking at the surrounding music.
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